2- induction machine control pages de flux and speed estimation techniques for sensor less control...
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2.3 Induction Machine Control
2.3.1 V/Hz Control
The open-loop Volts/Hz control was by far the most popular method to control
the machine speed, especially because of its simplicity. The method is based on the
control of the stator frequency. The objective is to control the machine speed while
keeping constant the magnitude of the stator flux. As a result, the machine retains its
torque/ampere capability at any speed. By neglecting the stator resistance drop, the stator
flux is kept constant if e
ss
Vω
λ = and the name of the method comes from this equation.
Early approaches assume that the rotor speed ωr is approximately equal to the
synchronous speed ωe (slip speed is neglected). For speed control, the speed reference ωr
is set and the stator voltage Vs is computed to maintain the desired stator flux. Integration
of the reference speed gives the angle of the stator voltage (θe). Finally, the space vector
described by Vs and θe is used as command voltage for the three-phase inverter that
powers the machine.
The approach can be improved by considering the effect of the non-zero stator
resistance and of the slip speed. To compensate for the stator resistance, a boost voltage
can be added to the stator voltage. This is especially useful at low speed since the stator
resistance absorbs the major amount of the stator voltage. The slip speed is also different
from zero. To compensate, the slip is estimated using model equations and is added in the
integration of the voltage angle. The control scheme is presented in Figure 2.6.
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IM
PI
Estimator
*rω
^
rω
*eω
*slω
- +
Inverter
*sV
Figure 2.6 V/Hz control scheme
A detailed discussion regarding the V/Hz method and other scalar control schemes can be
found in [2]. Generally, the method is very robust and works well even at very low stator
frequencies. The robustness of the method stems from the approach used in computation
of the voltage angle θe. A good-quality θe waveform (straight and undistorted) is obtained
and this results in smooth shaft motion without ripple torque or oscillations.
The major disadvantage of the V/Hz method is its sluggish dynamic response
since the method disregards the inherent machine coupling. A step change in the speed
command produces a slow torque response. During the transient, the magnitude of the
stator flux is not maintained (the magnitude decreases) and the machine’s torque response
is not sufficiently fast. In addition, there is some amount of under damping in the
machine’s flux and torque responses that increases at lower frequencies. In some
operating regions, the system may become unstable.
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2.3.2 Field-Oriented or Vector Control
The modern approach for induction machine control is based on vector or field-
oriented control. The invention of vector-control in early 1970’s brought a renaissance in
the high-performance control of ac drives. This is because, in spite of the coupled and
nonlinear machine model, the induction machine can be controlled similarly to a
separately excited dc machine.
In a dc machine, neglecting the armature reaction and saturation, the expression of
the torque is:
afe IKT λ= (2.38)
where K is a constant. The construction of a dc machine is such that the field flux λf is
proportional with the field current If and is orthogonal with the flux produced by the
armature current Ia. These two fluxes are kept orthogonal by the collector-brush
assembly. They are decoupled and stationary in space. This means that when torque is
controlled by controlling the current Ia, the field flux is not affected and vice-versa.
The induction machine exhibits the same behavior when viewed in the rotational
reference frame aligned with the rotor flux. The field current (id) and the torque current
(iq) appear as dc quantities in steady state and are orthogonal and decoupled. Therefore,
the flux and torque currents can be independently controlled to obtain torque production
in the same manner as in a dc machine. Accurate torque control has two prerequisites:
Accurate control of the currents id and iq with no steady-state error and desired
dynamics.
Accurate estimation of the rotor flux angle θe that allows transformation of the
variables from the stationary to the rotating reference frame.
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Generally, the first condition is easy to achieve. Traditional PI controllers are the most
common solution and they yield good experimental results; other types of controllers
have also been used (fuzzy-logic, sliding mode etc).
Estimation of the angle θe based on the equations of the model can be done in two
ways: by DFO or by IFO.
2.3.3 Direct Field Orientation (DFO)
This method computes the rotor flux angle based on the projections of the flux
vector on the stationary reference frame (Figure 2.7). The flux components and
are needed. Several model-based observers can be used to estimate them. The difficulties
of the method come from the various problems associated with implementation of the
observers (integration, dependency on machine parameters etc).
rαλ rβλ
d
α
β
q
θ
−
rλ
rαλ
rβλ
Figure 2.7 Principle of Direct Field Orientation (DFO)
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With the rotor fluxes known, the angle of the flux vector (also called rotor position) is
given by:
r
re
α
β
λ
λθ 1tan −= (2.39)
However, since sin and are really needed for the Park transformation, these can
be found directly by:
eθ eθcos
22sin
rr
re
βα
β
λλ
λθ
+= (2.40)
22cos
rr
re
βα
α
λλ
λθ
+= (2.41)
2.3.4 Indirect Field Orientation (IFO)
An alternative approach to obtain the rotor flux angle is by Indirect Field
Orientation (IFO). The method is based on Equation (2.36). The right-hand side terms in
(2.36) are the rotor electrical speed and the slip speed. Their integration provides the
desired angle. For accurate estimation, the method requires correct values for both the
rotor speed and the rotor time constant. Also, the integration can produce incorrect rotor
angle estimates if the initial condition is not properly chosen. Generally, IFO works best
for drives that use a speed sensor to measure the rotor speed (sensored drives). In
sensorless drives, the speed information is not available by direct measurement and it
must be estimated. The accuracy of the angle produced by IFO depends heavily on the
speed estimate.
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Many speed estimators are available, however, steady-state errors, floating of the
machine parameters, estimation delay due to low pass filtering are common problems that
influence the speed estimation bandwidth and accuracy. An incorrect speed estimate can
generally be acceptable for speed feedback but has severe effects on the drive stability
and performance if the transformation angle is found by IFO.
Various topics regarding sensorless control are presented in the subsequent
chapters. The basic IM control scheme used in this research is shown in Figure 2.8.
3-PhaseInverter
IM
PWM
*αV
*βV
*aV*
bV
*cV
αβ
αβ
αβ
abc
abc
abcT
dcV
dq
dq
*dV
*qV
PI
PI
Speed and Flux
Estimator
dcVabcT
aibi
- -
-
PI
mL1*
rλ*di
*qi
*rω
rω
rω
rαλ
rβλr
r
α
β
λλ1tan −
αβ
θ
θ
di
qi
αi
βi
+
+
compdqV
Figure 2.8 Block diagram of sensorless DFO induction motor control
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The control scheme presented has the following characteristics:
PI controllers are used to regulate the currents and the speed.
The angle θe is computed using (2.39) for convenience of computations.
Various flux and speed estimators have been used and they are not specifically
shown in the control scheme. Details will be presented in the subsequent chapters.
For easy implementation, the flux magnitude λr is not regulated directly. Instead,
the desired flux level is obtained by setting the reference d-axis current. The
approach significantly simplifies the software and is equivalent to flux regulation
as long as the magnetizing inductance Lm does not saturate.
Note the block that adds two compensation voltages to the outputs of the current
controllers. Generally, these are used in order to completely decouple the
dynamics of the d and q-axis currents. Their expressions are:
+−=
r
qmqrps
compd
iLinLV
ληωσ
2
(2.42)
++=
r
dqmdrprrps
compq
iiLinnLV
ληωλωβσ (2.43)
The addition of the two decoupling voltages is not mandatory. For the motor
under study, it was found through simulation that the addition of the terms in
(2.42)-(2.43) may not significantly improve the dynamics. The calculation of the
above terms is computationally intensive and requires both the speed and the
magnitude of the rotor flux. In the work related to Chapters 4 and 5, the
compensation voltages have been omitted.
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2.4 Experimental Setup
The experimental setup used in this research consists of the following:
Dayton model 2N863M 3-phase induction motor. The motor plate data and rated
parameters are presented in Table 1.
Rating ¼ hp Pole # 4
Speed 1725 rpm Voltage 220 V
Rs 10.98 Ω
Lls,Llr 0.0149 H
Lm 0.297 H
Rr 5.572 Ω
Table 1 Rated parameters of Dayton motor model 2N863M
Spectrum Digital DMC 1500 3-phase inverter. The rated values for the inverter
are: 350V dc bus maximum value; 5 A continuous current; 10 A peak current.
Current sensor interface: this current acquisition board was built in the laboratory.
The board has 2 LEM current sensors model HY 5-P (maximum peak current: 5
A) and two differential op-amp structures to allow signal interfacing with the DSP
board.
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Spectrum Digital TMS 320F2407-PGEA Evaluation Module. This is the
controller board of the setup. It contains the Texas Instruments 16 bit, fixed-point
Digital Signal Processor as well as analog interfaces and emulator port. The board
has a digital to analog converter (D/A) with 4 channels that has been used to
display the waveforms of interest.
A block diagram of the experimental setup is shown in Figure 2.9.
Spectrum Digital3-PhaseInverter
Dayton 2N863M
D/A
LEM a
LEM b
Spectrum DigitalTMS320F2407
Evaluation Board
PWMSignals
AnalogSignalsVdc,ia,ib
DigitalScope
Currents ia,ib
350 V (max)
5 V 12 V
Figure 2.9 Block diagram of the experimental setup
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