direct torque control of permanent magnet

8/13/2019 Direct Torque Control of Permanent Magnet

1/56

i

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


2/56

ii

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:


3/56

iii

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


4/56

iv

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


5/56

v

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


6/56

vi

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


7/56

vii

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.


8/56


9/56

ix

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


10/56

x

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)


11/56

xi

(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


12/56

xii

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.


13/56

xiii

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.


14/56

xiv

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,


15/56

xv

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.


16/56

xvi

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)


17/56

xvii

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.


18/56

xviii

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"


19/56

xix

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.


20/56

xx

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)


21/56

xxi

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.##)


22/56

xxii

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:


23/56

xxiii

(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,


24/56

xxiv

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.


25/56

xxv

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)


26/56

xxvi

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:


27/56

xxvii

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


28/56

xxviii

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.


29/56

xxix

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.


30/56

xxx

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


31/56

xxxi

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.


32/56

xxxii

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.


33/56

xxxiii

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


34/56

xxxiv

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


35/56

xxxv

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


36/56

xxxvi

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


37/56

xxxvii

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.


38/56

xxxviii

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


39/56

xxxix

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


40/56

xl

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


41/56

xli

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..


42/56

xlii

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.


43/56

xliii

The simulation results are

shown:

Figure 6.2 The dynamic performance of the modified DTC

The training datas are given below:


44/56

xliv

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


45/56

xlv

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.


46/56

xlvi

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


47/56

xlvii

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.


48/56

xlviii

%=============================================================

================

%

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 = [];

%


49/56

xlix

% 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

%


50/56

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


51/56

li

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


52/56

lii

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


53/56

liii

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


54/56

liv

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);


55/56

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


56/56

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

direct torque control of permanent magnet

Documents