chapter (1) mathematical modeling of dc machines...chapter (1) mathematical modeling of dc machines...
TRANSCRIPT
(1)
Chapter (1)
Mathematical Modeling of DC Machines
11 DC Motor Overview
The direct current (DC) motor is one of the first machines devised to
convert electrical power into mechanical power and its origins can be
traced to the disc-type machines conceived and tested by Michael
Faraday
Direct current motors (the subject of this study) convert electrical
energy into mechanical energy through the interaction of two magnetic
fields One field is produced by a magnet of poles assembly the other
field is produced by an electrical current flowing in the motor windings
These two fields result in a torque which tends to rotate the rotor As the
rotor turns the current in the windings is commutated to produce a
continuous torque output
A DC motor can be seen to be comprised of three main parts current-
carrying conductors called an armature a circuit for magnetic field
provided by magnets of poles and a commutator that switches the
direction of current in the armature as it passes a fixed point in space
Since electric motor design is based upon the placement of conductors
in a magnetic field a discussion of magnetic circuit principles will help
facilitate the understanding of motor action If a conductor were wound
into a coil with many turns the magnetic contribution of each individual
turn would add to the magnetic field intensity which exists in the space
enclosed by the coil In this way extremely strong magnetic fields can be
developed The force which acts to push the magnetic flux through a
space is called variously magnetomotance manetomotive force or simply
(2)
mmf The term magnetic flux is used to describe how much magnetism
there is in the space around a coil or permanent magnet or in the air gap
of a motor
Condition assessment of DC motors requires a basic understanding of
the design and operating characteristics of the various types available the
separately excited DC motor the PM DC motor the series motor the
shunt motor and the compound motor Each type has unique operating
characteristics and applications These characteristics enable the operator
to perform a wide variety of tasks
12 Types of DC Motors
121 Separately Excited DC Motor
The schematic circuit diagram of separately excited DC motor is
illustrated in following Figure 11 When the armature of a DC machine
rotates in the stator field a voltage is induced in the armature winding In
a DC motor it is called counter emf or back emf In either case the level
of this voltage can be calculated using Faradays Law which states that a
voltage is induced The field and armature circuits are totally separate
The field current is supplied from a secondary source
Figure 11 Separately Excited DC Motor
(3)
122 Permanent Magnets (PM) DC Motor
The magnetic field of (PM) motors is generated by permanent magnets so
no power is used to create the magnetic field structure The stator
magnetic flux remains essentially constant at all levels of armature
current and therefore the speed vs torque curve of the PM motor is
linear over an extended range The schematic circuit diagram of a
permanent magnets DC motor is illustrated in following Figure 12
Figure 12 PM DC Motor
123 Series DC Motor
Components of a series motor include the armature labeled A1 and A2
and the field S1 and S2 The same current is impressed upon the
armature and the series field The coils in the series field are made of a
few turns of large gauge wire to facilitate large current flow This
provides high starting torque approximately 2 frac14 times the rated load
torque Series motor armatures are usually lap wound Lap windings are
good for high current low voltage applications because they have
additional parallel paths for current flow Series motors have very poor
speed control running slowly with heavy loads and quickly with light
loads A series motor should never drive machines with a belt If the belt
breaks the load would be removed and cause the motor to over speed and
destroy itself in a matter of seconds The schematic circuit diagram of a
series DC motor is illustrated in following Figure 13
(4)
Figure 13 Series DC Motor
Common uses of the series motor include crane hoists where large heavy
loads will be raised and lowered and bridge and trolley drives on large
overhead cranes The series motor provides the starting torque required
for moving large loads Traction motors used to drive trains are series
motors that provide the required torque and horsepower to get massive
amounts of weight moving On the coldest days of winter the series
motor that starts your car overcomes the extreme cold temperatures and
thick lubricant to get your car going
124 Shunt DC Motor
The shunt motor is probably the most common dc motor used in industry
today Components of the shunt motor are the armature labeled A1 and
A2 and the field labeled F1 and F2 The coils in the shunt field are
composed of many turns of small wire resulting in low shunt field
current and moderate armature current This motor provides starting
torque that varies with the load applied and good speed regulation by
controlling the shunt field voltage If the shunt motor loses itrsquos field it
will accelerate slightly until CEMF rises to a value sufficient to shut off
the torque producing current In other words the shunt motor will not
destroy itself if it loses its field but it wonrsquot have the torque required to
do the job it was designed for The schematic circuit diagram of a shunt
DC motor is illustrated in following Figure 14
(5)
Figure 14 Shunt DC Motor
Some of the common uses of the shunt motor are machine shop lathes
and industry process lines where speed and tension control are critical
125 Compound DC Motor
When comparing the advantages of the series and shunt motors the
series motor has greater torque capabilities while the shunt motor has
more constant and controllable speed over various loads These two
desirable characteristics can be found in the same motor by placing both a
series field and shunt field winding on the same pole Thus we have the
compound motor The schematic circuit diagram of a compound DC
motor is illustrated in following Figure 15
The compound motor responds better to heavy load changes than a
shunt motor because of the increased current through the series field coils
This boosts the field strength providing added torque and speed
If a shunt coil is added to a series motor at light loads (when a series
motor tends to over speed) the added shunt field flux limits the top speed
eliminating self-destruction
Figure 15 Compound DC Motor
(6)
Common uses of the compound motor include elevators air
compressors conveyors presses and shears Compound motors can be
operated as shunt motors by disconnecting the series field Many
manufacturing process lines are designed this way The reason being that
most off the shelf motors are compound motors and the series field can
always be connected later to provide additional torque if needed
Compound motors can be connected two ways cumulatively and
differentially When connected cumulatively the series field is connected
to aid the shunt field providing faster response than a straight shunt
motor When connected differentially the series field opposes the shunt
field Differentially connected compound motors are sometimes referred
to as ldquosuicide motorsrdquo because of their penchant for self-destruction If
perhaps the shunt field circuit were to suddenly open during loading the
series field would then assume control and the polarity of all fields would
reverse This results in the motor stopping and then restarting in the
opposite direction It then operates as an unloaded series motor and will
destroy itself Differentially connected motors can also start in the
opposite direction if the load is too heavy Therefore it is seldom used in
industry
13 Separately Excited DC Motor Differential Equations
The DC machine as dynamic system including the interactions of the
electromagnetic and the mechanical effect is dealing within the following
section The equivalent circuit of the separately exited dc machine can be
represented in schematic from as shown in Fig 11 The electrical
equation of a DC motor is derived from the simple motor circuit
illustrated in Figure 11 The electrical relation between these variables is
given by equations (11-16) where Eb the internally generated voltage is
proportional to the motor velocity
(7)
The motor back emf constant Kv is a measure of the voltage per unit
speed generated when the rotor is turning The magnitude and polarity of
Kv are functions of the shaft angular velocity r and direction of rotation
respectively Also Kv is the motor torque constant that is a measure of
the torque-per-unit-current produced by the motor The dynamic
equation of a motor is given by
b
a
aaaa Edt
diLRiV (11)
rfafb iLE (12)
faf iLK (13)
dt
diLRiV
f
ffff (14)
ae iKT (15)
Lr
r
e Tdt
dJT
(16)
Va applied voltage
Ia motor current
Eb induced back emf voltage
La armature winding inductance
Ra armature resistance
Te motor output torque
r motor output speed
14 Block Diagram and Transfer Function of Separately Excited DC
Motor
It is necessary to depict the voltage and torque equations of DC
machine in block diagram form when considering the machine as a part
of an overall system Accurately the equations which we have already
(8)
derived for the separately excited DC motor which we will put into block
diagram form From the block diagrams we can derive the transfer
function of the DC motor which are used in the design of current and
speed controllers
141 Time Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with time-domain equations using the p operator to denote
differentiation with respect to time dtd and the operator p1 denote
integration ion Therefore we will have no trouble converting the time-
domain block diagram so transfer functions by using the Laplace
operator dt Arranging the equation of the separately excited DC
machine into a block diagram representation is straight forward The
field and armature voltage equations and the relationship between torque
and rotor speed (11-16) may be Combined produces the armature
current torque field current and motor speed as follows
)1(
1)(
p
REVi
a
a
aaa
(17)
)(
1)(
JpTT Ler (18)
)1(
1
p
RVi
f
f
ff
(19)
Where aaa RL and fff RL
From equations (11-19) the time-domain block diagram is obtained as
shown in Fig 16
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(2)
mmf The term magnetic flux is used to describe how much magnetism
there is in the space around a coil or permanent magnet or in the air gap
of a motor
Condition assessment of DC motors requires a basic understanding of
the design and operating characteristics of the various types available the
separately excited DC motor the PM DC motor the series motor the
shunt motor and the compound motor Each type has unique operating
characteristics and applications These characteristics enable the operator
to perform a wide variety of tasks
12 Types of DC Motors
121 Separately Excited DC Motor
The schematic circuit diagram of separately excited DC motor is
illustrated in following Figure 11 When the armature of a DC machine
rotates in the stator field a voltage is induced in the armature winding In
a DC motor it is called counter emf or back emf In either case the level
of this voltage can be calculated using Faradays Law which states that a
voltage is induced The field and armature circuits are totally separate
The field current is supplied from a secondary source
Figure 11 Separately Excited DC Motor
(3)
122 Permanent Magnets (PM) DC Motor
The magnetic field of (PM) motors is generated by permanent magnets so
no power is used to create the magnetic field structure The stator
magnetic flux remains essentially constant at all levels of armature
current and therefore the speed vs torque curve of the PM motor is
linear over an extended range The schematic circuit diagram of a
permanent magnets DC motor is illustrated in following Figure 12
Figure 12 PM DC Motor
123 Series DC Motor
Components of a series motor include the armature labeled A1 and A2
and the field S1 and S2 The same current is impressed upon the
armature and the series field The coils in the series field are made of a
few turns of large gauge wire to facilitate large current flow This
provides high starting torque approximately 2 frac14 times the rated load
torque Series motor armatures are usually lap wound Lap windings are
good for high current low voltage applications because they have
additional parallel paths for current flow Series motors have very poor
speed control running slowly with heavy loads and quickly with light
loads A series motor should never drive machines with a belt If the belt
breaks the load would be removed and cause the motor to over speed and
destroy itself in a matter of seconds The schematic circuit diagram of a
series DC motor is illustrated in following Figure 13
(4)
Figure 13 Series DC Motor
Common uses of the series motor include crane hoists where large heavy
loads will be raised and lowered and bridge and trolley drives on large
overhead cranes The series motor provides the starting torque required
for moving large loads Traction motors used to drive trains are series
motors that provide the required torque and horsepower to get massive
amounts of weight moving On the coldest days of winter the series
motor that starts your car overcomes the extreme cold temperatures and
thick lubricant to get your car going
124 Shunt DC Motor
The shunt motor is probably the most common dc motor used in industry
today Components of the shunt motor are the armature labeled A1 and
A2 and the field labeled F1 and F2 The coils in the shunt field are
composed of many turns of small wire resulting in low shunt field
current and moderate armature current This motor provides starting
torque that varies with the load applied and good speed regulation by
controlling the shunt field voltage If the shunt motor loses itrsquos field it
will accelerate slightly until CEMF rises to a value sufficient to shut off
the torque producing current In other words the shunt motor will not
destroy itself if it loses its field but it wonrsquot have the torque required to
do the job it was designed for The schematic circuit diagram of a shunt
DC motor is illustrated in following Figure 14
(5)
Figure 14 Shunt DC Motor
Some of the common uses of the shunt motor are machine shop lathes
and industry process lines where speed and tension control are critical
125 Compound DC Motor
When comparing the advantages of the series and shunt motors the
series motor has greater torque capabilities while the shunt motor has
more constant and controllable speed over various loads These two
desirable characteristics can be found in the same motor by placing both a
series field and shunt field winding on the same pole Thus we have the
compound motor The schematic circuit diagram of a compound DC
motor is illustrated in following Figure 15
The compound motor responds better to heavy load changes than a
shunt motor because of the increased current through the series field coils
This boosts the field strength providing added torque and speed
If a shunt coil is added to a series motor at light loads (when a series
motor tends to over speed) the added shunt field flux limits the top speed
eliminating self-destruction
Figure 15 Compound DC Motor
(6)
Common uses of the compound motor include elevators air
compressors conveyors presses and shears Compound motors can be
operated as shunt motors by disconnecting the series field Many
manufacturing process lines are designed this way The reason being that
most off the shelf motors are compound motors and the series field can
always be connected later to provide additional torque if needed
Compound motors can be connected two ways cumulatively and
differentially When connected cumulatively the series field is connected
to aid the shunt field providing faster response than a straight shunt
motor When connected differentially the series field opposes the shunt
field Differentially connected compound motors are sometimes referred
to as ldquosuicide motorsrdquo because of their penchant for self-destruction If
perhaps the shunt field circuit were to suddenly open during loading the
series field would then assume control and the polarity of all fields would
reverse This results in the motor stopping and then restarting in the
opposite direction It then operates as an unloaded series motor and will
destroy itself Differentially connected motors can also start in the
opposite direction if the load is too heavy Therefore it is seldom used in
industry
13 Separately Excited DC Motor Differential Equations
The DC machine as dynamic system including the interactions of the
electromagnetic and the mechanical effect is dealing within the following
section The equivalent circuit of the separately exited dc machine can be
represented in schematic from as shown in Fig 11 The electrical
equation of a DC motor is derived from the simple motor circuit
illustrated in Figure 11 The electrical relation between these variables is
given by equations (11-16) where Eb the internally generated voltage is
proportional to the motor velocity
(7)
The motor back emf constant Kv is a measure of the voltage per unit
speed generated when the rotor is turning The magnitude and polarity of
Kv are functions of the shaft angular velocity r and direction of rotation
respectively Also Kv is the motor torque constant that is a measure of
the torque-per-unit-current produced by the motor The dynamic
equation of a motor is given by
b
a
aaaa Edt
diLRiV (11)
rfafb iLE (12)
faf iLK (13)
dt
diLRiV
f
ffff (14)
ae iKT (15)
Lr
r
e Tdt
dJT
(16)
Va applied voltage
Ia motor current
Eb induced back emf voltage
La armature winding inductance
Ra armature resistance
Te motor output torque
r motor output speed
14 Block Diagram and Transfer Function of Separately Excited DC
Motor
It is necessary to depict the voltage and torque equations of DC
machine in block diagram form when considering the machine as a part
of an overall system Accurately the equations which we have already
(8)
derived for the separately excited DC motor which we will put into block
diagram form From the block diagrams we can derive the transfer
function of the DC motor which are used in the design of current and
speed controllers
141 Time Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with time-domain equations using the p operator to denote
differentiation with respect to time dtd and the operator p1 denote
integration ion Therefore we will have no trouble converting the time-
domain block diagram so transfer functions by using the Laplace
operator dt Arranging the equation of the separately excited DC
machine into a block diagram representation is straight forward The
field and armature voltage equations and the relationship between torque
and rotor speed (11-16) may be Combined produces the armature
current torque field current and motor speed as follows
)1(
1)(
p
REVi
a
a
aaa
(17)
)(
1)(
JpTT Ler (18)
)1(
1
p
RVi
f
f
ff
(19)
Where aaa RL and fff RL
From equations (11-19) the time-domain block diagram is obtained as
shown in Fig 16
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(3)
122 Permanent Magnets (PM) DC Motor
The magnetic field of (PM) motors is generated by permanent magnets so
no power is used to create the magnetic field structure The stator
magnetic flux remains essentially constant at all levels of armature
current and therefore the speed vs torque curve of the PM motor is
linear over an extended range The schematic circuit diagram of a
permanent magnets DC motor is illustrated in following Figure 12
Figure 12 PM DC Motor
123 Series DC Motor
Components of a series motor include the armature labeled A1 and A2
and the field S1 and S2 The same current is impressed upon the
armature and the series field The coils in the series field are made of a
few turns of large gauge wire to facilitate large current flow This
provides high starting torque approximately 2 frac14 times the rated load
torque Series motor armatures are usually lap wound Lap windings are
good for high current low voltage applications because they have
additional parallel paths for current flow Series motors have very poor
speed control running slowly with heavy loads and quickly with light
loads A series motor should never drive machines with a belt If the belt
breaks the load would be removed and cause the motor to over speed and
destroy itself in a matter of seconds The schematic circuit diagram of a
series DC motor is illustrated in following Figure 13
(4)
Figure 13 Series DC Motor
Common uses of the series motor include crane hoists where large heavy
loads will be raised and lowered and bridge and trolley drives on large
overhead cranes The series motor provides the starting torque required
for moving large loads Traction motors used to drive trains are series
motors that provide the required torque and horsepower to get massive
amounts of weight moving On the coldest days of winter the series
motor that starts your car overcomes the extreme cold temperatures and
thick lubricant to get your car going
124 Shunt DC Motor
The shunt motor is probably the most common dc motor used in industry
today Components of the shunt motor are the armature labeled A1 and
A2 and the field labeled F1 and F2 The coils in the shunt field are
composed of many turns of small wire resulting in low shunt field
current and moderate armature current This motor provides starting
torque that varies with the load applied and good speed regulation by
controlling the shunt field voltage If the shunt motor loses itrsquos field it
will accelerate slightly until CEMF rises to a value sufficient to shut off
the torque producing current In other words the shunt motor will not
destroy itself if it loses its field but it wonrsquot have the torque required to
do the job it was designed for The schematic circuit diagram of a shunt
DC motor is illustrated in following Figure 14
(5)
Figure 14 Shunt DC Motor
Some of the common uses of the shunt motor are machine shop lathes
and industry process lines where speed and tension control are critical
125 Compound DC Motor
When comparing the advantages of the series and shunt motors the
series motor has greater torque capabilities while the shunt motor has
more constant and controllable speed over various loads These two
desirable characteristics can be found in the same motor by placing both a
series field and shunt field winding on the same pole Thus we have the
compound motor The schematic circuit diagram of a compound DC
motor is illustrated in following Figure 15
The compound motor responds better to heavy load changes than a
shunt motor because of the increased current through the series field coils
This boosts the field strength providing added torque and speed
If a shunt coil is added to a series motor at light loads (when a series
motor tends to over speed) the added shunt field flux limits the top speed
eliminating self-destruction
Figure 15 Compound DC Motor
(6)
Common uses of the compound motor include elevators air
compressors conveyors presses and shears Compound motors can be
operated as shunt motors by disconnecting the series field Many
manufacturing process lines are designed this way The reason being that
most off the shelf motors are compound motors and the series field can
always be connected later to provide additional torque if needed
Compound motors can be connected two ways cumulatively and
differentially When connected cumulatively the series field is connected
to aid the shunt field providing faster response than a straight shunt
motor When connected differentially the series field opposes the shunt
field Differentially connected compound motors are sometimes referred
to as ldquosuicide motorsrdquo because of their penchant for self-destruction If
perhaps the shunt field circuit were to suddenly open during loading the
series field would then assume control and the polarity of all fields would
reverse This results in the motor stopping and then restarting in the
opposite direction It then operates as an unloaded series motor and will
destroy itself Differentially connected motors can also start in the
opposite direction if the load is too heavy Therefore it is seldom used in
industry
13 Separately Excited DC Motor Differential Equations
The DC machine as dynamic system including the interactions of the
electromagnetic and the mechanical effect is dealing within the following
section The equivalent circuit of the separately exited dc machine can be
represented in schematic from as shown in Fig 11 The electrical
equation of a DC motor is derived from the simple motor circuit
illustrated in Figure 11 The electrical relation between these variables is
given by equations (11-16) where Eb the internally generated voltage is
proportional to the motor velocity
(7)
The motor back emf constant Kv is a measure of the voltage per unit
speed generated when the rotor is turning The magnitude and polarity of
Kv are functions of the shaft angular velocity r and direction of rotation
respectively Also Kv is the motor torque constant that is a measure of
the torque-per-unit-current produced by the motor The dynamic
equation of a motor is given by
b
a
aaaa Edt
diLRiV (11)
rfafb iLE (12)
faf iLK (13)
dt
diLRiV
f
ffff (14)
ae iKT (15)
Lr
r
e Tdt
dJT
(16)
Va applied voltage
Ia motor current
Eb induced back emf voltage
La armature winding inductance
Ra armature resistance
Te motor output torque
r motor output speed
14 Block Diagram and Transfer Function of Separately Excited DC
Motor
It is necessary to depict the voltage and torque equations of DC
machine in block diagram form when considering the machine as a part
of an overall system Accurately the equations which we have already
(8)
derived for the separately excited DC motor which we will put into block
diagram form From the block diagrams we can derive the transfer
function of the DC motor which are used in the design of current and
speed controllers
141 Time Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with time-domain equations using the p operator to denote
differentiation with respect to time dtd and the operator p1 denote
integration ion Therefore we will have no trouble converting the time-
domain block diagram so transfer functions by using the Laplace
operator dt Arranging the equation of the separately excited DC
machine into a block diagram representation is straight forward The
field and armature voltage equations and the relationship between torque
and rotor speed (11-16) may be Combined produces the armature
current torque field current and motor speed as follows
)1(
1)(
p
REVi
a
a
aaa
(17)
)(
1)(
JpTT Ler (18)
)1(
1
p
RVi
f
f
ff
(19)
Where aaa RL and fff RL
From equations (11-19) the time-domain block diagram is obtained as
shown in Fig 16
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(4)
Figure 13 Series DC Motor
Common uses of the series motor include crane hoists where large heavy
loads will be raised and lowered and bridge and trolley drives on large
overhead cranes The series motor provides the starting torque required
for moving large loads Traction motors used to drive trains are series
motors that provide the required torque and horsepower to get massive
amounts of weight moving On the coldest days of winter the series
motor that starts your car overcomes the extreme cold temperatures and
thick lubricant to get your car going
124 Shunt DC Motor
The shunt motor is probably the most common dc motor used in industry
today Components of the shunt motor are the armature labeled A1 and
A2 and the field labeled F1 and F2 The coils in the shunt field are
composed of many turns of small wire resulting in low shunt field
current and moderate armature current This motor provides starting
torque that varies with the load applied and good speed regulation by
controlling the shunt field voltage If the shunt motor loses itrsquos field it
will accelerate slightly until CEMF rises to a value sufficient to shut off
the torque producing current In other words the shunt motor will not
destroy itself if it loses its field but it wonrsquot have the torque required to
do the job it was designed for The schematic circuit diagram of a shunt
DC motor is illustrated in following Figure 14
(5)
Figure 14 Shunt DC Motor
Some of the common uses of the shunt motor are machine shop lathes
and industry process lines where speed and tension control are critical
125 Compound DC Motor
When comparing the advantages of the series and shunt motors the
series motor has greater torque capabilities while the shunt motor has
more constant and controllable speed over various loads These two
desirable characteristics can be found in the same motor by placing both a
series field and shunt field winding on the same pole Thus we have the
compound motor The schematic circuit diagram of a compound DC
motor is illustrated in following Figure 15
The compound motor responds better to heavy load changes than a
shunt motor because of the increased current through the series field coils
This boosts the field strength providing added torque and speed
If a shunt coil is added to a series motor at light loads (when a series
motor tends to over speed) the added shunt field flux limits the top speed
eliminating self-destruction
Figure 15 Compound DC Motor
(6)
Common uses of the compound motor include elevators air
compressors conveyors presses and shears Compound motors can be
operated as shunt motors by disconnecting the series field Many
manufacturing process lines are designed this way The reason being that
most off the shelf motors are compound motors and the series field can
always be connected later to provide additional torque if needed
Compound motors can be connected two ways cumulatively and
differentially When connected cumulatively the series field is connected
to aid the shunt field providing faster response than a straight shunt
motor When connected differentially the series field opposes the shunt
field Differentially connected compound motors are sometimes referred
to as ldquosuicide motorsrdquo because of their penchant for self-destruction If
perhaps the shunt field circuit were to suddenly open during loading the
series field would then assume control and the polarity of all fields would
reverse This results in the motor stopping and then restarting in the
opposite direction It then operates as an unloaded series motor and will
destroy itself Differentially connected motors can also start in the
opposite direction if the load is too heavy Therefore it is seldom used in
industry
13 Separately Excited DC Motor Differential Equations
The DC machine as dynamic system including the interactions of the
electromagnetic and the mechanical effect is dealing within the following
section The equivalent circuit of the separately exited dc machine can be
represented in schematic from as shown in Fig 11 The electrical
equation of a DC motor is derived from the simple motor circuit
illustrated in Figure 11 The electrical relation between these variables is
given by equations (11-16) where Eb the internally generated voltage is
proportional to the motor velocity
(7)
The motor back emf constant Kv is a measure of the voltage per unit
speed generated when the rotor is turning The magnitude and polarity of
Kv are functions of the shaft angular velocity r and direction of rotation
respectively Also Kv is the motor torque constant that is a measure of
the torque-per-unit-current produced by the motor The dynamic
equation of a motor is given by
b
a
aaaa Edt
diLRiV (11)
rfafb iLE (12)
faf iLK (13)
dt
diLRiV
f
ffff (14)
ae iKT (15)
Lr
r
e Tdt
dJT
(16)
Va applied voltage
Ia motor current
Eb induced back emf voltage
La armature winding inductance
Ra armature resistance
Te motor output torque
r motor output speed
14 Block Diagram and Transfer Function of Separately Excited DC
Motor
It is necessary to depict the voltage and torque equations of DC
machine in block diagram form when considering the machine as a part
of an overall system Accurately the equations which we have already
(8)
derived for the separately excited DC motor which we will put into block
diagram form From the block diagrams we can derive the transfer
function of the DC motor which are used in the design of current and
speed controllers
141 Time Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with time-domain equations using the p operator to denote
differentiation with respect to time dtd and the operator p1 denote
integration ion Therefore we will have no trouble converting the time-
domain block diagram so transfer functions by using the Laplace
operator dt Arranging the equation of the separately excited DC
machine into a block diagram representation is straight forward The
field and armature voltage equations and the relationship between torque
and rotor speed (11-16) may be Combined produces the armature
current torque field current and motor speed as follows
)1(
1)(
p
REVi
a
a
aaa
(17)
)(
1)(
JpTT Ler (18)
)1(
1
p
RVi
f
f
ff
(19)
Where aaa RL and fff RL
From equations (11-19) the time-domain block diagram is obtained as
shown in Fig 16
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(5)
Figure 14 Shunt DC Motor
Some of the common uses of the shunt motor are machine shop lathes
and industry process lines where speed and tension control are critical
125 Compound DC Motor
When comparing the advantages of the series and shunt motors the
series motor has greater torque capabilities while the shunt motor has
more constant and controllable speed over various loads These two
desirable characteristics can be found in the same motor by placing both a
series field and shunt field winding on the same pole Thus we have the
compound motor The schematic circuit diagram of a compound DC
motor is illustrated in following Figure 15
The compound motor responds better to heavy load changes than a
shunt motor because of the increased current through the series field coils
This boosts the field strength providing added torque and speed
If a shunt coil is added to a series motor at light loads (when a series
motor tends to over speed) the added shunt field flux limits the top speed
eliminating self-destruction
Figure 15 Compound DC Motor
(6)
Common uses of the compound motor include elevators air
compressors conveyors presses and shears Compound motors can be
operated as shunt motors by disconnecting the series field Many
manufacturing process lines are designed this way The reason being that
most off the shelf motors are compound motors and the series field can
always be connected later to provide additional torque if needed
Compound motors can be connected two ways cumulatively and
differentially When connected cumulatively the series field is connected
to aid the shunt field providing faster response than a straight shunt
motor When connected differentially the series field opposes the shunt
field Differentially connected compound motors are sometimes referred
to as ldquosuicide motorsrdquo because of their penchant for self-destruction If
perhaps the shunt field circuit were to suddenly open during loading the
series field would then assume control and the polarity of all fields would
reverse This results in the motor stopping and then restarting in the
opposite direction It then operates as an unloaded series motor and will
destroy itself Differentially connected motors can also start in the
opposite direction if the load is too heavy Therefore it is seldom used in
industry
13 Separately Excited DC Motor Differential Equations
The DC machine as dynamic system including the interactions of the
electromagnetic and the mechanical effect is dealing within the following
section The equivalent circuit of the separately exited dc machine can be
represented in schematic from as shown in Fig 11 The electrical
equation of a DC motor is derived from the simple motor circuit
illustrated in Figure 11 The electrical relation between these variables is
given by equations (11-16) where Eb the internally generated voltage is
proportional to the motor velocity
(7)
The motor back emf constant Kv is a measure of the voltage per unit
speed generated when the rotor is turning The magnitude and polarity of
Kv are functions of the shaft angular velocity r and direction of rotation
respectively Also Kv is the motor torque constant that is a measure of
the torque-per-unit-current produced by the motor The dynamic
equation of a motor is given by
b
a
aaaa Edt
diLRiV (11)
rfafb iLE (12)
faf iLK (13)
dt
diLRiV
f
ffff (14)
ae iKT (15)
Lr
r
e Tdt
dJT
(16)
Va applied voltage
Ia motor current
Eb induced back emf voltage
La armature winding inductance
Ra armature resistance
Te motor output torque
r motor output speed
14 Block Diagram and Transfer Function of Separately Excited DC
Motor
It is necessary to depict the voltage and torque equations of DC
machine in block diagram form when considering the machine as a part
of an overall system Accurately the equations which we have already
(8)
derived for the separately excited DC motor which we will put into block
diagram form From the block diagrams we can derive the transfer
function of the DC motor which are used in the design of current and
speed controllers
141 Time Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with time-domain equations using the p operator to denote
differentiation with respect to time dtd and the operator p1 denote
integration ion Therefore we will have no trouble converting the time-
domain block diagram so transfer functions by using the Laplace
operator dt Arranging the equation of the separately excited DC
machine into a block diagram representation is straight forward The
field and armature voltage equations and the relationship between torque
and rotor speed (11-16) may be Combined produces the armature
current torque field current and motor speed as follows
)1(
1)(
p
REVi
a
a
aaa
(17)
)(
1)(
JpTT Ler (18)
)1(
1
p
RVi
f
f
ff
(19)
Where aaa RL and fff RL
From equations (11-19) the time-domain block diagram is obtained as
shown in Fig 16
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(6)
Common uses of the compound motor include elevators air
compressors conveyors presses and shears Compound motors can be
operated as shunt motors by disconnecting the series field Many
manufacturing process lines are designed this way The reason being that
most off the shelf motors are compound motors and the series field can
always be connected later to provide additional torque if needed
Compound motors can be connected two ways cumulatively and
differentially When connected cumulatively the series field is connected
to aid the shunt field providing faster response than a straight shunt
motor When connected differentially the series field opposes the shunt
field Differentially connected compound motors are sometimes referred
to as ldquosuicide motorsrdquo because of their penchant for self-destruction If
perhaps the shunt field circuit were to suddenly open during loading the
series field would then assume control and the polarity of all fields would
reverse This results in the motor stopping and then restarting in the
opposite direction It then operates as an unloaded series motor and will
destroy itself Differentially connected motors can also start in the
opposite direction if the load is too heavy Therefore it is seldom used in
industry
13 Separately Excited DC Motor Differential Equations
The DC machine as dynamic system including the interactions of the
electromagnetic and the mechanical effect is dealing within the following
section The equivalent circuit of the separately exited dc machine can be
represented in schematic from as shown in Fig 11 The electrical
equation of a DC motor is derived from the simple motor circuit
illustrated in Figure 11 The electrical relation between these variables is
given by equations (11-16) where Eb the internally generated voltage is
proportional to the motor velocity
(7)
The motor back emf constant Kv is a measure of the voltage per unit
speed generated when the rotor is turning The magnitude and polarity of
Kv are functions of the shaft angular velocity r and direction of rotation
respectively Also Kv is the motor torque constant that is a measure of
the torque-per-unit-current produced by the motor The dynamic
equation of a motor is given by
b
a
aaaa Edt
diLRiV (11)
rfafb iLE (12)
faf iLK (13)
dt
diLRiV
f
ffff (14)
ae iKT (15)
Lr
r
e Tdt
dJT
(16)
Va applied voltage
Ia motor current
Eb induced back emf voltage
La armature winding inductance
Ra armature resistance
Te motor output torque
r motor output speed
14 Block Diagram and Transfer Function of Separately Excited DC
Motor
It is necessary to depict the voltage and torque equations of DC
machine in block diagram form when considering the machine as a part
of an overall system Accurately the equations which we have already
(8)
derived for the separately excited DC motor which we will put into block
diagram form From the block diagrams we can derive the transfer
function of the DC motor which are used in the design of current and
speed controllers
141 Time Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with time-domain equations using the p operator to denote
differentiation with respect to time dtd and the operator p1 denote
integration ion Therefore we will have no trouble converting the time-
domain block diagram so transfer functions by using the Laplace
operator dt Arranging the equation of the separately excited DC
machine into a block diagram representation is straight forward The
field and armature voltage equations and the relationship between torque
and rotor speed (11-16) may be Combined produces the armature
current torque field current and motor speed as follows
)1(
1)(
p
REVi
a
a
aaa
(17)
)(
1)(
JpTT Ler (18)
)1(
1
p
RVi
f
f
ff
(19)
Where aaa RL and fff RL
From equations (11-19) the time-domain block diagram is obtained as
shown in Fig 16
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(7)
The motor back emf constant Kv is a measure of the voltage per unit
speed generated when the rotor is turning The magnitude and polarity of
Kv are functions of the shaft angular velocity r and direction of rotation
respectively Also Kv is the motor torque constant that is a measure of
the torque-per-unit-current produced by the motor The dynamic
equation of a motor is given by
b
a
aaaa Edt
diLRiV (11)
rfafb iLE (12)
faf iLK (13)
dt
diLRiV
f
ffff (14)
ae iKT (15)
Lr
r
e Tdt
dJT
(16)
Va applied voltage
Ia motor current
Eb induced back emf voltage
La armature winding inductance
Ra armature resistance
Te motor output torque
r motor output speed
14 Block Diagram and Transfer Function of Separately Excited DC
Motor
It is necessary to depict the voltage and torque equations of DC
machine in block diagram form when considering the machine as a part
of an overall system Accurately the equations which we have already
(8)
derived for the separately excited DC motor which we will put into block
diagram form From the block diagrams we can derive the transfer
function of the DC motor which are used in the design of current and
speed controllers
141 Time Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with time-domain equations using the p operator to denote
differentiation with respect to time dtd and the operator p1 denote
integration ion Therefore we will have no trouble converting the time-
domain block diagram so transfer functions by using the Laplace
operator dt Arranging the equation of the separately excited DC
machine into a block diagram representation is straight forward The
field and armature voltage equations and the relationship between torque
and rotor speed (11-16) may be Combined produces the armature
current torque field current and motor speed as follows
)1(
1)(
p
REVi
a
a
aaa
(17)
)(
1)(
JpTT Ler (18)
)1(
1
p
RVi
f
f
ff
(19)
Where aaa RL and fff RL
From equations (11-19) the time-domain block diagram is obtained as
shown in Fig 16
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(8)
derived for the separately excited DC motor which we will put into block
diagram form From the block diagrams we can derive the transfer
function of the DC motor which are used in the design of current and
speed controllers
141 Time Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with time-domain equations using the p operator to denote
differentiation with respect to time dtd and the operator p1 denote
integration ion Therefore we will have no trouble converting the time-
domain block diagram so transfer functions by using the Laplace
operator dt Arranging the equation of the separately excited DC
machine into a block diagram representation is straight forward The
field and armature voltage equations and the relationship between torque
and rotor speed (11-16) may be Combined produces the armature
current torque field current and motor speed as follows
)1(
1)(
p
REVi
a
a
aaa
(17)
)(
1)(
JpTT Ler (18)
)1(
1
p
RVi
f
f
ff
(19)
Where aaa RL and fff RL
From equations (11-19) the time-domain block diagram is obtained as
shown in Fig 16
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(9)
)1(
1
p
R
a
a
)1(
1
p
R
f
f
)(
1
Jp
afL ai
fi fV
eT LT
r aV
bE
Fig 16 Time domain block diagram of separately excited DC motor
142 State Equation of Separately Excited DC Motor
The so-called state equations of the system represent the formulation
of the state variables into a matrix form convention for computer
implementation The state variable of a system are define as a minimal
set of variables such that knowledge of these variables at any initial
condition time t plus information on the input excitation subsequently
applied is sufficient to determine the state of the system at any time tt
In the case of DC machine the field current fi armature current ai and
the rotor speed r The formulation of the state equations for the
separately excited dc machine can be achieved by straight forward
manipulation of the field and armature voltage equations given by (11-
14) and the equation relating torque and rotor speed given by (15-16)
In particular solving equations (11 14 16) for dt
dia dt
di f and
dt
d r
yields
a
a
rf
a
af
a
a
a VL
iL
Lii
dt
d 11
(110)
f
f
f
f
f VL
iidt
d 11
(111)
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(10)
J
Tii
J
L
Jdt
d L
af
af
rr
(112)
These equations can be written in matrix form as follows
L
a
f
a
f
af
af
rf
a
af
r
a
f
a
f
r
a
f
T
V
V
J
L
L
iiJ
L
iL
Li
i
J
i
i
dt
d
1 0 0
0 1
0
0 0 1
0
0 0
0 1
0
0 0 1
(113)
143 Time Domain Transfer Functions of Separately Excited DC
Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 17 as follows
)1)(1()1(
)1(
)(
)(2
0JpJp
K
tV
t
maa
ma
Ta
r
L
(114)
Where 2
K
JRa
m
)1)(1()1(
)1)(1()(2
0JpJp
pJ
T
t
maa
a
VL
r
a
(115)
)1)(1()1(
)1()(2
0JpJp
K
T
ti
maa
ma
VL
a
a
(116)
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(11)
)1)(1()1(
))(1(
)(
)(2
0JpJp
JpR
tV
ti
maa
aa
Ta
a
L
(117)
)1(
1
p
R
a
a
)(
1
Jp K
ai eT LT
r aV
bE
Fig 17 Time domain block diagram of separately excited DC motor at
constant flux
144 S-Domain Block Diagram of Separately Excited DC Motor
Block diagram which portray the interconnection of the system
equations is used extensively in control system design we shall work
with S-domain equations using the s operator to denote differentiation
with respect to time dtd and the operator s1 denote integration ion
Therefore we will have no trouble converting the time-domain block
diagram so transfer functions by using the Laplace operator Arranging
the equation of the separately excited DC machine into a block diagram
representation is straight forward The field and armature voltage
equations and the relationship between torque and rotor speed (11-16)
may be Combined produces the armature current torque field current
and motor speed as follows
)1(
1)(
s
REVi
a
a
aaa
(118)
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(12)
)(
1)(
JsTT Ler
(119)
)1(
1
s
RVi
f
f
ff
(120)
From equations (118-120) the S-domain block diagram is obtained as
shown in Fig 18
145 S-Domain Transfer Functions of Separately Excited DC Motor
After identified all the major components in the block diagram the transfer
functions of all parts in the diagram have been defined An open loop
represents the single direction of flow in a system with no knowledge of
the response On the other hand we have a closed loop system The
output of the system is being measured and fed back to the input to form
a close loop system All these explanation can be summarized by a
complete transfer function representation made up of all the block
diagrams defined in the previous sections The closed loop transfer
function is easily obtained from all blocks in the block diagram shown in
Fig 19 as follows
)1)(1()1(
)1(
)(
)(2
0JsJs
K
sV
s
maa
ma
Ta
r
L
(121)
)1)(1()1(
)1)(1()(2
0JsJs
sJ
T
s
maa
a
VL
r
a
(122)
)1)(1()1(
)1()(2
0JsJs
K
T
si
maa
ma
VL
a
a
(123)
)1)(1()1(
))(1(
)(
)(2
0JsJs
JsR
sV
si
maa
aa
Ta
a
L
(124)
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(13)
)1(
1
s
R
a
a
)1(
1
s
R
f
f
)(
1
Js
afL ai
fi fV
eT LT
r aV
bE
Fig 18 S-domain block diagram of separately excited DC motor
)1(
1
s
R
a
a
)(
1
Js K
ai eT LT
r aV
bE
Fig 19 S-domain block diagram of separately excited DC motor at
constant flux
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(14)
Chapter (2)
Performance Characteristics of Separately Excited
DC Motor
21 Operation of the Separately Excited DC Motor
The operation of a DC motor is described briefly at first A symbolic
representation of a separately-excited DC motor is shown above The
resistance of the field winding is Rf and its inductance is Lf whereas the
resistance of the armature is Ra and its inductance is La In the
description of the motor the armature reaction effects are ignored It is
justifiable since the motor used has either interpoles or compensating
winding to minimize the effects of armature reaction The field current is
described by equation (21) If a steady voltage Vf is applied to the field
the field current settles down to a constant value as shown in equation
(22) When the field current is constant the flux induced by the field
winding remains constant and usually it is held at its rated value If
the voltage applied to the armature is Va then the differential equation
that is to be applied to the armature circuit is shown in equation (23) In
steady-state equation (24) applies The voltage ea is the back emf in
volts In a separately-excited DC motor the back emf is proportional to
the product of speed of motor r (rads) and the field ( webers) as
shown by equation(25)
dt
diLRiV
f
ffff (21)
fff RVi (22)
b
a
aaaa Edt
diLRiV (23)
baaa ERiV (24)
rb KE (25)
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(15)
In equation (25) K is a coefficient and its value depends on the armature
winding If the armature current in steady-state be Ia then the power P
that is supplied to the armature is EbIa This electric power is converted to
mechanical power by the armature of the DC motor Let the torque
developed by the armature be Te the unit for torque being Nm (Newton-
metre) Then power and torque can be related as shown in equation (26-
28) On canceling the common term on both sides the torque Te
developed by the armature is obtained as presented in equation (29) If
the instantaneous armature current is ia then equation (28) applies
Torque has been denoted by Te in both equations
aba IEP (26)
rb KE (27)
raa IKP (28)
ae IKT (29)
Speed of the motor can be controlled by varying Va and holding Vf
constant at its rated value Then as the voltage applied to the armature is
raised the armature current increases first As the armature current
increases the torque developed by motor increases and hence speed of
the motor increases The drop across the armature resistance tends to be
small and hence the motor speed rises almost proportionately with the
voltage applied to the armature But there is a limit to the voltage that
can be applied to the armature and that limit is the rated voltage of the
armature voltage The speed of the motor corresponding to the rated
armature voltage and the rated field voltage is its rated speed Thus the
speed of a motor can be varied below its rated speed by controlling the
armature voltage It would be desirable that the motor should be able to
develop as high as a torque as possible and hence the voltage rated
applied to the field is held at its rated value Applying higher than the
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(16)
rated voltage to either the field or the armature is not recommended
When the rated voltage is applied to the field the flux would be near the
saturation level in the poles If a voltage higher than its rated voltage is
applied to the field the flux would saturate and there would not be any
significant increase in the torque that the motor can deliver On the other
hand this would only result in increased losses in the winding Since the
total heat which the DC motor can dissipate is fixed due to its surface
area and cooling system increased losses from the excitation system
would mean that the other losses would have to reduce implying that the
armature current cannot be at its rated level and the maximum torque that
the motor can deliver may reduce Increasing the armature voltage above
its rated value is not recommended because the insulation of the armature
is designed for operation of the motor with the rated voltage applied to its
armature Moreover the torque that the motor can deliver depends on the
armature current and the field current If the motor is operated
continuously the maximum armature current should not be higher than
its rated value When the armature current and the field voltage are at
their rated level the motor generates the rated torque Hence the
maximum torque the motor can deliver continuously over a long period
of time is its rated torque when its speed is varied from a low value to its
rated speed
If the speed of the motor is to be increased beyond its rated value the
voltage applied to the armature can be held at its rated value and the field
can be weakened by reducing the voltage applied to it When the speed
of the motor is varied in this manner the maximum power that can be
supplied to the armature is fixed since both the voltage applied to the
armature and the armature current cannot exceed the rated level over a
long period
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(17)
22 Dynamic Characteristics of Separately Excited DC Motor
The separately-excited DC motor are widely used and therefore the
dynamic performance of a typical DC motor is illustrated Two modes of
dynamic operation are of interest-starting from stall and changes in load
torque with the machine supplied from a constant voltage source
221 Dynamic Performance During Starting From a Constant DC
Source
This block implements a separately excited DC machine using
SIMULINKMATLAB as shown in Fig 21 An access is provided to
the field connections so that the machine model can be used as a shunt-
connected or a series-connected DC machine
Fig 21 Separately excited DC machine using SIMULINKMATLAB
The details of the SIMULINK diagram is shown in Fig 22 The first
block simulate the equation aidt
d the second block simulate the equation
fidt
d the third block simulate the equation ae iKT and the fourth block
simulate the equation )(
1)(
JsTT Ler
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(18)
Fig 22 Details of Separately excited DC motor SIMULINK diagram
The no load starting characteristics of separately excited DC motor are
shown in Fig 23 The armature voltage the armature current and the
rotor speed are plotted Initially the motor is stall and at time zero 240 V
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(19)
is applied to the armature terminals The peak transient current reaches to
500 A and rotor speed has an overshoot of 60 radsec (large)
Fig 23 No load starting characteristics of separately excited DC motor
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(20)
222 Dynamic Performance During Sudden Change in Load Torque
The dynamic characteristics following a step change in load torque from
zero to 25 Nm are shown in Fig 24 The armature current and rotor
speed are plotted It is noted that the change in steady state rotor speed is
quite large
Fig 24 Dynamic performance of separately excited DC motor following
a sudden change in load torque
223 Dynamic Performance Using Starting Resistance
As the DC motor starts to turn the interaction of the magnetic fields
inside it causes it to generate a voltage internally This back voltage
opposes the applied voltage and the current that flows is governed by the
difference between the two So as the motor speeds up the internally
generated voltage rises the effective voltage falls less current is forced
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(21)
through the motor and thus the torque falls The motor naturally stops
accelerating when the drag of the train matches the torque produced by
the motors To continue accelerating the train resistors are switched out
in steps each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up This can be
heard and felt in older DC trains as a series of clunks under the floor
each accompanied by a jerk of acceleration as the torque suddenly
increases in response to the new surge of current When no resistor is left
in the circuit the full line voltage is applied directly to the motor The
trains speed remains constant at the point where the torque of the motor
governed by the effective voltage equals the drag - sometimes referred to
as balancing speed If the train starts to climb a grade the speed reduces
because drag is greater than torque But the reduction in speed causes the
back voltage to decline and thus the effective voltage rises - until the
current forced through the motor produces enough torque to match the
new drag
On an electric train the driver originally had to control the cutting out
of resistance manually This was achieved by an accelerating relay often
called a notching relay in the motor circuit as shown in Fig 25 which
monitored the fall of current as each step of resistance was cut out All
the driver had to do was select low medium or full speed called shunt
series and parallel from the way the motors were connected in the
resistance circuit) and the equipment would do the rest
As we have seen DC motors are controlled by a notching relay set
into the power circuit But there are other relays provided for motor
protection Sharp spikes of current will quickly damage a DC motor so
protective equipment is provided in the form of an overload relay
which detects excessive current in the circuit and when it occurs
switches off the power to avoid damage to the motors Power is switched
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(22)
off by means of Line Breakers one or two heavy-duty switches similar to
circuit breakers which are remotely controlled They would normally be
opened or closed by the action of the drivers controller but they can also
be opened automatically by the action of the overload relay
On a historical note early equipment had a huge fuse instead of an
overload relay Some of these lasted into the 1970s and recall the
complications of changing one which involved inserting a wooden board
(called a paddle) between the shoes and the current rail This was to
isolate the current from the locomotive while you changed the fuse
A further protective device is also provided in the classic DC motor
control circuit This is the no-volt relay which detects power lost for
any reason and makes sure that the control sequence is returned to the
starting point (ie all the resistances are restored to the power circuit)
before power could be re-applied This is necessary to ensure that too
much current is not applied to a motor which lost speed while current was
off The following circuit illustrates the starting of a 5 HP 240 V DC
Machine with a three-step resistance starter Figure 25
Fig 25 Starting of a separately excited DC motor with a three-step
resistance starter
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(23)
The block implements a separately excited DC machine An access is
provided to the field connections so that the machine model can be used
as a shunt-connected or a series-connected DC machine The armature
circuit and the field circuit of the DC machine model are built with blocks
from SIMULINK library It is represented by a DC motor block created
in series with a Controlled Voltage Source and a Current Measurement
block
Four internal signals are multiplexed on the SIMULINK measurement
output vector (third block output) returning
Rotor speed in rads
Armature current in A
Field current in A
Electromechanical torque in Nm
The following circuit illustrates the starting of a 5 HP 240 V DC Machine
with a three-step resistance starter using SIMULINK as shown Fig 26
The Motor Starter subsystem is shown in Figure 27
Figure 26 Starting DC motor SIMULINK diagram
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(24)
Figure 27 Starter SIMULINK diagram
The DC motor current voltage torque and speed waveforms obtained at
the end of the starting test are shown in Figure 28
Fig 28 Starting performance of DC motor using starter
It is noted from this Figure that the starting current reaches to 50 A
instead of 500 A as mentioned before but the response time is very long
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(25)
Chapter (3)
Open Loop Speed Control of DC Motor Drive Using Solid
State Power Devices
31 Rectification
Rectifiers can be classified as uncontrolled and controlled rectifiers
and the controlled rectifiers can be further divided into semi-controlled
and fully-controlled rectifiers Uncontrolled rectifier circuits are built
with diodes and fully-controlled rectifier circuits are built with SCRs
Both diodes and SCRs are used in semi-controlled rectifier circuits
There are several rectifier circuits rectifier configurations The popular
rectifier configurations are listed below
Single-phase semi-controlled bridge rectifier
Single-phase fully-controlled bridge rectifier
Three-phase three-pulse star-connected rectifier
Three-phase semi-controlled bridge rectifier
Three-phase fully-controlled bridge rectifier and
For low voltage high current applications a pair of three-phase three-
pulse rectifiers interconnected by an inter-phase transformer(IPT) is used
For a high current output rectifiers with IPT are preferred to connecting
devices directly in parallel There are many applications for rectifiers
Some of them are
Variable speed dc drives
32 AC to DC Conversion
321 Full Wave Rectification
A thyristor controlled rectifier employs four thyristors to achieve full
wave rectification If we a DC machine as a load this has both L and R
and generates a back emf as shown in Fig 31
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(26)
Assuming that there is sufficient inductance to ensure the motor
current is continuous with the lag associated the waveforms are as above
We can see that Io and Vo are both positive therefore power is being
delivered from the supply to the motor This is normal rectification mode
If the firing angle is delayed to say 135O then the waveforms change
Fig 31 Schematic and waveforms diagrams of full wave converter
fed DC motor
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(27)
We now see that Vo is ndashve and Io +ve This means that the power flow is
into the supply This is called INVERSION MODE In both cases we can
see that as S3 and S4 turn on the reverse voltage appears across S1 and S2
this is called LINE COMMUTATION
In both cases the average value of the output voltage is
cos22 V
V (31)
Fig 32 Schematic and waveforms diagrams of full wave converter
fed DC motor in inversion mode
The variation of the converter output Vo as defined by (31) is shown in
Fig 33
Fig 33 Output voltage variations of full wave converter
fed DC motor
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(28)
322 The semi-converter
In the semi-converter two of the thyristors are replaced with diodes The
operation is the same as the full bridge converter except that the diodes
do not allow any negative voltage to the load as shown in Fig 34
Fig 34 Schematic and waveforms diagrams of full wave semi-converter
fed DC motor
The average output voltage is now given by
)cos1(2
V
V (32)
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(29)
323 Three Phase Circuits
Higher power applications above several kW are best met using 3 phase
rectifiers Various configurations of rectifier are available
a- The Half Wave Rectifier
In the case of an uncontrolled diode circuit we have the following
diagram as shown in Fig 35
Fig 35 Schematic and waveforms diagrams of full wave converter
At any time the diode whose voltage is the most +ve will conduct We
can see that each diode conducts for a span of 120O also when D1
conducts the voltage across D2 is vBA and across D3 is vCA During this
time D2 and D3 are reverse biased Using D1 we can also say
VV
63 (34)
The thyristor controlled versions is shon in Fig 36
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(30)
Fig 36 Schematic and waveforms diagrams of full wave converter
The output voltage waveform is given by
)cos1(63
V
V (35)
b- The Thyristor Full Wave Converter
This is by far the most common controller rectifier circuit It has the
following configuration Both diagrams represent the same format This
is the 3 phase equivalent of the full bridge rectifier S123 are fired during
the +ve half cycles of the phases to which they are connected and S456
are fired during the ndashve half cycles of the respective phases Again let us
assume that the load has significant inductance to maintain constant
current such as the DC machine examined earlier The output current will
be continuous and operation will be as follows
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(31)
It should be noted that each device conducts for 120O per cycle but the
average output voltage can be expressed as
cos63 V
V (36)
This gives us waveforms as follows
Fig 37 Schematic and waveforms diagrams of full wave converter
Similarly to the single phase converters firing angles of 0 lt lt 90 give
+ve Vo but firing angles of 90 lt lt 180 cause vo to go ndashve and the
converter works in inversion mode this gives us Vo vs for continuous
current
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(32)
Fig 38 Output voltage variations of full wave converter
fed DC motor
33 DC-to-DC Conversion
When the SCR came into use a dc-to-dc converter circuit was called a
chopper Nowadays an SCR is rarely used in a dc-to-dc converter Either
a power BJT or a power MOSFET is normally used in such a converter
and this converter is called a switch-mode power supply A switch-mode
power supply can be of one of the types listed below
Step-down switch-mode power supply
Step-up chopper
Fly-back converter and
Resonant converter
The typical applications for a switch-mode power supply or a chopper
are
DC drive
Battery charger and
DC power supply
332 Description of the Open Loop Drive System
In this section illustrates application of the SIMULINKMATLAB to
the operation of a DC motor drive in which the armature voltage is
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(33)
controlled by a GTO thyristor chopper The objective of this section is to
demonstrate the use of electrical blocks in combination with SIMULINK
blocks in the simulation of an electromechanical system with a control
system The electrical part of the DC motor drive including the DC
source the DC motor and the chopper is built using blocks from the
SIMULINK and Power Electronics libraries The DC Machine block of
SIMULINK models both electrical and mechanical dynamics The load
torque-speed characteristic and the control system are built using
SIMULINK blocks
A simplified diagram of the drive system is shown in Figure 39 The
DC motor is fed by the DC source through a chopper that consists of the
GTO thyristor Th1 and the free-wheeling diode D1 The DC motor
drives a mechanical load that is characterized by the inertia J friction
coefficient B and load torque TL (which can be a function of the motor
speed)
Figure 39 Chopper-Fed DC Motor Drive
In this diagram the DC motor is represented by its equivalent circuit
consisting of inductor La and resistor Ra in series with the counter
electromotive force (emf) E
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(34)
Thyristor Th1 is triggered by a pulse width modulated (PWM) signal to
control the average motor voltage Theoretical waveforms illustrating the
chopper operation are shown in Fig 310
The average armature voltage is a direct function of the chopper duty
cycle
dca VV (37)
Note that this relation is valid only when the armature current is
continuous In steady-state the armature average current is equal to
a
baa
R
EVI
(38)
The peak-to-peak current ripple is
)1(
)1(
)1(
e
eee
R
Vi
a
dc (39)
where is the duty cycle and r is the ratio between the chopper period
and the DC motor electrical time constant
)( aa RL
T (310)
Figure 310 Waveforms Illustrating the Chopper Operation
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(35)
34 Steady-State Voltage and Current Waveforms
When the steady-state is attained you can stop the simulation and plot the
current and voltage waveforms using the variables Va and Ia sent back in
MATLAB workspace by the scope The DC motor current and voltage
waveforms obtained at the end of the starting test are shown in Fig 311
Figure 311 Steady-State Motor Current and Voltage Waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(36)
Chapter (4)
Design and Simulation for Current amp Speed Controllers
of Separately Excited DC Motor Drive
41 Introduction
This chapter describes how a separately-excited DC motor can be
controlled in closed-loop with a Chopper-controlled supplying DC source
to its armature In a control system the system dynamics is often
described by differential equations By applying Laplace transformation
to the system differential equations the system output variables can be
related to the input variables in an algebraic form In our single input
single output system (SISO) where one input position expect one
corresponding output position We use a transfer function to model the
inputoutput relationship System Transfer Function = Ratio of the output
over the input to a control system Hence every component in a control
circuit will have a transfer function This is obvious because every
component in a control system will receive some input signal and
manipulate this signal to provide a required output Therefore we have a
series of transfer functions within the system We can relate these systems
together by a block diagram representation where the transfer functions of
each component is put into representative blocks
A separately-excited dc motor can be controlled either by varying the
voltage applied to the field winding or by varying the voltage applied to
the armature This Chapter describes how the motor can be controlled by
varying the armature voltage and it is assumed that the field is excited by
a constant voltage equaling the rated voltage of the field winding It
means that the discussion to follow assumes that the field current remains
steady at its rated value
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(37)
42 Control System Design
Classical Feedback Control describes design and implementation of high-
performance feedback controllers for engineering systems This Chapter
emphasizes the pole placement and root locus approaches which is widely
used in practical engineering It presents the design methods for high-
order SISO linear and nonlinear analog and digital control systems
Modern technology allows implementation of high-performance
controllers at a very low cost Conversely several analysis tools which
were previously considered an inherent part of control system courses
limit the design to low-order (and therefore low-performance)
compensators Among these are the root-locus method the detection of
right-sided polynomial roots using the Routh-Hurwitz criterion and
manual calculations using the Laplace and Fourier transforms These
methods have been rendered obsolete by structural simulation of complex
systems multi-loop systems and nonlinear controllers all of which are
essential for good design practice
Nonlinear dynamic compensation is employed to provide global and
process stability and to improve transient responses The nearly-optimal
high-order compensators are then economically implemented using
analog and digital technology
43 Current Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
)1(
)1(
)(
)(
0 aa
a
Ta
a
s
R
sV
si
L
(41)
If we use the desired response
22
2
2)(
)(
nn
n
ssR
sC
(42)
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(38)
We can design the current controller as follows
)1(
1
s
R
a
a
s
KsK i
i
i
p
ai
ai
Fig 41 Block diagram of the current control loop
The closed loop transfer function can be deduced as
aa
i
iaa
i
pa
i
i
i
paa
Ta
a
RKRKs
KsKR
sI
sI
L
)1(
))(1(
)(
)(2
0
(43)
By comparing equations (42 43) yields the controller parameters
)12( anaa
i
p RK (44)
2
naa
i
i RK (45)
Now we can select the damping ratio and then we can calculate n as
follows
For s
sR1
)( therefore
22
2
2
1)(
nn
n
sssC
(46)
The inverse Laplace Transform for equation (46) will yield
)1(1)( tetC n
tn
(47)
From this equation we can calculate n at the rise time rt and 90)( rtC
44 Speed Controller Design Using Pole Placement
With approximate model of the current loop the transfer function is given
by
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(39)
)(
)(
)(
0Js
JK
sV
s
LTa
r
(48)
We can design the current controller as follows
)(
Js
JK
s
KsK ip
a
r
Fig 42 Block diagram of the speed control loop
The closed loop transfer function can be deduced as
)()(
))((
)(
)(2
0
JKKsJKKJs
KsKJK
s
s
ip
ip
Tr
r
L
(49)
By comparing equations (42 49) yields the controller parameters
)2( JK np (410)
KJK ni 2 (411)
Now we can select the damping ratio and then we can calculate n as
before
45 Operation of the Current Controller of DC Motor
The current controller has two inputs the reference current signal
which is the output of the speed controller and a feedback signal
proportional to armature current The feedback corresponding to
armature current signal can be obtained in several ways A current
transformer can be introduced in the path of ac current from the ac
supply Another option would be to use a DC current transducer that
makes use of a Hall-effect sensor or an isolated opamp The transducer
used produces a voltage proportional to current in the armature The
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(40)
difference between these two signals is processed by another PI controller
and its output is also limited to correspond to 0o and 180
o firing angle
Output of the current controller may vary between 0 V and 10 V with 0
V corresponding to 180o firing angle and 10 V corresponding 0
o firing
angle If the firing angle be and the output of current controller VC
then
)10(180 cV (412)
As output voltage of the current controller increases due to the
difference between the reference signal and the current feedback signal
the firing angle is advanced towards 0o and average output voltage of the
bridge rectifier increases This in turn leads to increased torque
generation and the motor accelerates
If the speed reference is brought down suddenly the current in the
motor cannot be reversed and hence the motor slows down due to friction
and the load This process can be slow
The question that can be raised is whether we need the current loop
The answer is that it improves the performance If there is a change in
the supply voltage even by a small amount output of the bridge circuit
tends to a fall a bit for the same firing angle The reduction in output
voltage causes a large change in armature current with speed remaining
more or less constant Then the current loop comes into action
correcting firing angle to the required value The time constant of the
armature due to its inductance and resistance tends to be of the order of
a few tens of ms and the mechanical time constant due to the moment of
inertia of motor and load and the friction is of the order of a few tenths of
a second If a current controller is not used speed would have to change
before the speed controller can come into action Since the mechanical
time constant is about at least 10 times greater there would be a
significant change in speed if there be no current controller
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(41)
Normally a filter may be necessary in the feedback circuit for speed The
tacho signal usually contains a small ripple superimposed on its dc
content The frequency of the ripple is usually dependent on the speed
and the lower the speed is the lower is the frequency of this ripple
Hence the time constant of the filter may have to be set to correspond to
the lowest speed at which the motor would be required to run Since
power output varies proportionately with speed there is usually no
justification to run the motor at an extremely low speed The next section
describes how the simulation is carried out
46 Operation of Speed Controller of DC Motor
The block diagram of a dc drive is shown above It does not show all
details The DC motor has not been represented in the form of a block
diagram and the details of the load the motor drives have also not been
shown The block diagram functions as follows
For the system described here output of the system is speed of the motor
Hence when this system is to be controlled in closed-loop the parameter
that is to be set is what that speed should be It is denoted to be
r In
order to control speed in closed-loop we need a feedback signal that
corresponds to speed It can be obtained in several ways A digital tacho
or an analogue tachogenerator can be used It is assumed that an
analogue tachogenerator is used here It is coupled to the motor shaft and
its output voltage varies linearly with its speed Let the speed feedback
signal be
r This signal can be compared with the speed reference
signal and the error can be processed by the speed controller The
controller can be of one of several types It can be an integral (I)
controller or a proportional (P) controller controller or a derivative (D)
controller or PI or PD or PID controller Here both the controllers used
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(42)
are PI (proportional plus integral) controllers A PI controller can lead to
fast response and zero-error for a step input
The PI controller for speed has as its input the error between the two
signals
r and r If the speed feedback signal r is lower than the
reference signal
r it means that the DC motor speed is below the set
speed and the motor needs to be accelerated In order to accelerate the
motor it should develop greater torque To develop greater torque its
armature current has to increase Hence the output of speed controller is
set to function as the reference signal for armature current It will be a
voltage corresponding to armature current with an appropriate coefficient
linking the two quantities When r lt
r the difference causes output
of the speed controller to increase Since output of speed-controller is set
to function as the armature current reference signal an increase in the
value of speed-controller output would in turn lead to an increase in
armature current
47 Operation of DC Chopper Fed of DC Motor
The rectifier circuit is made up of SCRs and the SCRs have a current
rating Hence it is necessary to ensure that current through the SCRs
remains within a safe level Hence output of the speed controller is
limited at both ends Its maximum value corresponds to the safe level for
SCRs It is not normally the rated current of the motor and it is usually
set at a value ranging from 15 times to 2 times the rated armature current
The reason is that the motor may have to develop more than the rated
torque under transient conditions to achieve fast response In order to
ensure that the motor armature current remains within its rated value
another supervisory loop may be used Another option is to use a circuit-
breaker The instantaneous trip action in the circuit breaker can be due to
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(43)
magnetic effect and the overload trip can be due to thermal action A bi-
metallic strip within the circuit-breaker expands due to temperature and
would trip the circuit-breaker The lower limit on the output of speed-
controller would correspond to zero current in the armature since the
motor current in this scheme cannot be in the reverse direction
48 Simulation of the Separately Excited DC Motor Drive Using
SIMULINKMATLAB
In this section we consider a variable-speed DC motor drive using a
cascade control configuration A block diagram of this drive is shown in
Figure 43 The motor torque is controlled by the armature current Ia
which is regulated by a current control loop The motor speed is
controlled by an external loop which provides the current reference Ia
for the current control loop
Figure 43 Variable-Speed DC Motor Drive
The drive system diagram is built using electrical blocks contained in the
SIMULINK library Voltage Measurement and Current Measurement
blocks are used as the interface between the two block types The system
diagram of the DC motor using SIMULINK is shown in Fig 44
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(44)
Figure 44 DC Motor Drive Using SIMULINKMATLAB
The DC machine parameters are set to the desired values by using the
dialog mask of the DC Machine block
The load torque-speed characteristic can be implemented by a
SIMULINK Function block
The motor used in this case study is a separately excited 5 HP240 V DC
motor having the following parameters Ra = 05 La = 10 mH Kv
=123 V(rads) Kv = 123 NmA
A 10mH inductor (Ls) is connected in series with the DC motor to
smooth out the armature current The constant excitation is implemented
by connecting a DC Voltage Source block to the field winding
The required trigger signal for the GTO thyristor is generated by a
hysteresis current controller which forces the motor current to follow the
reference within +h2 and -h2 limits (h is the hysteresis band) as shown
in Fig 45
The current controller is a masked block that contains
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(45)
Figure 45 The hysteresis current controller
The speed control loop uses a proportional-integral (PI) controller which
is implemented by SIMULINK blocks as shown in Figure 46
Figure 46 The PI speed controller
49 Simulation Results of the DC Drive
Run the simulation by selecting Start from the Simulation menu in
Simulink Set the simulation parameters in the Simulation Parameters
menu as follows
Simulation time Start Time0 Stop time 12
Solver Type Variable-step ode23tb (stiffTR-BDF2)
Max Step Size auto
Initial Step Size auto
Relative Tolerance 1e-3
Absolute Tolerance 1e-3
The motor voltage current waveforms and motor speed are displayed on
three axes of the scope connected to the variables Vd Ia and
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(46)
Once the simulation is completed you can return to the MATLAB
command window to examine the results with more details by using the
plot function
491 Drive Performance at No Load
In this test we simulate the starting transient of the DC drive The
inertia of the mechanical load is small in order to bring out the details of
the chopper commutation details The speed reference is stepped from 0
to 120 rads at t=00 s and we observe the DC motor speed and current
The transient responses for the starting of the DC motor drive are shown
in Figure 47 Note that the final system state vector x Final can be saved
by selecting Workspace IOSave to workspaceFinal state in the
Simulation Parameters window It can be used as initial state in
subsequent simulation so that the simulation can start under steady-state
conditions
492 Speed Regulation Dynamic Performance
We can study the drive dynamic performance (speed regulation
performance versus reference and load torque changes) by applying two
successive changing operating conditions to the DC drive a step change
in speed reference and a step change in load torque
Replace the block named
r (rads) and the block named Load_torque
(Nm) in the diagram by two SIMULINK step blocks with different
starting times The speed reference steps from 120 rads to 160 rads at t =
04 s and the load torque steps from 5 Nm to 25 Nm at t = 12 s The
final state vector obtained with the previous simulation can be used as
initial condition so that the simulation will start from steady-state Select
Workspace IOLoad from workspaceInitial state in the Simulation
Parameters window and restart the simulation
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(47)
The obtained response of the DC motor drive to successive changes in
speed reference and load torque is shown in Figure 48
Figure 47 Starting of the DC Motor Drive
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(48)
Figure 48 Dynamic Transient of the DC Motor Drive
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(49)
Chapter (5)
Implementation of the Open Loop Control for Separately
Excited DC Motor
51 Introduction
In this Chapter the implementation of the DC Chopper feeding DC
motor is presented Power supply circuits driving circuits of IGBT
transistor and control circuit that generate the control signal of the
Chopper are designed and implemented
52 Experimental Setup
511 The Power Supply with Voltage Regulator Circuit
Power is supplied to the control circuit through a +5 -5 -15 +15 volt
DC power supply Power form the output of the bridge rectifier is
applied to a voltage regulators circuits that steps the voltage down to -5
+5 +15 -15 volt pure DC This circuit is fairly simple to build because
the support circuitry for the LM7805 (5-Volt voltage regulator IC)
LM7905 LM7815 and LM7915 require very few components Each
circuit consists of step down transformer an input jack a power switch a
resistor one LED a voltage regulator IC and two capacitors The out of
the bridge rectifier is brought in through the input jack and then routed to
a double pole double throw switch (DPDT) This switch is used to turn
the power to the microcontroller on and off The reason for using the
DPDT switch is to allow for disconnecting both the hot and neutral lines
The LED is used to indicate whether power to the circuit is on or off
The tantalum capacitors are used to filter the input and output voltages of
the all voltage regulators Once this testing is completed power is
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(50)
applied to the circuit The student then checks the voltage regulator for
overheating Figure (51) displays the voltage regulator circuit
Fig 51 The voltage regulator circuit
522 Linear Control of Phase Angle
In this scheme illustrated in Fig 52 a control voltage Ec changes linearly
the phase angle The voltage V1 is converted to a square voltage e1 and
then to a ramp voltage e2 which is then compared with a control voltage
Ec If e2 is higher than Ec a signal ea is obtained at the output of the
comparator The time at which the rising edge of ea occurs is proportional
to Ec and defines the firing angle α This signal ea is next fed to a pulse
amplifier circuit and is used to fire IGBT The firing angle is given by
ckE (51)
This circuit was used to generate a ramp that is synchronized with the
line voltage Each comparator compares the line voltage with zero and
the RC circuit integrates the resulting square wave The reverse diode
resets the ramp to zero at each zero crossing and the series diode circuit
ORs the ramp outputs to achieve an increasing ramp which resets at each
zero crossing of the source voltage The final comparator stage is used to
dial the firing angle and the transistor drive circuit bias the IGBT
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(51)
The ramp waveform and the pulse waveform for degrees were plotted
The circuit was constructed powered by a DC power supply (15V) and
its operation was confirmed The circuit diagram is shown in Fig 53
Fig 52 Linear control of phase angle
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(52)
Fig 53 Circuit diagram phase angle control
523 Pulse Amplifier Circuit (Driving Circuit)
The pulses ei or ej in Fig 54 may not be strong enough to bias an IGBT
Besides the gate and emitter terminals of the IGBT are at higher
potentials of the power circuit and the control circuit should not be
directly connected to the power circuit An optical isolation or pulse-
transformer isolation is commonly used in practice to provide physical
isolation between the control circuit and the power circuit Figure 54
shows a pulse amplifier circuit using a pulse transformer isolation A
Darlington transistor is used to amplify the pulse-current If the pulses are
long (ex has a long width ) they may saturate the pulse-transformer and
the whole width of the pulse may not be transmitted The whole pulse-
width may not be necessary In such a case the pulse is modulated at a
high frequency (10-1 MHz) as shown in Fig 54 using a 555 timer or any
oscillator The duly cycle of the timer should be less than 50 so that the
flux in the transformer can reset A modulated pulse also reduces gate
dissipation in the IGBT Processing of the pulse signal (obtained from
the firing or driving circuit) at various stages is illustrated by the timing
diagram in Fig 54
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(53)
Fig 54 A typical pulse amplifier circuit
524 Chopper Control
Chopper converters in general require firing pulses to turn on a main SCR
and a commutating IGBT The time interval between the firing of the
two IGBTs determines the duty cycle and hence the output voltage A
control voltage is used to control the duty cycle of the chopper Figure
55 shows a chopper firing circuit that consists mainly of four parts a
triangular wave generator a voltage comparator edge detection and pulse
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(54)
amplifiers The waveforms at various parts of the circuit are also shown
in Fig 55
The three operational amplifiers Q1 and Q2 together form a triangular
wave generator that generates the triangular wave ea shown in Fig 55b
As the voltage ea decreases below 06 V (which is the forward bias
voltage of the diode D2) the output of Q2 changes from 135 V to -135
V and it in turn triggers Q3 to change state The output of Q3 which is
now negative (-135 V) makes D1 forward biased and the 22 k path
takes control of the integrator input summing junction The output of Q1
quickly rises to 135 V which in turn triggers Q2 and Q3 and changes
their outputs to positive voltages Now the diode D1 is reverse biased the
feedback loop through D1 is reverse biased and the feedback loop
through D1 is open With the diode D1 reverse biased control of the
integrator Q1 reverts to the 200 k path and the output voltage e has a
constant slope that depends on the values of the capacitor C the input
resistor R and the input voltage Vi In fact this oscillator can be used as
a voltage-controlled oscillator (VCO) The purpose of using Q2 is to
introduce a time delay so that there is enough lime to charge up the
capacitor so that ea rises to 135 V The diode D2 is used for the offset
adjustment so that ea is always above zero voltage
The operational amplifier Q4 is used as a voltage comparator If the
control voltage Ec exceeds the voltage ea the output of Q4 changes as
shown by waveform ea in Fig 55
The two monostable multivibrators are connected in such a way that
one of them is triggered by the rising edge and the other by the falling
edge of the signal On receiving the rising or falling edge the
monostable multivibrators produce two output signals whose width can
be adjusted A pulse-width in the range of 20 to 200 sec is sufficient
for firing IGBT
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(55)
Fig 55 Chopper driving circuit
525 OPEN-LOOP AND CLOSED-LOOP CONTROL
The control voltage Ec in Figs 51 52 53 and 55 changes the output
voltage of the converter In an open-loop control as shown in Fig 56 the
control voltage Ec is varied by using a potentiometer In a closed-loop
control the control voltage is obtained from the difference between a
reference and the quantity to be controlled For example if the dc motor
armature current is to be controlled in a closed-loop feedback control
system as shown Fig 56 the control voltage is derived from the
difference between the reference current and the actual motor current
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(56)
The Opamp comparator is used to compare values of 2 input voltages In
this control system the Opamp received voltage signal from the
potentiometer Then the Opamp amplifies the systems error voltages so
that the output voltage is enough to drive the motor For example the
input signal may be the order of a few miliamperes This is hardly
enough to actuate the motors This illustrates the need for an increase
gain It is worth mentioning that this amplifier compares the values of the
input and feedback voltage and then amplify this voltage to a magnitude
suitable to be transmitted
Fig 56 Open loop and closed loop control circuit
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms
(57)
53 Experimental Results
We test the practical system using a resistive load and a small DC motor
Fig 57 shows the steady state voltage and current waveforms
Fig 57 Steady state voltage and current waveforms