direct torque control of permanent magnet
TRANSCRIPT
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DIRECT TORQUE CONTROL OF PERMANENT MAGNET
SYNCHRONOUS MOTOR BASED ON NEURAL NETWORKS
By
MARAN.M.P
(REG NO.16103010)
A PROJECT REPORTSubmitted to the Department of electricals&electronics Engineering
in the FACULTY OF ENGINEERING & TECHNOLOGY
In partial fulfillment of the requirements for the award of the degree
of
MASTER OF TECHNOLOGY
IN
POWER ELECTRONICS AND DRIVES
S.R.M. ENGINEERING COLLEGE
S.R.M. INSTITUTE OF SCIENCE AND TECHNOLOGY
(Deemed University)
May 2005
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BONAFIDE CERTIFICATE
Certified that this project report titled DIRECT TORQUE CONTROL
OF PERMANENT MAGNET SYNCHRONOUS MOTOR BASED
ON NEURAL NETWORKS is the bonafide work of MARAN.M.P.
(REG NO.16103010) Who carried out the research under my supervision. Certified
further, that to the best of my knowledge the work reported herein does not form part of
any other project report or dissertation on the basis of which a degree or award was
conferred on an earlier occasion on this or any other candidate.
Signature of the Guide Signature of the H.O.D
Name of the Guide
Signature of the Internal examiner Signature of the external examiner
Name: Name:
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ABSTRACT
!"The proposed control is implemented on a prototype PMSM, which has a standardinduction motor stator, and the experimental results shows that the torque response is
extremely fast.
A new DTC for PMSM motor which feature in low torque and low flux ripple.
Direct torque control of PMSM is done by MATLAB/SIMULINK MODEL
BASED ON POWER SYSTEM BLOCKSET. Simulation shows the flux and torque
ripples are greatly reduced. Also, neural network is used to emulate the state selector of
conventional DTC. The training algorithm used for this purpose is back propagation.
The Training data are taken from the conventional DTC.
ACKNOWLEDGEMENT
I take this opportunity with utmost alacrity and enthusiasm to offer my most
sincere and humble gratitude to our beloved chairman Thiru.T.R.PACHAMUTHU,
for providing me to do this M.Tech, course with all the resources required for the timely
completion of my project.
I express my heartfelt and sincere thanks to Prof.R.VENKATARAMANI,
principal for giving us encouragement whenever needed.
To pay my profound sense of gratitude and indebtedness to
Dr.G.SAMBANDAN, M.E., PhD.,HOD, Department of electrical & electronics and
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Engineering, SRM Institute of Science and Technology, for having provided me
opportunity to work under his guidance and motivation for shaping this project work.
His constant encouragement and vision enabled me to take this new endeavor to the
success path and I am so thankful to you for providing such an environment and
infrastructure par excellence.
I am extremely grateful to my project coordinator Mrs.N. KRISHNA
KUMARI M.E for her kind and valuable suggestions methodically and step wise
through out my studentship through encouragement.
TABLE OF CONTENTS
#. INTRODUCTION #
#.#REQUIREMENTS OF THE DIRECT TORQUE CONTROLLER 2
2. PERMANENT MAGNET SYNCHRONOUS MOTOR MODEL
GENERALITIE 3
2.#INTRODUCTION 3
2.2 MACHINE EQUATIONS 4
2.3 FLUX AND CONTROL BY MEANS OF SPACE VECTORMODULATION 6
3. DIRECT TORQUE CONTROL PRINCIPLES AND GENERALITIES 9
3.#PMSM MOTOR CONTROLLERS 9
3.#.#VOLTAGE / FREQUENCY 9
3.#.2 VECTOR CONTROLLERS 9
3.#.3 FIELD ACCELERATION METHOD #0
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3.#.4 DIRECT TORQUE CONTROL #0
3.2 PRINCIPLES OF DTC ##
3.2.#INTRODUCTION ##
3.2.2 DTC CONTROLLERS ##
3.3 DTC SCHEMATIC #3
3.4 STATOR F AND T ESTIMATOR USING Wm& CURRENT #4
3.5 STATOR F AND T ESTIMATOR USING Vdc &
CURRENTS #6
4. IMPLEMENTATION OF DTC #8
4.#DTC ARCHITECTURE #8
4.2 VOLTAGE AND CURRENT MEASUREMENTS #8
4.3 ADAPTIVE MOTOR MODEL #8
4.3.#ESTIMATING ACTUAL FLUX #9
4.3.2 ESTIMATING THE ACTUAL TORQUE #9
4.4 TORQUE AND FLUX COMPARATOR #9
4.5 OPTIMUM PULSE SELECTOR 20
4.6 TORQUE AND FLUX REF.CONTROLLER 23
4.7 SPEED CONTROLLER 24
5. NEURAL NETWORKS 25
5.#RESEARCH HISTORY 25
5.2 THE BRAIN AS INFORMATION PROCESSING SYSTEM 265.3 NEURONS AND SYNAPSES 27
5.4 SYNAPTIC LEARNING 28
5.5 ARTIFICIAL NEURAL NETWORK MODEL 29
5.6 THE LEARNING PROCESS 3#
5.7 TRANSFER FUNCTION 33
5.8 THE UPS AND DOWNS OF NEURAL NETWORK 34
6. RESULTS 35
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6.#SIMULATION RESULTS 35
7. CONCLUSION 39
8. APPENDIX 4#
9. REFERENCES 50
FIG.NO LIST OF FIGURES PAGE NO.
#. DTC system diagram 4
2. Eight voltage space vectors of 3 phase VSI 5
3. Selection of voltage vectors according to error vector of flux linkage
with SVM 7
4. Proposed DTC system 8
5. Stator flux vector locus and different possible switching voltage
vectors #26. Typical DTC System Diagram #4
7. Biological Neuron 27
8. Synaptic Learning 28
9. A Neuron Model 29
#0. Backpropagation Network 30
##. Three different transfer functions 33
#2. Matlab/Simulink model ofthe proposed DTC PMSM drive System 35
#3. The dynamic performance of the modifiedDTC 36
TAB NO. LIST OF TABLES PAGE NO
#. Look up table #3
2. The simulation results 36
3. Parameters of the Interior Permanent Magnet Synchronous Machine
Used Simulation 39
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CHAPTER 1
#. INTRODUCTION
With the revolutionary DTC (Direct Torque Control) technology developed by
ABB, field orientation is achieved without feedback using advanced motor theory to
calculate the motor torque directly and without using modulation. The controlling
variables are magnetizing flux and motor torque.
DTC main features are follows:
Direct control of flux and torque. Indirect control of stator currents and voltages. Approximately sinusoidal stator fluxed and stator currents. High dynamic performance even at standstill.
The main advantages of DTC are: -
#. Absence of co-ordinate transforms.2. Absence of voltage modulator block, as well as other controllers such as PID for
motor flux and torque.
3. Minimal torque response time, even better than the vector controllers.However some disadvantages are also present such as:-
#. Possible problems during starting.2. Requirement of torque and flux estimator, implying the consequent parameters
identification.
3. Inherent torque and stator flux ripple.
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flux linkage and torque. The most common way to carry out the DTC is a switching
table and hysteresis controller, as in. Fig 2.#is a typical DTC system. It includes flux
and torque estimators, flux and torque hysteresis controllers and a switching table.
Usually a DC bus voltage sensor and two output current sensors are needed for the flux
and torque estimator. Speed sensor is not necessary for the torque and flux control. The
switching state of the inverter is updated in each sampling time. Within each sampling
interval, the inverter keeps the state until the output states of the hysteresis controller
change. Therefore, the switching frequency is usually not fixed; it changes with the
rotor speed, load and bandwidth of the flux and torque controllers.
Although DTC is getting more and more popular, it also has some drawbacks,
such as the high torque and flux ripples. Many researchers already paid some attention
to these problems. For example, D. Casadei et al replaced one switching table with
more switching tables; which is called discrete space vector modulation in their paper.
Isao Takahashi et al proposed new inverter structure and C.G. Mei et al used variable
switching sector to minimize the torque and flux ripple. However, the common problem
of these methods is that they can not work at zero-error state, i.e. these DTC algorithm
can not work properly if the torque error or flux error is zero. Zero error state is not a
steady state under the basic DTC. Therefore, if we can reduce the steady state error to
zero, the steady state performance should be improved.
Figure2.#: Typical DTC system diagram
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Second problem for DTC is the changing switching frequency. Although Isao
Takahashi et al proposed a dithering signal method to fix the frequency, we also noticed
that this require high speed hardware to carry out this scheme. A new DTC algorithm is
proposed to minimize the flux and torque ripple. It is based on the mathematical model
of an interior permanent magnet synchronous machine and Space Vector Modulation of
the inverter, which is used to carry out the algorithm. A Matlab/Simulink model is built
to test the algorithm. Then steady state and dynamic response are compared with basic
DTC. Results show that both the torque ripple and flux ripples are greatly reduced. The
steady state performance is better than the basic DTC, and also the switching frequency
remains fixed at a constant value
2.2 Machine equations:
In the 3-phase PWM inverter in Fig.2.2, there exist only 8 voltage space vectors,
which are defined as V0-V7.
We will use space vectors defined as:
Vs= Vd + j Vq (2.#)
Is = id + jiq (2.2)
Figure 2.2 Eight voltage space vectors of 3 phase VSI
The equations for the IPMSM would be as:
(2.3)
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(2.4)
R#: stator armature resistance;
L d , L q : direct and quadrature inductance;
$: rotor speed in electrical
T: electromagnetic torque;
P: pole pairs
(2.5)
Under the condition of constant amplitude of fx, By differentiating equation
(#.4) with respect to time, the rate of change of torque can be obtained.
(2.6)
According to [4], stable torque control can be achieved if (2.7), (2.8) are satisfied
(2.7)
(2.8)
From (4), we can find that electromagnetic torque in the IPMSM is determined
by the d angle; quick dynamic response can be achieved by means of as high as possible
d and this is the basis of DTC of PMSM. In other words, the electromagnetic torque can
be controlled by means of control of rate of change of load angle. Due to , ,
we can use a controller to control the rate of change of load angle in order to control the
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electromagnetic torque. That is the basis of DTC, and it is also the basis of the new
DTC algorithm.
The control of the rate of change of load angle is often carried out by means of
switching table. By selecting the accelerating or de-accelerating voltage vectors, we can
roughly control the torque close to the reference value, if the sampling time is not too
big. In fact, under the basic DTC, the duration of each voltage vector is fixed to the
sampling time, which that means the rate of change of load angle was not precisely
controlled [3]. The rotor is running at frequent acceleration and de-acceleration, because
of the selection of accelerating vector and de-accelerating vectors. If we use space
vector modulation to control the rate of change of load angle in each sampling interval,
so that it agrees with the required torque, the torque ripple should be minimized. That is
the point of the modified DTC.
2.3. Flux and Torque Control By Means Of Space Vector Modulation
Due to the structure of the inverter, the DC bus voltage is fixed, therefore the
speed of voltage space vectors are not controllable, but we can adjust the speed by mean
of inserting zero voltage vectors to control the electromagnetic torque generated by the
PMSM. The selection rule of vectors is also changed; it is not based on the region of
flux linkage, but on the error vector, i.e. the error of the expected flux linkage vector
and the estimated flux linkage vector. For example, if the error flux linkage vector V eis between the vectors of V4 and V6, V4 and V6 are selected to adjust the error vector,
such that the error vector is fully compensated. T# , T 2 and T0 are calculated
according to the amplitude and phase angle of the error vector. This is indicated in Fig.
2.3.
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Figure2.3: Selection of voltage vectors according to error vector of flux linkage
with SVM
In the triangle formed by Ve,T#V4 and T2V6, we can get following equations:
(2.9)
(2.#0)
(2.##)
(2.#2)
Here, as in the equations above, T is the sampling interval of the system.
According to these equations, we can determine the duration time of all the vectors used
in this algorithm. Fig.2.4 is the system diagram of the proposed DTC system.
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Figure 2.4 Proposed DTC system
In this proposed system, flux and torque estimators are also used to determine
the actual value of the flux linkage and torque. Instead of the switching table and
hysteresis controllers, a PI controller and numeric calculation are used to determine the
duration time of voltage vectors, such that the error vector in flux plane can be fully
compensated.
CHAPTER 3
3. DIRECT TORQUE CONTROL PRINCIPLES AND GENERALITIES
3.#PMSM Motor Controllers:
3.#.#Voltage / Frequency:
There are many different ways to drive PMSM motor. The main difference
between them are the motors performance and the viability and cost in its real
implementation.
Despite the fact that voltage-frequency (v/f) is the simplest controller, it is the
most wide spread, being in the majority of the industrial applications. It is known as
scalar control and acts by imposing a constant relation between voltage and frequency.
The structure is very simple and it is normally used without speed feedback. However,
this controller doesnt achieve a good accuracy in both speed and torque responses,
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mainly due to the fact that the stator flux and the torque are not directly controlled.
Even though, as long as the parameters are identified, the accuracy in the speed can be
2% (except in a very low speed), and the dynamic response can be approximately
around 50ms.
3.#.2 Vector controllers:
In these types of controller there are control loops for controlling both the torque
and the flux. The most widespread controllers of this type are the once that use vector
transform such as either park or ku. Its accuracy can reach values such as 0.5%
regarding the speed and 2% regarding the torque, even when at standstill. The main
disadvantages are the huge computational capability required and the compulsory good
identification of the motor parameters.
3.#.3 Field acceleration method:
This method is based on maintaining the amplitude and the phase of the stator
current, while avoiding electromagnetic transients. Therefore, the equations used can be
simplified saving the vector transformation, which occurs in vectors controllers. This
technique has achieved some computational reduction, thus overcoming the main
problem with vector controllers and allowing this method to become an important
alternative to vector controllers.
3.#.4 Direct Torque Control:
In Direct Torque Control it is possible to control directly the stator flux and the
torque by selecting the appropriate inverter state.
Its main features are as follows:
Direct control of flux and torque. Indirect control of stator currents and voltages.
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Approximately sinusoidal stator fluxes and stator currents. High dynamic performance even at standstill.
This method presents the following advantages:
Absences of co-ordinate transform. Absence of voltage modular block, as well as other controllers such as PID for
motor flux and torque.
Minimal torque response time, even better that the vector controllers.
Although some disadvantages are present:
Possible problems during starting. Requirement of torque and flux estimator, implying the consequent parameters
identification.
Inherent torque and stator flux ripples.
3.2 Principles of Direct Torque Control
3.2.#Introduction:
As it has been introduced in the torque expression, the electromagnetic torque in
the three-phase PMSM motor can be expressed as follows:
(3.#)
Where is the stator flux, i is the stator current (both fixed to the stationary
reference frame fixed to the stator) and P the number of pairs of poles. The previous
equation can be modified and expressed as follows:
(3.2)
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Where Pi is the stator flux angle and i is the stator current one, both referred to the
horizontal axis of the stationary frame fixed to the stator.
(3.3)
If the stator flux modules are kept constant and the angle Ps is changed quickly,
then the electromagnetic torque is directly controlled. The same conclusion can be
obtained using another expression for the electromagnetic torque.
Because of the rotor time constant is larger than the stator one, the rotor
flux changes slowly compared to the stator flux; infact the rotor flux can be assumed
constant. As long as the stator flux modules is kept constant, then the electromagnetic
torque can be rapidly changed and controlled by means of changing the angle.
3.2.2 DTC Controllers:
The way to impose the required stator flux is by means of choosing the most
suitable voltage inverter state. If the ohmic drops are neglected for simplicity, then the
stator voltage impresses directly the stator flux in accordance with the following
equation:
(3.4)
Decoupled control of the stator flux modules and torque is achieved by acting on
the radial and tangential components respectively of the stator flux linkage space vector
in its locus. These two components are directly proportional (Rs = 0) to the components
of the some voltage space vector in the same directions.
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Fig#.5 shows the possible dynamic locus of the stator flux, and its different
variation depending on the VSI states chosen. The possible global locus is divided in to
six different sectors by the discontinuous line
In accordance with the figure, the general table-#, can be written. It can
be seen from table-# that the states Vk and Vk+3, are not considered in the torque
because they can both increase or decrease the torque at the same sector depending on
the stator flux position.
Figure 3.# Stator flux vector locus and different possible switching voltage
vectors.
FD: flux decrease.FI: Flux increase .TD: Torque Decrease, TI: torque increase
The usage of these states for controlling the torque is considered one of the aims
to develop in the present thesis, dividing the total locus into twelve sectors instead of
just six.
Table 3.#: Selection Table for Director control being k the sector number
VOLTAGE VECTOR INCREASE DECREASE
Stator flux Vk,Vk+#,Vk-# Vk+2,Vk-2,Vk+3
Torque Vk+#,Vk+2 Vk-#,Vk-2
Formatted:Justified, Indent:
line: 0"
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Finally, the DTC classical look up table is as follows:
Table 3.2: Look up table
The sectors of the stator flux space vector are denoted from S# to S6. Stator flux
modulus error after the hysteresis block can take just two values. Torque error after the
hysteresis block can take three different values. The zero voltage vectors Vo and V7 are
selected when the torque error is with in the given hysteresis limits, and must remain
unchanged.
3.3 DTC Schematic
In figure#.6 shown is a possible schematic of Direct Torque Control. As it can
be seen, there are two different loops corresponding to the magnitudes of the stator flux
and torque. The reference values for the flux stator modulus and the torque are
compared with the actual values, and the resulting error values are fed in to the two-
level and three-level hysteresis blocks, together with the position of the stator flux are
used as inputs of the look-up table-2. The position of the stator flux is divided into six
different sectors. In accordance with the below figure 3.2. The stator flux modulus and
torque errors tend to be restricted within its respective hysteresis bands. It can be proved
that the flux hysteresis band affects basically to the stator current distortion in terms of
low order harmonics and the torque hysteresis bank effects the switching frequency.
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The DTC requires the flux and torque estimations, which can be performed as it
is proposed in the below fig3.2. By means of two different phase currents and the state
of the inverter.
invertor
Figure3.2 Typical DTC System Diagram
However, flux and torque estimations can be performed using other magnitudes
such as two stator currents and the mechanical speed, or two stator currents again and
the shaft position.
3.4 Stator flux and torque estimator using Wm, ISA and ISB magnitudes.
This estimator does not require co-ordinate transform. It is used the motor model
fixed to the stationary reference frame fixed to the stator.
Firstly, all three-phase currents must be converted in to its D and Q components.
By means of the parks transformation defined in previous equations, it can be said:isD = c.#.5.isA
isQ = c.%3/2.(2.isB+isA)
If rotor current is isolated
(3.5)
And if this expression is re-arranged:
(3.6)
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Expanding the previous equation into its D and Q components is obtained:
(3.7)
And taking in to account that this expression will be evaluated in a computer it should
be expressed in Z operator instead of p one. Therefore doing the z transform of above 2
equations, the following equations are obtained:
(3.8)
And in time variable:
(3.9)
Finally, the stator flux can be obtained as follows:
(3.#0)
Torque is obtained by using these stator fluxes:
(3.##)
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3.5 Stator flux and torque estimator using Vdc , isa and isb magnitudes.
In case that sensor-less direct torque control is desired, neither rotor speed nor
rotor position are available. In order to obtain an estimation of the stator flux space
vector, two possible methods may be applied:
An estimation that does not require speed or position signals may be used. The motor speed may be estimated and fed into a flux estimator.
Stator flux and torque estimation based on the stator voltage equation does not
require speed or position information when stationary co-ordinates are applied. Thus,
from the VSI state and having the instantaneous value of the Vdc, it can be deducted the
voltages in each phase. Once the voltage and the current values are calculated and
measured respectively, they are transformed in D and Q components by means of park
transformations.
Finally the equation from the space phasor voltage equations in the stationary
reference frame fixed to the stator:
(3.#2)
And expressing this equation in z operator by means of the z transform:
(3.#3)
Expressing the previous equation in time and in its D and Q components:
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(3.#4)
The actual value of torque is evaluated from the Direct and Quadrature axis of
the stator flux and stator current.
(3.#5)
It may by deduct that the stator voltage space vector components are derived
from the inverter internal switch settings. This fact avoids the measurement of the stator
voltage pulses. In practice, the D.C. link voltage is measured, thus D and Q components
of the stator voltage space phasor can be derived. It should be noted that co-ordinate
transform is not required, however the accuracy of the estimation is limited due to the
open loop integration that can lead to large flux estimation errors.
CHAPTER 4
4. IMPLEMENTATION OF DIRECT TORQUE CONTROL
4.#. DTC Architecture
DTC algorithm is implemented in an architecture composed by five main
blocks:
Adaptive motor model Optimum pulse selector Torque comparator and flux comparator Torque and flux reference controllers Speed controller
The schematic diagram of Direct Torque Control is as shown in the fig3.2, the
individual blocks are explained below,
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4.2 Voltage and current measurements:
In normal operation, two motor phase currents and the DC bus voltage are
simply measured, together with the inverters switch positions.
4.3. Adaptive Motor Model:
It can be seen that the adaptive motor model is responsible for generating four
internal feedback signals:
Actual flux (stator); Actual torque; Actual speed; Actual frequency.
The first two values, which are critical to proper direct torque control operation,are calculated every 25ms. The latter two values, which are used by outer loop
controllers, are calculated once per millisecond.
Dynamic inputs to the adaptive motor model include:
Motor current from two stator phases; DC link voltage; Powers switch positions.
Static motor data is also utilized in making calcuations.#) User input data and 2)
information determined automatically from a motor identification run that occurs during
commissioning. The user input data include motor nominal voltage, motor nominal
current, motor nominal frequency, motor nominal speed, and motor nominal power. The
data collected during the motor identification run include motor inductances, stator
resistance, and stator saturation effects. The exact mathematical details of how the
adaptive motor calculated its outputs are shown.
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The measured information from the motor is fed to the Adaptive Motor Model.
The sophistication of this Motor Model allows precise data about the motor to be
calculated. Before operating the DTC drive, The Motor Model is fed information about
the motor, which is collected during a motor identification run. This is called auto-
tuning and data such as stator resistance, mutual inductance and saturation coefficients
are determined along with the motors inertia. The identification of motor model
parameters can be done without rotating the motor shaft. This makes it easy to apply
DTC technology also in the retrofits. The extremely fine-tuning of motor model is
achieved when the identification run also includes running the motor shaft for some
seconds. There is no need to feed back any shaft speed or position with tachometers or
encoders if the static speed accuracy requirement is over 0.5%, as it is for most
industrial applications. This is a significant advance over all other AC drive technology.
The Motor Model is, in fact key to DTCs unrivalled low speed performance. The
Motor Model outputs control signals, which directly represent actual motor torque and
actual stator flux. Also shaft speed is calculated within the Motor Model.
4.3.#. Estimating the Actual flux:
The actual value of the stator flux space vector is evaluated from the stator voltage
equation
(4.#)
(4.2)
Direct and Quadrature axis of stator fluxes can be expressed as follows:
(4.3)
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4.3.2. Estimating the Actual Torque:
The actual value of torque is evaluated from the Direct and Quadrature axis of
the stator flux and stator current.
(4.#4
4.4. Torque Comparator and Flux Comparator:
The torque comparator and the flux comparator are both contained in the
hysteresis control block. These function to compare the torque reference with actual
torque and the flux reference with actual flux. The adaptive motor model calculates
actual levels. When actual torque drops below its differential hysteresis limit, the torque
status output goes high. Likewise, when actual torque rises above its differential
hysteresis limit, the torque status output goes low. Similarly, when actual flux drops
below its differential hyteresis limit, the flux status output goes high, and when actual
flux rises above its differential hysteresis limit, the flux status output goes low. The
upper and lower differential limit, the flux status output goes low. The upper and lower
differential limit switching points for both torque and flux are determined by the
hysteresis window input. This input is used to vary the differential hysteresis limit
windows, such that the switching frequencies of the power output devices are
maintained within the range of #.5-3.5kHz.
The information to control power switches is produced in the Torque and Flux
Comparator. Both actual torque and actual flux are fed to the comparators where they
are compared, every 25 microseconds, to a torque and flux reference value. Torque and
flux status signals are calculated using a two level hysteresis control method. These
signals are then fed to the Optimum Pulse Selector.
4.5 Optimum Pulse Selector:
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The optimum pulse selector is the latest 40MHz digital signal processor (DSP)
together with ASIC hardware to determine the switching logic of the inverter.
Furthermore, all control signals are transmitted via optimal links for high speed data
transmission. This configuration brings immense processing speed such that every 25
microseconds the inverters semiconductor switching devices are supplied with an
optimum pulse for reaching, or maintaining, an accurate motor torque. The correct
switch combination is determined every control cycle. There is no predetermined
switching pattern DTC has been referred to as just-in-time switching, because, unlike
traditional PWM drives where up to 30% of all switch changes are unnecessary, with
DTC each and every switching is needed and used. This high speed of switching is
fundamental to the success of DTC. The main motor control parameters are updated
40,000 times a second. This allows extremely rapid response on the shaft and is
necessary so that the motor Model can update this information. It is this processing
speed that brings the high performance figures including static speed control accuracy,
without encoder, of +0.5% and the torque response of less than 2ms.
Processing of the torque status output and the flux status output is handled by
the optimal switching logic contained in the ASIC block. The function of the optimal
switching logic is to select the appropriate stator voltage vector that will satisfy both the
torque status output and the flux status output. In reality, there are only six voltage
vectors and two zero voltage vectors that a voltage-source inverter can produce.
The analysis performed by the optimal switching logic is based on the
mathematical spatial vector relationships of stator flux, rotor flux, stator, current, and
stator vector. These relationships are shown as a vector diagram. The torque developed
by the motor is proportional to the cross product of the stator flux is normally kept as
constant as possible, and torque is controlled by varying the angle between the stator
flux vector and the rotor flux vector. This method is feasible because the rotor time
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constant is much larger than the stator time constant. Thus, rotor flux is relatively stable
and changes quite slowly, compared to stator flux.
When an increase in torque is required, the optimal switching logic selects a
stator voltage vector that develops a tangential pull on the stator flux vector, tending to
motor current from #) two stator phases; 2) Link voltage; and 3) Power switch
positions. Static motor data is also utilized in rotate it counterclockwise with respect to
the rotor flux vector. The enlarged angle created effectively increases the torque
produced. When a decrease in torque is required, the optimal switching logic selects a
zero voltage vector, which allows both stator flux and produced torque to decay
naturally. If stator flux decays below its normal lower limit the flux status output will
again request an increase in stator flux. If the torque status output is still low, a new
stator voltage vector is selected that tends to increase stator flux while simultaneously
reducing the angle between the stator and rotor flux vectors.
Note that the combination of the hystersis control block (torque and flux
comparators) and the ASIC control block(optimal switching logic) eliminate the need
for a traditional PWM modulator. This provides two benefits. First, small signal delays
associated with the modulator are eliminated; and second, the discrete constant carrier
frequencies used by the modulator are no longer present.
4.6. Torque and Flux Reference Controller:
With in the Torque Reference Controller, the speed control output is limited by
the torque limits and DC bus voltage. It also includes speed control for cases when an
external torque signal is used. The internal torque reference from this block is fed to the
Torque Comparator.
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Flux Reference Controller
An absolute value of stator flux can be given from the Flux Reference Controller
to the Flux Comparator block. The ability to control and modify this absolute value
provides an easy way to realize many inverter functions such as Flux Optimizations and
Flux Braking.
Flux Braking
It is common to inject dc into one or more stator windings to provide braking of
an ac drive. This is effective, but is accompanied by a required delay, to allow the flux
to decay both before the dc can be applied and afterwards, before normal a.c can be
reapplied. Direct torque control uses a different method to achieve similar results. The
stator is overexcited in a controlled manner, to allow the breaking energy to dissipate in
the stator as losses. Since direct torque control directly controls stator flux, this is a
straightforward approach.
In addition, because the flux continues to be applied at the appropriate excitation
frequency, there is no delay required to either initiate this method or to reinitiate the
normal powering mode. Thus, this method of braking can be used dynamically to slow
the motor between any two normal operating points with immediate transfer back to
normal powering mode. it should be noted, however, that this method is primarily
useful at lower speeds, since the necessary voltage is not available to appreciable
overexcite the stator at higher frequencies.
Flux Optimization a lightly loaded motor does need full stator flux to produce
the required torque. Direct torque control takes advantage of this by selecting an
optimal magnetizing level based on load. When full torque is required, full stator flux is
requested. At reduced load levels, a reduced level of stator flux is developed. An
unloaded motor may run with as little as 50% of its nominal magnetizing current.
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Dependent on the application, this may lead to significant reductions in motor heating
and improvements in overall efficiency.
4.7 Speed Controller
The Speed controller block consists both of a PID controller and an acceleration
compensator. The external speed reference signal is compared to the actual speed
produced in the Motor Model. The error signal is then fed to both the PID controller and
the acceleration compensator. The output is the sum of outputs from both of them.
CHAPTER 5
5.#NEURAL NETWORKS
5.#RESEARCH HISTORY
McCulloch & Pitts (McCulloch, #943) [2] are generally recognized as being the
designers of the first neural network. They recognized that combining many simple
processing units together could lead to an overall increase in computational power.
Many of the ideas they suggested are still in use today. For example, the idea that a
neuron has a threshold level and once that level is reached the neuron fires is still the
fundamental way in which artificial neural networks operate.
The McCulloch and Pitts network had a fixed set of weights and it was Hebb
(Hebb, #949) who developed the first learning rule. His premise was that if two neurons
were active at the same time then the strength between them should be increased.
In the fifties and throughout the sixties many researchers worked on the
perceptron (Block, #962, Minsky & Papert, #988 (originally published in #969) and
Rosenblatt,#958,#959and#962).This neural network model can be proved to converge
to the correct weights, if there are weights that will solve the problem. The learning
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algorithm (i.e. weight adjustment) used in the perceptron is more powerful than the
learning rules used by Hebb.
Due to Minsky and Papert's proof that the perceptron could not learn certain
type of (important) functions, research into neural networks went into declinethroughout the #970's.
It was not until the mid 80's that two people (Parker, #985) and (LeCun, #986)
independently discovered a learning algorithm for multi-layer networks called
backpropogation that could solve problems that were not linearly separable. In fact, the
process had been discovered in (Werbos, #974) and was similar to another algorithm
presented by (Bryson & Ho, #969) but it took until the mid eighties to make the link to
neural networks.
5.2 THE BRAIN AS AN INFORMATION PROCESSING SYSTEM
The human brain contains about #0 billion nerve cells, or neurons[#6]. On
average, each neuron is connected to other neurons through about #0 000 synapses.
(The actual figures vary greatly, depending on the local neuroanatomy.) The brain's
network of neurons forms a massively parallel information processing system. This
contrasts with conventional computers, in which a single processor executes a single
series of instructions.
Against this, consider the time taken for each elementary operation: neurons
typically operate at a maximum rate of about #00 Hz, while a conventional CPU carries
out several hundred million machine level operations per second. Despite of being built
with very slow hardware, the brain has quite remarkable capabilities:
its performance tends to degrade gracefully under partial damage. In contrast,most programs and engineered systems are brittle: if you remove some arbitrary
parts, very likely the whole will cease to function.
it can learn (reorganize itself) from experience.
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this means that partial recovery from damage is possible if healthy units canlearn to take over the functions previously carried out by the damaged areas.
it performs massively parallel computations extremely efficiently. For example,complex visual perception occurs within less than #00 ms, that is, #0 processing
steps!
it supports our intelligence and self-awareness. (Nobody knows yet how thisoccurs.)
As a discipline of Artificial Intelligence, Neural Networks attempt to bring
computers a little closer to the brain's capabilities by imitating certain aspects of
information processing in the brain, in a highly simplified way.
5.3 NEURONS AND SYNAPSES
The basic computational unit in the nervous system is the nerve cell, or neuron. A
neuron has:
Dendrites (inputs) Cell body Axon (output)A simplified view of a neuron is shown in the figure 5.#below.
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Figure5.#: Biological Neuron.
A neuron receives input from other neurons (typically many thousands). Inputs
sum (approximately). Once input exceeds a critical level, the neuron discharges a spike
- an electrical pulse that travels from the body, down the axon, to the next neuron(s) (or
other receptors). This spiking event is also called depolarization, and is followed by a
refractory period, during which the neuron is unable to fire.
The axon endings (Output Zone) almost touch the dendrites or cell body of the
next neuron. Transmission of an electrical signal from one neuron to the next is effected
by neurotransmitters, chemicals which are released from the first neuron and which
bind to receptors in the second. This link is called a synapse. The extent to which the
signal from one neuron is passed on to the next depends on many factors, e.g. the
amount of neurotransmitter available, the number and arrangement of receptors, amount
of neurotransmitter reabsorbed, etc.
5.4 SYNAPTIC LEARNING
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Brains learn. Of course. From what we know of neuronal structures, one way
brains learn is by altering the strengths of connections between neurons, and by adding
or deleting connections between neurons[#6]. Furthermore, they learn "on-line", based
on experience, and typically without the benefit of a benevolent teacher. The following
figure 5.2 illustrates it.
Figure 5.2 Synaptic Learning.
The efficacy of a synapse can change as a result of experience, providing
both memory and learning through long-term potentiation (An enduring (>#
hour) increase in synaptic efficacy that results from high-frequency stimulation
of an afferent (input) pathway ). One way this happens is through release of
more neurotransmitter. Many other changes may also be involved.
Hebbs Postulate:
"When an axon of cell A... excites[s] cell B and repeatedly or persistently takes part in
firing it, some growth process or metabolic change takes place in one or both cells so
that A's efficiency as one of the cells firing B is increased."
5.5 ARTIFICIAL NEURAL NETWORK MODEL
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The simplest definition of a neural network, more properly referred to as an
'artificial' neural network (ANN), is provided by the inventor of one of the first
neurocomputers, Dr. Robert Hecht-Nielsen[#5]. He defines a neural network as: "...a
computing system made up of a number of simple, highly interconnected processing
elements, which process information by their dynamic state response to external inputs.
Neural networks are models of biological neural structures. The starting point
for most neural networks is a model neuron, as in Figure 5.3. This neuron consists of
multiple inputs and a single output. Each input is modified by a weight, which
multiplies with the input value. The neuron will combine these weighted inputs and,
with reference to a threshold value and activation function, use these to determine its
output. This behavior follows closely our understanding of how real neurons work.
Figure 5.3: A Neuron Model
While there is a fair understanding of how an individual neuron works, there is
still a great deal of research and mostly conjecture regarding the way neurons organize
themselves and the mechanisms used by arrays of neurons to adapt their behavior to
external stimuli. There are a large number of experimental neural network structures
currently in use reflecting this state of continuing research.
In our case, we will only describe the structure, mathematics and behavior of
that structure known as the backpropagation network [#5]. This is the most prevalent
and generalized neural network currently in use. If the reader is interested in finding out
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more about neural networks or other networks, please refer to the material listed in the
bibliography.
To build a back propagation network, proceed in the following fashion. First,
take a number of neurons and array them to form a layer. A layer has all its inputs
connected to either a preceding layer or the inputs from the external world, but not both
within the same layer. A layer has all its outputs connected to either a succeeding layer
or the outputs to the external world, but not both within the same layer.
Next, multiple layers are then arrayed one succeeding the other so that there is
an input layer, multiple intermediate layers and finally an output layer, as in Figure 5.4.
Intermediate layers, that is those that have no inputs or outputs to the external world, are
called >hidden layers. Back propagation neural networks are usually fully connected.
This means that each neuron is connected to every output from the preceding layer or
one input from the external world if the neuron is in the f irst layer and, correspondingly,
each neuron has its output connected to every neuron in the succeeding layer.
Figure 5.4. Backpropagation Network
Generally, the input layer is considered a distributor of the signals from the
external world. Hidden layers are considered to be categorizers or feature detectors of
such signals. The output layer is considered a collector of the features detected and
producer of the response. While this view of the neural network may be helpful in
conceptualizing the functions of the layers, you should not take this model too literally
as the functions described may not be so specific or localized. The M-file program
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related to the back propagation network with training datas taken from the conventional
DTC is given in the TABLE #..
5.6 THE LEARNING PROCESS
The memorization of patterns and the subsequent response of the network can be
categorized into two general paradigms[#6]:
Associative mapping in which the network learns to produce a particularpattern on the set of input units whenever another particular pattern is
applied on the set of input units. The associative mapping can generally
be broken down into two mechanisms:
#. Auto-association an input pattern is associated with itself and thestates of input and output units coincide. This is used to provide
pattern completition, i.e. to produce a pattern whenever a portion
of it or a distorted pattern is presented. In the second case, the
network actually stores pairs of patterns building an association
between two sets of patterns.
2. Hetero-association is related to two recall mechanisms:a. Nearest-neighbour recall, where the output pattern
produced corresponds to the input pattern stored,
which is closest to the pattern presented, and
b. Interpolative recall, where the output pattern is asimilarity dependent interpolation of the patterns
stored corresponding to the pattern presented. Yet
another paradigm, which is a variant associative
mapping, is classification, i.e. when there is a fixed
set of categories into which the input patterns are to
be classified.
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Regularity detection in which units learn to respond to particularproperties of the input patterns. Whereas in associative mapping the
network stores the relationships among patterns, in regularity detection
the response of each unit has a particular 'meaning'. This type of learning
mechanism is essential for feature discovery and knowledge
representation.
Every neural network possesses knowledge which is contained in the values of
the connections weights. Modifying the knowledge stored in the network as a function
of experience implies a learning rule for changing the values of the weights.
Information is stored in the weight matrix W of a neural network. Learning is the
determination of the weights. Following the way learning is performed, we can
distinguish two major categories of neural networks:
#. Fixed networks in which the weights cannot be changed, i.e. dW/dt=0. In such
networks, the weights are fixed a priori according to the problem to solve.
2. Adaptive networks which are able to change their weights, i.e. dW/dt != 0.
All learning methods used for adaptive neural networks can be classified into two major
categories:
2. A Supervised learning which incorporates an external teacher, so that each output
unit is told what its desired response to input signals ought to be. During the learning
process global information may be required. Paradigms of supervised learning include
error-correction learning, reinforcement learning and stochastic learning.
An important issue concerning supervised learning is the problem of error convergence,
i.e. the minimizations of error between the desired and computed unit values. The aim is
to determine a set of weights which minimizes the error. One well-known method,
which is common to many learning paradigms, is the least mean square (LMS)
convergence.
2. b Unsupervised learning uses no external teacher and is based upon only local
information. It is also referred to as self-organization, in the sense that it self-organizes
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data presented to the network and detects their emergent collective properties.
Paradigms of unsupervised learning are Hebbian learning and competitive learning. We
say that a neural network learns off-line if the learning phase and the operation phase
are distinct. A neural network learns on-line if it learns and operates at the same time.
Usually, supervised learning is performed off-line, whereas unsupervised learning is
performed on-line.
5.7 TRANSFER FUNCTION
The behavior of an ANN (Artificial Neural Network) depends on both the weights
and the input-output function (transfer function) that is specified for the units[3]. This
function typically falls into one of three categories:
a. Linear (or ramp)b. Thresholdc. Sigmoid
For linear units, the output activity is proportional to the total weighted output.
f(h) = h.
For threshold units, the output is set at one of two levels (0, #), depending on whether
the total input is greater than or less than some threshold value.
For sigmoid units, the output varies continuously but not linearly as the input changes.
Sigmoid units bear a greater resemblance to real neurons than to linear or threshold
units, but all three must be considered rough approximations.
The following figure 5.5 illustrates the three different transfer function
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Figure 5.6 Three different transfer functions
5.8 THE UPS AND DOWNS OF NEURAL NETWORK
There are many good points to neural-networks and advances in this field will
increase their popularity[#9]. They are excellent as pattern classifiers/recognizors - and
can be used where traditional techniques do not work. Neural-networks can handle
exceptions and abnormal input data, very important for systems that handle a wide
range of data (radar and sonar systems, for example). Many neural networks are
biologically plausible, which means they may provide clues as to how the brain works
as they progress. Advances in neuroscience will also help advance neural networks to
the point where they will be able to classify objects with the accuracy of a human at the
speed of a computer! The future is bright, the present however...
Yes, there are quite a few down points to neural networks. Most of them,
though, lie with our lack of hardware. The power of neural-networks lie in their ability
to process information in a parallel fashion (that is, process multiple chunks of data
simultaneously). Unfortunately, machines today are serial - they only execute one
instruction at a time. Therefore, modeling parallel processing on serial machines can be
a very time-consuming process. As with everything in this day and age, time is of the
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essence, which often leaves neural networks out of the list of viable solutions to a
problem.
Other problems with neural networks are the lack of defining rules to help
construct a network given a problem - there are many factors to take into consideration:
the learning algorithm, architecture, number of neurons per layer, number of layers, data
representation and much more. Again, with time being so important, companies cannot
afford to invest to time to develop a network to solve the problem efficiently. This will
all change as neural networking advances.
CHAPTER 6
6.#. SIMULATION RESULTS
Matlab and Simulink were used to perform simulations on a number of control schemes.
The schemes were Field oriented control, Direct Torque Control, Direct Torque Control
using vector modulation.
The Direct Torque Control method and the space vector modulation method haven been
simulated using Matlab and Simulink..
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Figure6.#.Matlab/Simulink model of the proposed DTC PMSM drive system
Pure integrators are used for d and q-axis flux linkage estimation.The simulation
confirmed that the dynamic torque of PMSM is dependent on the instantaneous load
angle between the rotating flux and rotor.If we make the change of rate of load angle
less ripple.
The sampling time is set at 500us.The harmonics are pushed to higher frequency
side; the harmonic distribution of modified DTC is more concentrated near the sampling
frequency.
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The simulation results are
shown:
Figure 6.2 The dynamic performance of the modified DTC
The training datas are given below:
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TORQUE FLUX STATOR ANGLE SWITCHING STATES
0.0 0.9 0.90 0 #0 0 0
#.0 0.9 #.0 0 0 #0 #0
0.9 0.# 0.9 0 0 #0 ##
0.0 0.0 0.0 0 0 ###0
0.5 0.0 0.9 0 0 ####
0.5 0.5 0.0 0 ##0 0 0
0.0 0.# 0.0 0 ##0 0 #
0.# 0.0 0.# 0 ##0 #0
0.9 0.# 0.2 0 ###0 0
0.5 0.8 0.4 0 ####0
0.6 0.7 0.0 #0 0 0 0 #
0.6 0.# 0.6 # 0 0 0##
0.7 0.8 0.7 #0 0 #0 #
0.# 0.7 0.7 #0 #0 #0
0.# 0.0 0.8 #0 #0 ##
0.# 0.7 0.8 #0 ####
0.7 0.8 0.8 ##0 0 0 #
0.4 0.# 0.3 ##0 0 #0
0.8 0.7 0.8 ##0 #0 #
TABLE 6.#: Simulation results
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CHAPTER 7
CONCLUSION
The modeling and experimental results confirm that both torque and flux
linkage ripples are greatly reduced, while the switching frequency of the Direct Torque
Control is almost fixed for different load torque and speed. The advantage of the DTC is
it can work with low sampling frequency (2kHz in simulation). Another further
advantage is its simple control structure, it only needs one PI controller for torque, and
flux control is done without a PI controller. This can also reduce the requirement of the
real-time software. And this should enable this Direct torque control to have a wider
application area, because of lower requirement of the hardware and better performance
it will give.
As a result, both torque and flux linkage ripples are greatly reduced, and the
switching frequency is kept fixed. It does not need any rotor parameters, therefore it still
Retains less parameter dependence, which is the main advantage of DTC. However, it
needs a speed signal in the torque control loop.
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8. PARAMETERS OF THE INTERIOR PERMANENT MAGNET SYNCHRONOUS
MACHINE USED IN SIMULATION
Rated output power(Watt) 300W
Rated phase voltage(Volt) 240
Magnetic flux linkage (Wb.) 0.447
Poles 4
Rated torque(Nm) #.95
Base speed(rpm) #500
Crossover speed(rpm) 2400
Stator resistance (ohm) #8.6
q-axis inductance (mH) 388.5
d-axis inductance (mH) 475.5
Inertia (Kg.m) 0.00#5
Table 8.#: Parameters of the Interior Permanent Magnet Synchronous Machine
Used In Simulation
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APPENDIX
function [sys,x0,str,ts] = bpn(t,x,u,flag)
switch flag,
%%%%%%%%%%%%%%%%%%
% Initialization %
%%%%%%%%%%%%%%%%%%
case 0,
[sys,x0,str,ts]=mdlInitializeSizes;
%%%%%%%%%%%
% Outputs %
%%%%%%%%%%%
case 3,
sys=mdlOutputs(t,x,u);
%
case {#,2,4,9},
sys=[];
%%%%%%%%%%%%%%%%%%%%
% Unexpected flags %
%%%%%%%%%%%%%%%%%%%%
otherwise
error(['Unhandled flag = ',num2str(flag)]);end
% end sfuntmpl
%
%=============================================================
================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
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%=============================================================
================
%
function [sys,x0,str,ts]=mdlInitializeSizes
%
% call simsizes for a sizes structure, fill it in and convert it to a
% sizes array.
%
% Note that in this example, the values are hard coded. This is not a
% recommended practice as the characteristics of the block are typically
% defined by the S-function parameters.
%
sizes = simsizes;
sizes.NumContStates = 0;
sizes.NumDiscStates = 0;
sizes.NumOutputs = 6;
sizes.NumInputs = 3;
sizes.DirFeedthrough = #;
sizes.NumSampleTimes = #; % at least one sample time is needed
sys = simsizes(sizes);
%
% initialize the initial conditions%
x0 = [];
%
% str is always an empty matrix
%
str = [];
%
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% initialize the array of sample times
%
ts = [0 0];
% end mdlInitializeSizes
%
%=============================================================
================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================
================
%
function sys=mdlDerivatives(t,x,u)
sys = [];
% end mdlDerivatives
%
%=============================================================
================
% mdlUpdate
% Handle discrete state updates, sample time hits, and major time step
% requirements.
%=============================================================
================
%
function sys=mdlUpdate(t,x,u)
sys = [];
% end mdlUpdate
%
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l
%=============================================================
================
% mdlOutputs
% Return the block outputs.
%=============================================================
================
%
function sys=mdlOutputs(t,x,u)
%training
% input =same
%output = + 2 is added
%Testing
% subtract the outputs from 2
clc
%clear
%load rr.mat;
clear all
%t=0.0#:.0#:#;
%y#=sin(#00*t);
%y2=cos(200*t);
%y3=y#+y2;%mixing simple adding
%y3=[0.#0.#0.#% 0.#0.#0.9
% 0.#0.9 0.#
% 0.#0.9 0.9
%];
inp=[0.0 0.9 0.9
#.0 0.9 #.0
0.9 0.#0.9
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0.0 0.0 0.0
0.0 0.0 0.0
0.5 0.5 0.0
0.5 0.5 0.0
0.0 0.#0.0];
temp#=inp;
inpatt=(temp#);
% ij=.0#;
% for i=#:9#
% xorout(i)=ij;
% ij=ij+.0#;
% end
% xorout=xorout';
%outpatt=((horzcat(y#',y2')+2)/#00);
%
%//////////////////
%outpatt=[0.#0.#
% 0.9 0.3
% 0.9 0.5
% 0.#0.7
%];hl=3;%input('Number of nodes in hidden layer=');
desi=[0 0 #0 0 0
0 0 #0 #0
0 0 #0 ##
0 0 ###0
0 0 ####
0 ##0 0 0
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0 ##0 0 #
0 ##0 #0];
temp2=desi;
insize=size(inpatt);
nv=insize(#,2);
Actout=temp2;
outsize=size(Actout);
np=outsize(#,#);
nt=outsize(#,2);
%pause
ol=nt;
il=nv;
%assign weights between input layer and hidden
ijj=#;
for i=#:il%45
% i
for j=#:hl%46
wih(i,j)=rand;%ra3(ijj);
ijj=ijj+#;
end%46
end%45wih=wih(#:il,#:hl);
ij=#;
for i=#:hl%47
for j=#:ol%48
hou(i,j)=rand;%ra3(ij);
ij=ij+#;
end%48
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end%47
hou=hou(#:hl,#:ol);
eta=#;
%MSE=input('Desired Mean squared error');
MSE=0.35;
for ty=#:#00000%outer loop
erp=0;
for we=#:np %to form a cycle
for yty=#:nv
a#(yty)=inpatt(we,yty);
end
for yty=#:nt
tar(yty)=Actout(we,yty);
end
%BPABPABPABPABPABPABPABPA
%transpose a
%forward operation
%linear summation to nodes in hidden layer
a2=a#*wih;%inputs to nodes in the hidden layer
for y=#:hl %##
a2(y)= #/(#+exp(-a2(y)) );%outputs from nodes in the hidden layer
end %##%inputs to nodes in the output layer
a3=a2*hou;
%outputs from nodes in the output layer
for y=#:ol%#2
a3(y)=#/(#+exp(-a3(y)));
end%#2
%Error of pattern calculation
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sum=0;
for k=#:ol%#3
t=tar(k)-a3(k);
sum=sum+(t*t)/2;
end%#3
%error of pattern
erp=erp+sum;
% disp('erp')
%reverse operation
%Calculation of delta in the output layer
for k=#:ol%#4
t=tar(k)-a3(k);
t#=#-a3(k);
deloutput(k)=a3(k)*t#*t;
end%#4
%updating weights between output layer and hidden layer
for k=#:hl%#6
for kk=#:ol%#5
hou(k,kk)=hou(k,kk)+eta*deloutput(kk)*a2(k);
end%#5
end%#6
%calculation of summation for the nodes in the hidden layer
summa=deloutput*hou';
%Calculation of delta in the hidden layer
for k=#:hl%#7
t#=#-a2(k);
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lv
delhidden(k)=a2(k)*t#*summa(k);
end%#7
%weight updation in the input and hidden layer
for k=#:il%#9
for kk=#:hl%#8
wih(k,kk)=wih(k,kk)+eta*delhidden(kk)*a#(k);
end%#8
end%#9
%end of reverse
% disp('MSe')
end % %to form a cycle
if mod(ty,#)==0
wihspeech=wih;
houspeech=hou;
save wih.mat wih -ascii
save hou.mat hou -ascii
ty
erp
end
%pause
if erp
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lvi
end%outer loop
disp('sdsd')
sys = desi;
% end mdlTerminate
REFERENCES
#) A direct Torque Controller for Permanent Magnet Synchronous Motor DrivesL.zhong, M.F.Rahman, W.Y.Hu, K.W. Lim, M.A.Rahman
2) I.takahashi and T.Noguchi," A New Quick-Response and High efficiencycontrol strategy of an induction motor", IEEE Transaction on Industry
Application, Vol.IA-22,no.5,pp.820-827.#986
3) C.French and P.acarnley," Direct Torque Control Ofa. Permanent magnet Drive". Proc. of IEEE Industry
b. Application society annual meeting, Vol.#, pp.#99- 206, Florida, USA,#995.
4) R.MONEJEMY AND R.KRISHNAN, Implementation strategies forconcurrent flux weakening and torque control of synchronous motor, Proc. of
IEEE Industry application society annual meeting vol.#,pp. 238-245,USA. ,
#995.
5) M.F.Rahaman ,L.zhong and K.W.Lim A DSP Based Instanteneous Torquecontrol Startergy For Permanent Magnet Motor Drive With Speed Range and
Reduce Torque Pulsations, Proc.of the IEEE IAS Annual Meeting,pp.5#8-
524,San Diego ,California, October #996.
6) Hanselman, DC, Hung, JY and Keshura, M(#992):Torque ripple analysis inbrushless permanent magnet motor drives. Proceedings of the International
conference on Electrical machines, Manchester, UK,pp823-827.
a. Hanselman,DC (#994):Minimum torque ripple,maximumefficiency excitation of brushless permanent magnet
motorsIEEETrans,IE-4#,pp292-300