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Torque Ripple Reduction Based
Direct Torque Control for Induction
Motor Drives
A Thesis
Submitted to the College of Engineering University of Baghdad in
Partial Fulfillment of the Requirements for the Degree of Master ofScience in Electrical Engineering
By
Hayder S. Hameed
Supervised by Prof. Dr. J.H. Alwash Dr. Hanan M. Habbi
March 2014
REPUBLIC OF IRAQ
MINISTRY OF HIGHER EDUCATION AND SCIENTIFIC RESEARCH
UNIVERSITY OF BAGHDAD
COLLEGE OF ENGINEERING
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i
cknowledgement
First of all, I give my thanks forever to Allah Who Have Enabled me to
complete this work
I would like to express my sincere gratitude to my supervisors
Prof Dr J H Alwash and Dr Hanan M Habbi for their great help,
kind advice, guidance and encouragement during their supervision for this work.
I would like to thank my family who has given me support throughout my
academic years. Without them, I might not be the person I am today.
A special thanks to my wife for her kindness and support and without here
heartening I couldn’t finish this work.
Also, I would like to thank the staff of the department of Electrical
Engineering of University of Baghdad for their assistance and support.
Finally ,I would like to acknowledge all kind people who help me to complete
this work .
ayder Salim
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ii
ABSTRACT
Direct Torque Control (DTC) is a control technique used in AC drive systems
to obtain high performance torque control. The conventional DTC drive contains a
pair of hysteresis comparators, a flux and torque estimator and a voltage vectorselection table. The torque and flux are controlled simultaneously by applying
suitable voltage vectors, and by limiting these quantities within their hysteresis
bands, de-coupled control of torque and flux can be achieved. Conventional DTC
drives utilizing hysteresis comparators suffer from high torque ripple and variable
switching frequency.
Several techniques have been developed to improve the torque performance.
In this thesis, Proportional-Integral (PI) controller has been presented to improve
the system performance which gives better torque and flux response and also
reduces the undesirable torque ripple. The most common solution to high torque
ripple and variable switching frequency is to use the space vector pulse width
modulation (SV-PWM) that depends on the reference torque and flux. The
reference voltage vector is then realized by using a voltage vector modulator.
The conventional DTC and DTC with PI controller are implemented using
Xilinx System Generator (XSG) for MATLAB/Simulink environment through
Xilinx blocksets. The design was achieved in VHDL, based on a
MATLAB/Simulink simulation model.
The Hardware-in-the-Loop (HIL) method is used to verify the functionality
of the Xilinx FPGA estimator. The results are obtained and compared with
MATLAB/ Simulink results considering the implementation of the proposed model
on the Xilinx NEXYS2 Spartan 3E1200 FG320 Kit.
The simulations of the DTC-SVPWM were carried out using
MATLAB/ Simulink simulation package.
The design, implementation and simulation of the overall drive system is
performed using MATLAB/Simulink program version 7.13.0.564 (R2011ba) and
Xilinx ISE Design Suite 14.2.
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List of Contents
iii
List of Contents
UTitle Page
Acknowledgements ………………………………………………………........iAbstract ……… ……….………………...……………….….………………...ii
List of Contents ………… ………….…………….…………….…...….........iii
List of Abbreviations ………… …………………………….……….…….…..vi
List of Symbols ……… …………………………………..……………..…....vii
UChapter One: Introduction and Literature Survey
1.1
General Introduction …...………………….………………………....….…..1
1.2 Speed Control Techniques of Induction Motor …………………...…..…….2
1.3 Literature Survey …………………………………..………….……....…….7
1.4 Thesis Objective……………………………….……...…………………....12
1.5 Thesis Outline ………...……...………………….……...………………….12
UChapter Two: Direct Torque Control Technique and Xilinx System
Generator
2.1 Introduction …………………………………………………………..…....13
2.2 The Conventional DTC...… .……....………………………………………14
2.3 DTC Development …………………... …………………...…………….....16
2.3.1 Mathematical Model of Induction Motor.…….….…….………..…...16
2.3.2 Flux and Torque Estimator……...………………………………...….21
2.3.3 Torque and Flux Hysteresis Comparator ………………..……....…...23
2.3.4 Lookup Table……………………………………………………...….26
2.3.5 Three-Phase Voltage Source Inverter(VS……………………………27
2.4 Modified DTC Scheme …………………………………………………….29
2.5 Classic PI Controller………………….……..……………………………...30
2.6 Direct Torque Control With Space Vector Modulation (DTC – SVM)........31
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List of Contents
iv
2.7 Principle of Space Vector PWM …………………………………………..33
2.7.1 Step 1: Determining Vd , Vq , Vref , and Angle (α) ………..…………36
2.7.2 Step 2: Determining Time Duration T1, T2, T0 ………………….…38
2.7.3 Step 3 : Determining the Switching Time of Each
Transistor(S1toS6) ..……………………………………………………………39
2.8 Types of Different Schemes …………………………………………….…40
2.9 Field Programmable Gate Array ……………………………………….…44
2.10 Hardware in the Loop ……………………………………………………44
2.11 Usage of Xilinx System Generator in the Controller Design ……………44
2.12 System Modeling Using the Xilinx System Generator ………………..45
2.14 Integration in Xilinx Environment …………………………………….46
Chapter Three: Simulation Results of DTC and DTC-SVM
3.1 Introduction …………………………………………………….………….48
3.2 Implementation of DTC in MATLAB/Simulink …………………………48
3.2.1 Induction Motor ……………………………………………….…….49
3.3.2 Sector ,Flux and Torque estimator … ……….……....…….………..50
3.2.3 Flux and Torque Hysteresis Controller ………………………….…50
3.2.4 Lookup Table Using MATLAB/Simulink …...……....…………...…51
3.2.5 Voltage Source Inverter …………………………………………….51
3.3 Modified DTC Scheme Using MATLAB/Simulink ……………………...53
3.4 Modeling Space Vector PWM Using MATLAB/Simulink ....…………….54
3.5 Implementation DTC Using Xilinx Software ……………………………...56
3.5.1 Real Time System Modeling via Simulink…….……………..……...56
3.5.2 Xilinx Software Analysis ………….……………….…..…………....57
3.5.3 The MCode Block…………..........………………………………..…57
3.5.4 Implementation of Sector ,Flux and Torque Estimators Using
Xilinx/SIMULINK ………………………………………………………….....58
3.5.5 Flux and Torque hysteresis Controller ……………….....……..….….61
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List of Contents
v
3.5.6 Switching Table Using Xilinx Mcode Block …………………...……61
3.6 Modified DTC Scheme using Xilinx/SIMULINK ………………………...62
3.7 Hardware/Software Co-Simulation …….………………………………….63
3.8 Experiment Setup and Instrumentation…………………………………….66
3.9 Simulation Results for Conventional DTC…...….…………………………67
3.10 Simulation Results of DTC with Conventional PI Controller ……………71
3.11 Simulation Results of DTC-SVM ………………………………………..73
3.12 Simulation Results for CDTC Using Hardware/Software Co-Simulation
Xilinx Blocks …………………………………………………………………..75
3.13 Simulation Results of DTC-PI Controller Using Hardware/Software Co-
Simulation ………………………………………………………………….......77
3.14 Comparison among the Presented Controllers …………………………...79
Chapter Four: Conclusions and Suggestions for Future Works
4.1 Conclusions…………………………………………………………….......83
4.2 Suggestions for Future Work……..………………………………………..84
References ……………………………………………….………………….....85
Appendix A
Appendix B
Appendix C
Appendix D
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List of Abbreviations
vi
List of Abbreviations
DescriptionAbbreviation
Alternating CurrentAC
Configurable Logic BlockCLB
Direct CurrentDC
Digital Signal Processor DSP Direct Torque ControlDTC
Electric VehicleEV
Fuzzy LogicFL
Field Oriented ControlFOC
Field Programmable Gate Array FPGA
Hardware Description LanguageHDL
Hardware in the loopHIL
Induction MotorIM
Joint Test Action GroupJTAG
Look Up TableLUT
Magneto motive forcemmf
Metal-Oxide Semiconductor Field Effect TransistorsMOSFET
Proportional-IntegralPI
Proportional-Integral-DerivativePID
Pulse Width ModulationPWM
Sine Pulse Width ModulationSPWM
Space Vector Modulation SVM
Space Vector Pulse Width ModulationSVPWM
Total Harmonic Distortion THD
Very-high-speed Hardware Description LanguageVHDL
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List of Symbols
vii
List of Symbols
Symbol Description
d,q Rotating reference frame axes
d RsR,q Rs Stationary reference frame axes
f Frequency of AC Supply (Hz)
ia,ib,ic Stator Phase Currents (A)
iRqsR, iRdsR q and d–axis stator currents (A)
iRqr R, iRdr R q and d–axis rotor currents (A)
J Moment of Inertia (Kg.mP2P)
K R p Proportional Gain
K Ri Integral gain
LRm Mutual inductance
LRr Rotor Inductance (H)
LRs Stator Inductance (H)
m Modulation index
P Number of Poles
R Rr Rotor resistance( Ω)
Rs Stator Resistance (Ω)
s Stator variable
TR1R, TR2R, TRo Switching Time Intervals (sec)
TRe Electromechanical Torque (Nm)
TRL Load Torque (Nm)
TRs Sampling Time or Switching Time
1TVRaR,VR bR,VRc Stator Phase Voltages (V)
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List of Symbols
viii
Symbol Description
VRdc Supplied DC Voltage (V)
VRoR….VR7 Space Voltage Vectors
vRqsR, vRdsR q and d–axis stator voltages
vRqr R, vRdr q and d–axis rotor voltages
XRs Stator reactance ( Ω )
XRr Rotor reactance ( Ω )
XRm Magnetizing reactance ( Ω )
ΨRm Mutual flux (Wb)
ΨRdr d-axis Rotor Flux Linkage (Wb)
ΨRqr q-axis Rotor Flux Linkage (Wb)
ΨRds d-axis Stator Flux Linkage (Wb)
ΨRqs q-axis Stator Flux Linkage (Wb)
ΨRs Stator flux (wb)
ωe Stator angular electrical frequency (rad/sec)
ωRr Rotor angular electrical speed (rad/sec)
ωRs Synchronous Speed (rad/sec)
θ The angle of rotation
θR0 The initial angle offset
θRr Rotor angle(deg)
θRs Stator angle (deg)
θRsr Angle between the stator and rotor fluxes
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Chapter One Introduction and Literature Survey
1
Chapter One
Introduction and Literature Survey
U
1.1 General Introduction
Induction Motor (IM) drive is widely used in many residential, commercial
and high performance industry applications due to its compactness, offering many
benefits to industrial users, highest power density, high torque to inertia ratio and
dynamic control, and high efficiency over a wide speed range. There are two main
types of induction motors which are the wounded rotor and squirrel-cage design
and both of them are in widespread use. In the past, squirrel cage induction
machines were limited to constant speed applications, and were operated from a
fixed sinusoidal supply. The development of high power switching devices has
accelerated the growth in the market for variable speed drive systems incorporating
AC induction machines and variable speed drives . [1,2]
The simple control method is volt/hertz control, or scalar control. Vector or
field-oriented control (FOC) and direct torque control (DTC) are basically twomethods of electromagnetic torque controlled a.c. drives. The direct torque control
has been adopted in this thesis.
The concept of the vector control method or so called Field Orientation
method of AC motors was proposed by Hasse in 1969 and Blaschke in 1972, based
on making the well-established separately excited dc machine. Vector control
schemes have allowed the induction machine to achieve torque control performance similar to that of a separately excited DC machine and have led to the
replacement of the DC machine by the induction machine in many high
performance applications .The torque is defined as the cross vector product of the
magnetic field from the stator poles and the armature current. [1,3]
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Chapter One Introduction and Literature Survey
2
Direct Torque Control concepts were proposed by Takashi and Noguchi in
1986 [4]. The idea of this method is based on comparing the measured stator flux
and torque with the theoretically desired bands. The vector differences will control
the subsequent switching sequence of the SVPWM inverter voltage based on the
switching logic table. That, however, restricts the means of the stator flux and
torque to fall in the pre-established bands.[2]
U1.2 Speed Control Techniques of Induction Motor
There are different ways to control the speed of a rotational or linear
alternating current (AC) electric motor . The classification of the electrical drives is
depending on the application ; some of them are fixed speed and some are variable
speed. Before the invention of power electronics devices, the variable speed drives
had various limitations such as poor efficiencies, larger space, lower speed ,
etc. But now, variable speed drive are constructed in smaller size, high
efficiency and high reliability [5]. The effective way of producing variable
induction motor speed drive is to supply the induction motor with three phase
voltages of variable frequency and variable amplitude. A variable frequency is
required because the rotor speed depends on the speed of the rotating magnetic
field provided by the stator. A variable voltage is required because the motor
impedance is reduced at the low frequencies and consequently , the current has to
be limited by means of reducing the supply voltages. A variable-frequency drive
(VFD) is a specific type of adjustable-speed drive .
The control of the speed is achieved by controlling the frequency of the
electrical power supplied to the motor drives. There are three major types of
variable frequency control techniques of IM: scalar control, vector control and
field acceleration method [6,7] as shown in Figure 1.1 .
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Chapter One Introduction and Literature Survey
3
Scalar control: is known as V/f control which acts by imposing a constant
relation between voltage and frequency and it is the most widespread in the
majority of the industrial applications because it has simple structure and it is
normally used without speed feedback. The stator flux and the torque are not
directly controlled ,so this control does not achieve a good accuracy in both speed
and torque responses [8].
Vector Control: In this type of control, the control loops are used for
controlling both the torque and the flux. The controllers of this type use vector
transform such as either Park or Ku. The requirement of huge computational and
the compulsory good identification of the motor parameters are the main
disadvantages for this type of control [9] .
Field Oriented Control (FOC) was introduced for the first time by Blaschke in
the early 1970s. The main objective of this control method is, as in separately
excited DC machines, to independently control the torque and flux; this is done by
choosing a d-q rotating reference frame synchronously with the rotor flux space
vector [9,10].
Figure.1.1 : Overview of induction motor control methods.[11]
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Chapter One Introduction and Literature Survey
4
FOC is based on maintaining the amplitude and the phase of the stator current
constants, avoiding electromagnetic transients. FOC involves controlling the stator
currents represented by vectors. FOC method is based on projections which
transform a three phase time and speed dependent system into a two co-ordinate
(d and q co-ordinates) time invariant system [12].
DTC main features are as follows:
• Direct control of flux and torque by selecting the appropriate inverter state.
• Indirect control of stator currents and voltages.
• Approximately sinusoidal stator fluxes and stator currents.
• High dynamic performance even at stand still.
The main advantages of DTC are:
• Absence of co-ordinate transforms.
• Absence of voltage modulator block, as well as other controllers such as PID for
motor flux and torque.
• Minimal torque response time, even better than the vector controllers.
However, some disadvantages are also present such as:
• Possible problems during starting.
• Requirement of torque and flux estimators, implying the consequent parameters
identification.
• Inherent torque and stator flux ripple.
One of the major applications of DTC is in the Electric Vehicle (EV); electric
vehicles are an important step towards solving the environmental problems
produced by cars with internal combustion engines. Another advantage of the EV
is its devoid of pollution and high energy efficiency. Indeed, an electric motor
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Chapter One Introduction and Literature Survey
5
provides very fast response and can be controlled in a much better way. Therefore,
EV has definite advantages over the Internal Combustion Engine (ICE) driven
vehicles. The input of the IM controller is the reference speed, which is applied by
the vehicle pedal [13].
DTC control technique in its basic construction suffers from two major
problems: 1) variable switching frequency and 2) high torque ripple
The conventional DTC algorithm using the hysteresis-based voltage switching
method has relative merits of simple structure and easy implementation. Some
drawbacks such as large torque ripple in the low speed region and switching
frequency variation according to the change of the motor parameters and the motor
speed are exhibited. If the hysteresis bands of the torque and flux comparators
become relatively wide for high power applications with the low inverter switching
frequency, the resulting torque ripples are enlarged to an undesired level [14] .
In conventional DTC, the voltage vector selection is based on the torque and flux
errors, but small and large errors are not distinguished by the hysteresis controllers.
The voltage vectors are applied for the entire sample period; even for small errors,
resulting large torque overshoots in steady-state regime [15] .
In steady state with constant load, the active switching state causes the torque
to continue to increase past its reference value until the end of the switching
period. Then a zero voltage vector is applied for the next switching period causing
the torque to continue to decrease below its reference value until the end of the
switching period. That results in high torque ripple as shown in Figure 1.2 [16] .
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Chapter One Introduction and Literature Survey
6
Figure 1.2 Conventional DTC
By removing the hysteresis comparators and performing the switching at
regular intervals is a widely adopted method to reduce the torque ripple and
at the same time maintaining a constant switching frequency. Instead ofapplying a single voltage vector for the whole sampling period, two or more
voltage vectors are applied.
Figure 1.3(a) shows the torque waveforms for hysteresis based controller
with the width of the hysteresis marked as ∆T. Due to the delay in the
microprocessor implementation or sensors, the torque overshoot and
undershoot beyond and below the hysteresis bands will occur. The positiveslope is high at low speed, which will increase the possibility of the torque
touching the upper band. In Figure 1.3(b), fixed switching is employed but
with the whole sampling period applied with a single voltage vector. This
technique will result in a high torque ripple with all additional torque
oscillation [17,18] .
Figure 1.3: Various switching strategies in DTC .(a)Hystresis-based controller
,(b)Fixed switching torque.
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Chapter One Introduction and Literature Survey
7
U1.3 Literature Survey
During the last decade, many different techniques of control applied to IM
drives. The DTC technique has been recognized as an efficient alternative and
viable solution to get high performance in these drives. A lot of modifications have
been developed to conventional Direct Torque Control scheme. Therefore, a
literature survey for many previously published studies is presented as follows:
Toh, et al., 2003 [18] presented two simple controllers for the torque and flux
loops, which replaced the conventional hysteresis comparators. The controllers
work was based on waveform comparisons and hence retained the simple
control structure of the DTC. Simulations of the proposed controllers were
performed using MATLAB/SIMULINK simulation package. The results show
that the controllers managed to reduce the torque ripple significantly.
Rodriquez, et al , 2004 [19] presented a new method for Direct Torque Control
(DTC) based on load angle control . The use of simple equations to obtain the
control algorithm makes it easy to understand and implement. Fixed switching
frequency and low torque ripple are obtained using space vector modulation.
Buja, and Kazmierkowski , 2004 [11] presented a review of recently used direct
torque and flux control (DTC) techniques for voltage inverter fed induction and
permanent magnet synchronous motors. A variety of techniques and difference in
concept are described as follows: switching-table based hysteresis DTC, direct
self-control, constant switching frequency DTC with space-vector modulation
(DTC-SVM). Also, trends in the DTC-SVM techniques based on neuro-fuzzy logic
controllers are presented.
Garcia, and Arias, 2005 [20] presented a novel controller based on Direct Torque
Control (DTC) strategy. This controller is designed to be applied in the control of
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Chapter One Introduction and Literature Survey
8
Induction Motors (IM) fed with a three-level Voltage Source Inverter (VSI). This
type of inverter has several advantages over the standard two-level VSI, such as a
greater number of levels in the output voltage waveforms, lower dV/dt, less
harmonic distortion in voltage and current waveforms and lower switching
frequencies. In the new controller, torque and stator flux errors are used together
with the stator flux angular frequency to generate a reference voltage vector.
Ismail, 2005 [7] studied, evaluated and compared the various techniques of the
DTC-SVM applied to the induction machines through simulations. The simulations
were carried out using MATLAB/SIMULINK simulation package. Evaluation was
made based on the drive performance, which includes dynamic torque and flux
responses, feasibility and the complexity of the system.
Paturca, et al, 2006 [15] presented a simple solution, which consists in the
modulation of the nonzero voltage vector duration over a sampling period,
according to the instant values of the torque and stator flux errors. The introduced
duty ratio is calculated using a relation containing terms proportional to these
errors. The presented results show the torque, flux and current ripple reduction
obtained by using the proposed method. Its main advantage is that it requires an
insignificant additional computation, preserving the simplicity of the conventional
DTC.
Kostic, et al, 2009 [21] presented different direct torque and flux control of
induction motor schemes (DTC). Classical DTC method, its modifications for
torque and flux ripple reduction, as well as modified DTC method with PI
controllers (PI-DTC) based on space vector modulation (SVPWM) are considered.
For each method, theoretical principles and experimental results, at laboratory
condition using dSPACE development tool realized, are presented.
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Chapter One Introduction and Literature Survey
9
Tsoutsas, 2009 [22] An electromagnetic torque calculator of an induction motor is
designed in the MATLAB/ Simulink environment through XILINX block sets. The
accuracy of the torque estimator is verified using the Field Programmable Gate
Array (FPGA).
Kamble, and Bankar, 2010 [23] presented a Fuzzy Logic Direct Torque Control
(FLOTC) to improve the system performance which gives better torque and flux
response and also reduces the undesirable torque ripple in the conventional DTC.
Aarniovuori, 2010 [24] presented a coupled system simulator, based on analytical
circuit equations and a finite element method (FEM) model of the motor and it is
used to analyze a frequency-converter-fed industrial squirrel-cage induction motor.
Two control systems that emulate the behavior of commercial direct-torque-
controlled (DTC) and vector-controlled industrial frequency converters were
studied, implemented in the simulation software and verified by extensive
laboratory tests.
Zhang ,
and Zhu,2011 [25] presented a comparison between the performances of
three duty determination methods in detail and then proposed a very simple but
effective method to obtain the duty ratio. By appropriately arranging the sequence
of the vectors, the commutation frequency is reduced effectively without
performance degradation. To further improve the performance of system, a low-
pass filter-based voltage model with compensations of amplitude and phase is
employed to acquire accurate stator flux estimation.
Sutikno, et al, 2011 [26] presented an improved FPGA-based torque and stator
flux estimators for direct torque control (DTC) induction motor drives, which
permit very fast calculations. To avoid saturation due to DC offset present in the
sensed currents, the LP Filter is applied. The simulation results of DTC model in
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Chapter One Introduction and Literature Survey
10
MATLAB/ SIMULINK, which performed double-precision calculations, are used
as references to digital computations executed in FPGA implementation. The
Hardware-in-the-loop (HIL) method is used to verify the minimal error between
MATLAB/SIMULINK simulation and the experimental results, and thus the well
functionality of the implemented estimators.
Alwadie, 2012 [27] presented a practical implementation for direct torque
control of induction motor drive. Control system experiment is proposed
using Digital Signal Processor. This control scheme directly determines the
switching states of the inverter and gives optimal characteristics for stator
flux and torque control.
Shah, et al,2012 [28] presented the application of FPGA in Direct Torque
control induction motor drive. Modern AC drives require a fast digital
realization of many mathematical operations concerning control and
estimator’s algorithms, which are time consuming. Therefore developing of
custom built digital interfaces as well as digital data processing blocks and
sometimes even integration of ADC converters into single integrated circuit is
necessary.
Kumar , and Babu, 2012 [29] presented control method of DTC implementation
and improvement using Space Vector Pulse Width Modulation (SVPWM) to give
constant switching frequency and reduces torque ripple. A d-q coordinate reference
frame locked to the flux space vector is used to achieve decoupling between the
motor flux and torque.
Krishna,et al, 2012 [30] presented the modeling and simulation of induction
motor drive employing SVM-DTC, carried it out using MATLAB/SIMULINK
simulation package and the results were compared with Conventional DTC.
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Chapter One Introduction and Literature Survey
11
Sekhar , and Chandra, 2013 [31] presented a fuzzy logic duty ratio control
(FLDRC) and Space Vector Modulation (SVM) techniques to reduce torque ripple
in conventional DTC using a versatile simulation package, MATLAB/SIMULINK.
Sutikno, et al, 2013 [32] presented a novel direct torque control (DTC) approach
for induction machines, based on an improved torque and stator flux estimator and
its implementation using field-programmable gate arrays (FPGA). The DTC
performance is significantly improved by the use of FPGA, which can execute the
DTC algorithm at higher sampling frequency. The design was achieved in VHDL,
based on a MATLAB/Simulink simulation model. The Hardware-in-the-Loop
method is used to verify the functionality of the FPGA estimator. The design,
which was coded in synthesizable VHDL code for implementation on Altera
APEX20K200EFC484-2x device.
The presented work differs from the foregoing survey by the following:
1) The IM model, CDTC, and DTC- PI controller are designed with
MATLAB/ Simulink environment using m-file blocks which will make the
system design simple when implemented with Xilinx/Simulink because it
does not need to write the code in VHDL language.
2) The Hardware-in-the-Loop method is used to verify the whole system of
DTC algorithm without writing code for implementation on Xilinx
NEXYS2 Spartan 3E1200 FG320 Kit .
3) Different mechanical tests have been verified for the whole system with
MATLAB/ Simulink model and HIL model.
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Chapter One Introduction and Literature Survey
12
U1.4 Thesis Objective
• Analyzing and proving (DTC) by means of MATLAB/SIMULINK and
Xilinx /SIMULINK .
• Reduce the torque and stator flux pulsations, and constant switching
frequency , with PI controllers (PI-DTC),and (DTC) based on Space Vector
Modulation (DTC-SVM)
• Implement a practical controller of the conventional direct torque control
(CDTC) method by using field programmable gate array (FPGA) with
Hardware/Software Co-Simulation in Xilinx/SIMULINK .
U1.5 Thesis Outline
The contents of the chapters are briefly introduced here:
Chapter Two concentrates on the fundamentals of the principle of DTC of
induction motors and Direct Torque Control with Space Vector Modulation
(DTC-SVM) control techniques.
Chapter Three covers the MATLAB /SIMULINK model and Xilinx System
Generator simulation technique and simulation results and discussion of
comparing of conventional DTC ,DTC with PI controller and DTC-SVM . The
simulation results are presented and compared to the theoretical values.
Chapter Four has the conclusions and suggestion for future works
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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Chapter Two
Direct Torque Control Technique
and Xilinx System Generator
U2.1 Introduction
The concept of Direct Torque Control (DTC) was developed by Takahashi
and Dpenbrock [4,10].It has become a powerful control scheme for the control of
induction motor drives [27]. The scheme of DTC has good dynamic performance,
precise and quick control of stator flux and electromagnetic torque, robustness
against the motor parameter variations, and the simplicity of the algorithm [15].
The DTC aims to choose the best voltage vector in order to control both stator
flux and electromagnetic torque of machine simultaneously. Similar to hysteresis
band (HB)current control, there will be a ripple in current ,flux ,and torque . The
current ripple will give additional harmonic loss, and the torque ripple will try to
induce speed ripple in a low inertia system and possible problem during starting
.To improve the performance of DTC ,the torque ripple must be reduced [9].
This chapter discusses the mathematical model of the induction motor and the
principles, theories, mathematical equations, and procedures involved for the
software (MATLAB/Simulink package) implementation of the direct torque
control technique using different controllers (Conventional and modified DTC by
PI controller and SVPWM technique).
As field programmable gate array (FPGA) is used to run the algorithm, a
software Xilinx system generator, a toolbox of MATLAB/Simulink can be used.
It will simulate the hardware as well as generate the VHDL code needed for the
implementation in FPGA. It can automatically convert the model into VHDL
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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code. In this chapter, the Rapid Control Prototyping tool Xilinx System
Generator that runs from Simulink is here investigated. Implementation of the
Direct Torque Control algorithm for controlling a motor serves as main subject for
the investigation. A library with ready-to-use blocks is created for having the
possibility to implement other control algorithms in the future in a fast, graphical,
intuitive and user friendly way. It shows the advantage of using an FPGA with its
parallelism and re-programmable characteristics when implementing a motor
control algorithm. It provides a high bandwidth and therefore a possibility to
control several motors with one FPGA.
By programming the FPGA with a Rapid Control Prototyping tool like Xilinx
System Generator, the opportunity to an easy way change of different parts
becomes obvious. To use Model Based Design and Rapid Control Prototyping
concepts extensive code writing is avoided. The gap between the software engineer
and the hardware engineer is reduced and the possibility to work in both of the
domains is given[28, 33].
U2.2 The Conventional DTC
The structure of the conventional DTC was shown in Figure 2.1 which
consists of two hysteresis comparator, torque and flux estimators, voltage vector
selector and voltage source inverter (VSI) [29].In this method, the best voltage
vector should be chosen to maintain the stator flux and torque within a hysteresis
band around the proper flux and torque magnitudes by the selection of proper
inverter switching state. The hysteresis band is used to control the flux
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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and torque of the motor directly. So the drive system affected by the range of
hysteresis band control [14].
Figure 2.1: Block diagram of conventional DTC
The configuration is much simpler than the vector control system due to the
absence of coordinate transforms between stationary frame and synchronous
frame and PI regulators. It also does not need a PWM and position encoder,
which introduces delay and requires mechanical transducers respectively [4,34].
DTC based drives are controlled in the manner of a closed loop system without
using the current regulation loop.
S(K)
Torque hysteresis
IM
Vdc
2HBΨ
Flux hysteresis
2HBT
V_abc
EΨ
ETe
Look up
TableVSI
Te*
Ψs*
-
Ψs^ Sector, Flux
and Torque
Estimators
Te^
+
+
-
ia,ib
Sa
Sb
Sc
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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The main advantages offered by DTC are
• Decoupled control of torque and stator flux .
•
Excellent torque dynamics with minimal response time.• Inherent motion-sensorless control method since the motor speed
is not required to achieve the torque control.
•
Absence of coordinate transform .
• Absence of voltage modulator as well as other controllers.
• Robust for rotor parameter variation. Only the stator resistance is
needed for torque and flux estimation.
The major drawback of the DTC drive is the steady state ripples in torque and
flux. In case of constant load, when the torque increases the reference value until
the end of the switching period because of the active switching state, then applying
the vector of zero voltage for the next switching period which lead to making the
torque to continue to decrease under its reference value until the end of the
switching period will result in high ripple in flux and torque [35].
U2.3 DTC Development
U2.3.1 Mathematical Model of Induction Motor
The mathematical model of an electric machine represents all the equations
that describe the relationships between electromagnetic torque and the main
electrical and mechanical quantities. The mathematical models with concentrated
parameters are the most popular and are consequently employed both in scientific
literature and practice. The equations stand on resistances and inductances, which
can be used further for defining magnetic fluxes, electromagnetic torque, etc.
These models offer results, which are globally acceptable but cannot detect
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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important information concerning local effects. The family of mathematical
models with concentrated parameters comprises different approaches but two of
them are more popular: the phase coordinate model and the orthogonal (dq) model.
The first category works with the real machine. The equations include, among
other parameters, the mutual stator-rotor inductances with variable values
according to the rotor position. As a consequence, the model becomes non-linear
and complicates the study of dynamic processes. The orthogonal (dq) model began
with Park’s theory nine decades ago. These models use parameters that are often
independent to rotor position [36].
The dynamic equivalent circuit of the induction machine is used to understand
and analyze the transient behavior of the induction machine [3].The following
equivalent circuit is used to simulate a three-phase, P-pole, symmetrical induction
motor in the dqo reference frame which is known in the generalized machine
analysis as arbitrary reference frame.
Figure 2.2: The dynamic or d-q equivalent circuit of an induction machine
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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The complexity of the voltage and torque equations can be reduced by
eliminating all time varying inductance [37].
This equivalent circuit model is used to make all the machine variables
controllable and every single equation will be represented in one block [38]. The
following equations can be written for stator:
vqs = Rsiqs + ddt +ωeΨds (2.1)vds = Rsids + ddt ωeΨqs (2.2)The rotor equations:
vqr = Rriqr + dΨdt + ( )Ψdr R R(2.3)vdr = Rridr + dΨdt (ωe ωr )Ψqr (2.4)The flux linkage expressions in terms of the currents can be written from figure 2.4
as follows:
Ψqs= L
si
qs+ L
mi
qs+ i
qr (2.5)
Ψqr = Lriqr + Lm(iqs + iqr) (2.6)Ψqm = Lm(iqs + iqr) (2.7)Ψds = Lsids + Lm(ids + idr) (2.8)Ψdr = Lridr + Lm(ids + idr) (2.9)
Ψdm = Lm(ids + idr) (2.10)
Using the two-axis notation and the matrix form, the voltage equations can be
represented by[9]:
vqsvdsvqrvdr = Rs + pLs ωeLs pLm ωeLmωeLs Rs + pLs ωeLm pLm
pLm (ωe ωr )Lm Rr + pLr (ωe ωr )Lr(ωe ωr )Lm pLm (ωe ωr )Lr Rr + pLr iqsidsiqridr
(2.11)
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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The arbitrary reference frame rotates with electrical angle velocity of rotor (ωr );therefore, the electrical equation of the squirrel-cage induction motor becomes:
vqsvdsvqrvdr = Rs + pLs ωrLs pLm ωrLmωrLs Rs + pLs ωrLm pLm
pLm 0 Rr + pLr 00 pLm 0 Rr + pLr
iqsidsiqridr
(2.12)
In order to have fast simulation, the above equation should be represented in state
space form with currents as state variables as in the following [39]:
p[] = [L ]−1([] +ωr [])[] + [L ]−1[] (2.13)Where,
[
] = [i
qs i
qr i
ds i
dr]
, [V] = [v
qs v
qr v
ds v
dr]
, [R] =
Rs 0 0 00 R
s0 0
0 0 Rr 00 0 0 Rr
[L] = Ls 0 Lm 00 Ls 0 LmLm 0 Lr 00 Lm 0 Lr
, [] = 0 Ls 0 LmLs 0 Lm 00 0 0 0
0 0 0 0
Now the current equation of an induction motor in the two-axis stator referenceframe can be written as [40]:
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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idsiqsidri
qr
= ∫⎩Ls 0 Lm 00 Ls 0 LmLm 0 Lr 00 L
m0 L
r
−1
=0
⎝vdsvqsvdrvqr
Rs 0 0 00 Rs 0 00
P2ωrLm Rr P2ωrLr P2ωrLm 0 P2ωrLr Rridsiqsidriqr ⎠⎭
(2.14)The electromagnetic torque equation is
T
e= 1.5
P2L
m(i
qsi
dr i
dsi
qr) (2.15)
The speed R RωRr Rcannot be normally treated as a constant .It can be related to the
torques asR:
Te = TL + J ddt = TL + 2P J ddt (2.16)Where
d: direct axis
q: quadrature axis
s: stator variable
r: rotor variable
LRs R:stator inductance
LRm R:mutual inductance
LR
rR
:rotor inductance
Rr: rotor resistance
Rs: stator resistance
vRqsR, vRdsR: q and d–axis stator voltages
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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vRqr R, vRdr R: q and d–axis rotor voltages
iRqsR, iRdsR: q and d–axis stator currents
iRqr,R iRdr R: q and d–axis rotor currents
P: number of poles
J: moment of inertia
TReR: electrical output torque
TRLR: load torque
ωReR: stator angular electrical speed
ωRr R: rotor angular electrical speed
U2.3.2 Flux and Torque Estimator
The basic principle of the conventional DTC is to control the torque and the
modulus of the stator flux linkage directly by controlling the inverter switches
using the outputs of the hysteresis comparators and selecting the correct voltage
vector from the optimal switching table. Flux and torque estimators are used to
determine the actual value of torque and flux linkages. The VSI voltage vector
transformed to the d-q stationary reference frame.
The voltage across the stator coil can be expressed as follows [41]:
v
qs= R
si
qs+ L
s didt (2.17)
vds = Rsids + Ls didt (2.18)The terms Ls didt , Ls didt represent the change in stator flux in d and q axis ,
respectively. Reforming the above equations yields the following formulas
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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vqs = Rsiqs + ddt (2.19)v
ds= R
si
ds+ ddt
(2.20)
The estimate of the stator q and d axis flux linkages are an integral of the
stator EMF which can be written by solving (2.19) and (2.20) for (Ψqs ,Ψds) togive the following equationsΨqs = ∫(vqs Rsiqs) (2.21)Ψds = ∫(vds Rsids) (2.22)The stator flux vector can be obtained as follows
Ψs = Ψqs2 +Ψds2 (2.23)θs = tan−1() (2.24)
The developed electric torque is calculated from the estimated flux linkage
components and the measured stator currents in the two-axis stationary reference
frame.
Te = 1.5 P2 (iqsΨds idsΨqs) (2.25)According to (2.24), the stator flux angle is used to divide the electrical revolution
into six sectors denoted from Sec R1 Rto SecR6 Ras shown in Figure 2.3.
These sectors can be distributed as follows in Table 2.1:
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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Table 2.1 : Sectors distribution
U2.3.3 Torque and Flux Hysteresis Comparator
In the DTC, there is no fixed switching frequency but the average switching
frequency is controlled with flux linkage and torque hysteresis bands. The
hysteresis bands are controlled by the reference switching frequency to achieve the
desired average value. In the DTC, there is no predetermined switching pattern
either, and the frequency component content of the voltages is not known
beforehand [24]. The IM stator voltage equation can be written by:
vs = Rsis + ddt (2.26)Where vRs ,RiRsR, and ΨRsR are the stator voltage, current and stator flux
space vectors, respectively. If the stator resistance is small and can be
neglected, the change in stator flux,
∆Ψs will follow the stator voltage; i.e.,
∆Ψs = vs∆t (2.27)
Sector Degrees
1 -30 < θRs
R< 30Po
2 30Po
P< θRs R< 90Po
3 90Po
P < θRs R< 150Po
4 150Po
P < θRsR< 210Po
5 210Po
P < θRsR< 270Po
6 270Po
P < θRsR< 330Po
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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Therefore, variation of stator flux space vector can be achieved by the
application of stator voltage vRsR for a time interval of ∆t. The stator flux is
controllable if a proper selection of the voltage vector is made. In Figure 2.3, the
stator flux plane is divided into six sectors where each one has a set of voltage
vectors.
Figure 2.3 :Six sectors with different set of voltages
The reference stator flux and torque values are compared with the estimated values
in hysteresis flux and torque controllers. The digitized output signals of the flux
(HRψR) and torque (HRTeR) controllers are as follows:
Hψ = 1 For Eψ ≥ + HBψ (2.28)Hψ = 1 For Eψ ≤ HBψ (2.29)H = 1 For ETe
≥ + HBTe (2.30)
H = 0 For HBTe ≤ ETe ≤ + HBTe (2.31)H = 1 For ETe ≤ HBTe (2.32)Where ERψ Rand ERTe Rare the flux R Rand torque errors, HBRψR and HBRTe Rare the
acceptable predefined flux and torque errors and 2HB RψR and 2HBRTeR are the total
hysteresis band width of the flux and the torque control [31].
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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The flux error which is due to the difference between the estimated and
desired stator flux is fed to the 2–level hysteresis comparator which in turn
produces the flux error status. The error signal is processed in a comparator. If the
actual flux is smaller than the reference value, the comparator output is at state 1 ,
or else it will be at state -1. The states for Flux are shown in Figure 2.4.
Figure 2.4: Flux hysteresis states.
The instantaneous electromagnetic torque is a sinusoidal function of the
angle between the stator and rotor fluxes as given in the following equation:
Te = 32 P2 LΨsΨrL′ L sin θsr (2.33) The relation between Ψs and Ψr vectors can be illustrated by Figure 2.5where the angle between them is denoted by θ Rsr.
Figure 2.5: Space vector of stator and rotor fluxes
state
-1
1
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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R RTorque is controlled within its 3-level hysteresis band as shown in Figure 2.6
[41,18].
Figure 2.6: Torque hysteresis states .
U2.3.4 Lookup Table
The stator flux angle in addition to the torque and flux hysteresis status are
used to determine the suitable stator flux sector in order to apply the correct
voltage vector to the induction motor operating under DTC. The selection of the
appropriate voltage vector is based on the switching table given in Table 2.1. The
input quantities are the stator flux sector and the outputs of the two hysteresis
comparators. [41].
The feedback flux and torque are calculated from the machine terminal
voltages and currents. The signal computation block also calculates the sector
number S(k) in which the flux vector Ψs lies. There are six sectors each 3 anglewide. The Look up table block in figure 3.1 receives the input signals H RψR, H RTeR and
S(k) and generates the appropriate control voltage vector for the inverter by a look
up table, which is shown in Table 2.2.
state
0
1
-1
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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Table (2.2) Lookup table of inverter voltage vectors
If the stator flux lies in sector k with the motor rotating in counter clockwise,
active voltage vector V RS,k+l Ris used to increase both the stator flux and torque.
Voltage vector VRS,k+2
Ris selected to increase the torque but decrease the stator flux.
The two zero voltage vectors (V RS,7 Rand VRS,8R) are used to reduce the torque and at
the same time, freezes the stator flux. Reverse voltage vector V RS,k-2 Ris used to
decrease the torque and flux in forward braking mode. Whereas V RS,k.1 Rwill reduce
the torque and increase the flux[23].
U2.3.5 Three-Phase Voltage Source Inverter(VSI)
The VSI synthesizes the voltage vectors commanded by the switching table.
In DTC, this is quite simple since no pulse width modulation is employed, the
output devices stay in the same state during the entire sample period.
HRψ HRTe S(1) S(2) S(3) S(4) S(5) S(6)
1
1 VR2 VR3 VR4 VR5 VR6 VR1
0 VR0 VR7 VR0 VR7 VR0 VR7
-1 VR6 VR1 VR2 VR3 VR4 VR5
-1
1 VR3 VR4 VR5 VR6 VR1 VR2
0 VR7 VR0 VR7 VR0 VR7 VR0
-1 VR5 VR6 VR1 VR2 VR3 VR4
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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There are many topologies for the voltage source inverter used in DTC
control of induction motors that give high number of possible output voltage
vectors but the most common one is the six step inverter [8,42]. A six step voltage
inverter provides the variable frequency AC voltage input to the induction motor in
DTC method. The DC supply to the inverter is provided either by a DC source like
a battery, or a rectifier supplied from a three phase (or single phase) AC source.
The switching devices in the voltage source inverter bridge must be capable of
being turned off and on. The power metal-oxide semiconductor field effect
transistors (MOSFETs) are used because they have this ability and in addition they
offer high switching speed with enough power rating. Each MOSFET has an
inverse parallel-connected diode. This diode provides alternate path for the motor
current after the MOSFET is turned off [43,16].
Each leg of the inverter has two switches; one is connected to the high side
(+) of the DC link and the other is connected to the low side (-). Only one of the
two can be on at any instant. When the high side gate signal is on, the phase is
assigned the binary number 1, and assigned the binary number 0 when the low side
gate signal is on. Considering the combinations of status of phases a, b and c, the
inverter has eight switching modes (VRaR VR bR VRcR=000-111): two are zero voltage
vectors VR0R (000) and VR7R (111) where the motor terminals is short circuited and the
others are nonzero voltage vectors VR1 Rto VR6R . The waveforms of the branch voltage
for 180P0
P conduction mode will be as shown in Figure 2.7.
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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Figure 2.7: Leg voltage waveform of a three-phase (VSI).
From figure 3.7 for one cycle (360Po
P) the leg voltages will have six distinct and
discrete values because every state has been changed after an interval of (60 Po
P) [44].
U2.4 Modified DTC Scheme
When we need to regulate the speed of such a drive a speed controller is
needed. The speed controller takes the error signal between the reference and the
actual speed and produces the appropriate reference torque value. In Figure 2.8 we
can see the block diagram of the proposed drive, in speed control mode. A
reference speed signal ω Rr R* or, in other words, the speed command is given. The
actual speed ωRr R is estimated or measured with a speed encoder. This depends on
the precision requirements of each application. In this theses the classical PI
controller is also used for the comparison between the classic DTC and DTC-
SVM.
For that, it becomes essential to know the rotor mechanical speed. A
speed controller may be employed and augmented with the classical DTC
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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scheme. The block diagram of the modified DTC scheme is as shown in
Figure 2.8.
Figure 2.8 : The block diagram of the modified DTC scheme
U2.5 Classic PI Controller
A classic Proportional plus Integral (PI) controller is suitable enough to adjust
the reference torque value TReRP*
P. Nevertheless, its response depends on the gains K R pR
and K RiR, which are responsible for the sensitivity of speed error and for the speed
error in steady state. During computer analysis, we use a controller in a discrete
S(K)
Torque Hysteresis
IM
Vdc
2HB
Flux hysteresis
2H
V_abc
E
ETeLook
up
Table
VSI
Te*
Ψs*
-
Ψs^ Sector, Flux
and Torque
EstimatorsTe^
+
+
+
-
-
ia,ib
PI
Controller
Wr
Wr*
Sa
Sb
Sc
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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system in order to simulate a digital signal processor (DSP) drive system. Its block
diagram is shown in Figure 2.9, where T is the sampling time of the controller.
Figure 2.9: Block diagram of a discrete classic PI speed controller.
The response of the PI speed controller, in a wide range area of motor speed,
is very sensitive to gains K R pR and K RiR and it needs good tuning for optimal
performance. High values of the PI gains are needed for speeding-up the motor and
for rapid load disturbance rejection. This results to an undesired overshoot of
motor speed. A solution is to use a variable gain PI speed controller. However, in
the case of using a variable gain PI speed controller, it is also necessary to know
the behavior of the motor during start up and during load disturbance rejection in
several operation points in order to determine the appropriate time functions for PI
gains. This method is also time-consuming and depends on the control system
philosophy every time [45].
U2.6 Direct Torque Control With Space Vector Modulation (DTC –
SVM)
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Direct Torque Control drives utilizing hysteresis comparators suffer from
high torque ripple and variable switching frequency. The most common solution to
this problem is to use the space vector that depends on the reference torque and
flux. Space Vector Modulation is one of the PWM technique in which when the
drive is excited by three phase, balanced currents produces a voltage space
vector which traces a circle with uniform velocity by sampling that rotating
reference voltage space vector with high sampling frequency different
switching can be possible. The reference voltage vector is then realized using a
voltage vector modulator. There are various types of direct torque control-space
vector modulation (DTC-SVM) schemes that have been proposed. Each scheme
will perform the different control technique but its aims are still similar, which are
to attain the constant switching frequency and to reduce the torque ripple. The
differences between various DTC-SVM are on how the reference voltage is
generated the reference voltage is then implemented using SVM. Space Vector
Modulation is used to define the inverter switching state or voltage vector positions
different from six standard positions [7,37].
The SVPWM has been widely used in three phase inverter control system
because it has a higher utility efficiency of DC-side voltage than the sine pulse
width modulation (SPWM). Although the SVPWM has many advantages, it is
difficult to implement. The most difficult factor is calculating the duty cycles for
each power switch, as well as determining the vector sector and pulse sequence in
each switching cycle. The duty cycle calculation for the three phase 2- level
inverter was presented in many papers, and the vector sequence can be determined
in many ways (for example, the center-aligned method, which can be easily
implemented in MCU platform) [46].
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The implementation of the conventional SVPWM is especially difficult
because it requires complicated mathematical operations. In the SVPWM
technique, the duty cycles are computed rather than derived through comparison as
in SPWM. The SVPWM technique provides more efficient use of supply voltage
compared with sinusoidal modulation technique as shown in Figure 2.10 [47].
The fundamental voltage can be increased up to a square wave mode where a
modulation index of unity is reached. Moreover, the utilization of the DC bus
voltage can be further increased when extending into the over-modulation region
of SVPWM .Three-phase voltage source pulse-width modulation inverters have
been widely used for DC to AC power conversion since they can produce outputs
with variable voltage magnitude and variable frequency. For example, modern
power electronics controllers have been rapidly moving toward digital
implementation. Typical solutions employ microcontrollers or DSPs [48].
SV PWM
√ Vdc Vdc
Sine PWM
a
b
c
d
q
Vdc
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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Figure 2.10: Locus comparison of maximum linear control voltage in Sine PWM
and SVPWM.
U2.7 Principle of Space Vector PWM
The procedure for implementing a two-level space vector PWM can be
summarized as follows:
1. Calculate the angle α and reference voltage vector VRref R based on the input
voltage components.
2. Calculate the modulation index and determine if it is in the over-modulation
region.
3.Find the sector in which VR
refR
lies, and the adjacent space vectors of VR
k R
and VR
k
+ 1 R based on the sector angle α.
4. Find the time intervals T R1R and TR2R and TR0R based on TRzR, and the angle α.
5. Determine the modulation times for the different switching states [47] .
To implement the space vector PWM, the voltage equations in the abc
reference frame can be transformed into the stationary dq reference frame that
consists of the horizontal (d) and vertical (q) axes as depicted in Figure 2.11.
Figure 2.11: The relationship of abc reference frame and stationary dq reference
frame.
From this figure, the relation between these two reference frames is shown as:
d axis
q axis
b
c
a
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f dq0 = Ksf abc (2.34)
Where, Ks = 231 12 120 √ 32 √ 3212 12 12 , f dq0=[ f d f q f 0]
P
TP
, f dq0=[ f a f b f c]P
TP
, and f denoted
either a voltage or a current variable.
As described in Figure 2.11, this transformation is equivalent to an orthogonal
projection of [a, b, c]Pt
P onto the two-dimensional perpendicular to the vector
[1, 1, 1] Pt
P (the equivalent d-q plane) in a three-dimensional coordinate system. As a
result, six non-zero vectors and two zero vectors are possible. Six nonzero vectors(V1- V6) shape the axes of a hexagonal as depicted in Figure 2.12,and feed electric
power to the load. The angle between any adjacent two non-zero vectors is 60
degrees.
Figure 2.12: Basic switching vectors and sectors.
α
V3 (010) V2 (110)
V1 (100)
V6 (101)V5 (001)
V4 (011)V7 (111)
V0 (000)
q axis
d axis
(1/3,1/ 3) Vref
(2/3)Vdc
(1/3,1/ 3)
( 13
,1/ 3) (13
,1/ 3)
(2/3,0) (2/3,0) 1
2
3
4
5
6
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Meanwhile, two zero vectors (V0 and V7) are at the origin and apply zero
voltage to the load. The eight vectors are called the basic space vectors and are
denoted by V0, V1,V2, V3, V4, V5, V6, and V7. The same transformation can be
applied to the desired output voltage to get the desired reference voltage vector Vref
in the d-q plane. The objective of space vector PWM technique is to approximate
the reference voltage vector Vref using the eight switching patterns. One simple
method of approximation is to generate the average output of the inverter in a
small period; T is to be the same as that of Vref in the same period. Therefore, space
vector PWM can be implemented by the following steps:
Step 1. Determine Vd , Vq , Vref , and angle (α)
Step 2. Determine time duration T1, T2, T0
Step 3. Determine the switching time of each transistor (S1to S6)
U2.7.1 Step 1: Determining Vd, Vq, Vref , and Angle (α)
From Figure 2.13, the Vd , Vq , Vref , and angle (α) can be determined as
follows:
V = V V60 V60 = V 12V 12V (2.35)V = 0 + V30 V30 = V + √ 32 V √ 32 V (2.36)vvq = 23 1 12 120 √ 32 √ 32
vanvbnvcn (2.37)
|V ref | = V2 + Vq2 (2.38)
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α = tan−1 VV = = 2πf , where f= fundamental frequency
Figure 2.13: Voltage Space Vector and its components in (d,q) .
It is necessary to know in which sector the reference output lies in order to
determine the switching time and sequence. The identification of the sector where
the reference vector is located is straightforward. The phase voltages correspond to
eight switching states: six non-zero vectors and two zero vectors at the origin.
Depending on the reference voltages Vd and Vq , the angle of the reference vector
can be used to determine the sector as shown in Table 2.3.
Table 2.3: Sector Definition.
Sector Degrees
1 0 < α ≤ 60Po
2 60Po
P< α ≤ 120Po
3 120P
oP
< α ≤ 180P
o
4 180P
oP < α ≤ 240P
o
5 240Po
P < α ≤ 300Po
6 300Po
P < α ≤ 360Po
a, d axis
V
d
→ refVq α
q axis
b
c
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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U2.7.2 Step 2: Determining Time Duration T1, T2, T0
The duty cycle computation is done for each triangular sector formed by twostate vectors. The magnitude of each switching state vector is 2Vdc/3 and the
magnitude of a vector to the midpoint of the hexagon line from one vertex to
another is Vdc/√ 3 .From Figure 2.14, the switching time duration can be calculated as follows:
Switching time duration at sector 1
∫ V ref =T0 ∫ V 1 +T0 ∫ V 2 +T+TT ∫ V oTT+T (2.39)For sufficiently high switching frequency, the reference space vector V ref is
assumed constant during one switching cycle. Taking into account that the states
V 1 and V 2 are constant, one finds (see Figure 2.14):V ref T = V 1 T1 + V 2 T2 (2.40)23 T1V 10+ 23 T2 V �cos(π/3)sin(π/3) = T|V ref | � cos(α)sin(α) (2.41)(where , 0≤ α ≤60P
oP)
T1 = T sin (−)sin () (2.42)T2 = T sin
(
)
sin () (2.43)T0 = T (T 1 + T2), where, T = 1f and = |V |V Switching time duration at any sector
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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T1 = √ 3 T |V |V sin 3 α + −13 π = √ 3 T |V |V sin(3 π α) = √ 3
T |
V |
V sin 3 π . cosα 3 π . α (2.44)T2 = √ 3 T |V ref |
V sin α 13 π =
√ 3 T |V |V α. −13 π sin −13 π . cosα (2.45)T
0= T
T
1 T
2 where, n=1 through 6 (that is, Sector 1 to 6)
For the sectors II-VI, the same rules apply [49].
Figure 2.14: Reference vector as a combination of adjacent vectors at sector 1.
U2.7.3 Step 3: Determining the Switching Time of Each
Transistor (S1to S6)
It is necessary to arrange the switching sequence so that the switching
frequency of each inverter leg is minimized. There are many switching patterns
that can be used to implement SVPWM. To minimize the switching losses, only
two adjacent active vectors and two zero vectors are used in a sector [50,51]. To
meet this optimal condition, each switching period starts with one zero vector and
end with another zero vector during the sampling time Tz. This rule applies
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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normally to three-phase inverters as a switching sequence. Therefore, the switching
cycle of the output voltage is double the sampling time, and the two output voltage
waveforms become symmetrical during Tz. Table 2.4 presents asymmetric
switching sequence.
Referring to this table, the binary representations of two adjacent basic
vectors differ in only one bit, so that only one of the upper transistors switches is
closed when the switching pattern moves from one vector to an adjacent one. The
two vectors are time-weighted in a sample period Tz to produce the desired output
voltage.
Table 2.4: Seven-Segment Switching Sequence
Sector Switching Segment
1 2 3 4 5 6 7
1 V 0 , [000] V 1 , [100] V 2, [110] V 7, [111] V 2, [110] V 1 , [100] V 0 , [000] 2 V 0 , [000] V 3 , [010] V 2, [110] V 7, [111] V 2, [110] V 3 , [010] V 0 , [000] 3 V 0 , [000] V 3 , [010] V 4, [011] V 7, [111] V 4, [011] V 3 , [010] V 0 , [000] 4 V
0 , [000] V
5 , [001] V
4, [011] V
7, [111] V
4, [011] V
5 , [001] V
0 , [000]
5 V 0 , [000] V 5 , [001] V 6, [101] V 7, [111] V 6, [101] V 5 , [001] V 0 , [000] 6 V 0 , [000] V 1 , [100] V 6, [101] V 7, [111] V 6, [101] V 1 , [100] V 0 , [000] U2.8 Types of Different Schemes
There are two modes of operation available for the PWM waveform:
symmetric and asymmetric PWM. The pulse of an asymmetric edge aligned signal
always has the same side aligned with one end of each PWM period. On the other
hand, the pulse of symmetric signals is always symmetric with respect to the center
of each PWM period. The symmetrical PWM signal is often preferred because it
has been shown to have the lowest total harmonic distortion (THD). Output
patterns for each sector are based on a symmetrical sequence. There are different
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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schemes in space vector PWM and they are based on their repeating duty
distribution. In order to reduce the switching loss of the power components of the
inverter, it is required that at each time only one bridge arm is switched. After re-
organizing the switching sequences, the switching pulse patterns of six different
sectors in Figure 2.15 are shown for the upper and lower switches of a three-phase
inverter.
It is obvious that in the odd sector the active state sequence is in ascending-
descending order; whereas, it is in a descending-ascending order in an even sector.
For example:
1. In an odd sector 1, the state sequence of space vectors is in the order
V 0, V 1, V 2, V 7, V 7, V 2, V 1, V 0.2. In an even sector 2, the state sequence of space vectors is:
V 0, V 3, V 2, V 7, V 7, V 2, V 3, V 0.Following the same procedure, we have the switching sequence summarized
in Table 2.5 for all six sectors.
Table 2.5: Switching Sequence for Three-Phase PWM Technique
Sector Switching Sequence of the Three Phase Modulation
1 V 0 V 1 V 2 V 7 V 2 V 1 V 0 2 V 0 V 3 V 2 V 7 V 2 V 3 V 0 3 V 0 V 3 V 4 V 7 V 4 V 3 V 0 4 V
0 V
5 V
4 V
7 V
4 V
5 V
0
5 V 0 V 5 V 6 V 7 V 6 V 5 V 0 6 V 0 V 1 V 6 V 7 V 6 V 1 V 6
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Figure 2.15 shows space vector PWM switching patterns at each sector.
(a)Sector 1 (b)Sector 2
(c)Sector 3 (d)Sector 4
(e)Sector 5 (f)Sector 6
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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Figure 2.15 Space Vector PWM switching patterns at each sector.
Based on Figure 2.15 and according to the principle of symmetrical PWM, the
switching sequence in Table 2.6 is shown for the upper and lower switches and it
will be built in Simulink model to implement SVPWM.
Table 2.6 Switching Time Calculation at Each Sector
Sector Upper switches (S1,S3,S5) Lower switches (S4,S6,S2)
1S1=2(T1+T2)+T0 S3=2T2+T0
S5=T0
S4=T0 S6=2T2+T0
S2=2(T1+T2)+T0
2
S1=2T2+T0
S3=2(T1+T2)+T0
S5=T0
S4=2T2+T0
S6=T0
S2=2(T1+T2)+T0
3
S1=T0 /2
S3=2(T1+T2)+T0
S5=2T2+T0
S4=2(T1+T2)+T0S6=T0
S2=2T2+T0
4
S1=T0
S3=2T2+T0
S5=2(T1+T2)+T0
S4=2(T1+T2)+T0
S6=2T2+T0S2=T0
5
S1=2T2+T0
S3=T0
S5=2(T1+T2)+T0
S4=2T2+T0
S6=2(T1+T2)+T0S2=T0
6
S1=2(T1+T2)+T0
S3=T0
S5=2T2+T0
S4=T0
S6=2(T1+T2)+T0
S2=2T2+T0
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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U2.9 Field Programmable Gate Array
A Field Programmable Gate Array (FPGA) is a silicon device that containslogic. It is constructed of cells called Configurable Logic Block (CLB); each
configurable logic block contains more or less a Look Up Table (LUT), a Flip-Flop
and a multiplexer. In-between the CLBs, there are interconnections and at the
borders input and output cells. An FPGA is normally programmed with a
Hardware Description Language (HDL) like VHDL or Verilog. An FPGA can be
re-programmable and several tasks can be executed at the same time; in other
words, parallel programming can be applied to it.
U2.10 Hardware in the Loop
Hardware in the loop (HIL), or FPGA in the loop, is a concept that as
revealed by the name uses the hardware in the simulation loop. This leads to easy
testing and the possibility to see how the actual plant is behaving in hardware. By
having the stimuli in a software on the PC, implementing a part of the loop inhardware and then receiving the response from hardware back in the software, a
good indication of the design’s performance is given [52].
U2.11 Usage of Xilinx System Generator in the Controller Design
MATLAB SIMULINK software package provides a powerful high level
modeling environment for people who are involved in system modeling and
simulations. Xilinx System Generator Tool developed for MATLAB SIMULINK
package is widely used for algorithm development and verification purposes in
Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGAs).
System Generator Tool allows an abstraction level algorithm development while
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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keeping the traditional SIMULINK blocksets, but at the same time automatically
translating designs into hardware implementations that are faithful, synthesizable,
and efficient.
Here in this study, a direct field and torque controlled induction machine
driven by a Voltage Source Inverter (VSI) is analyzed by using a MATLAB
SIMULINK model. The control signals for the VSI in the related model are
generated by the Xilinx FPGA chip. But, the FPGA chip needs Very-high-speed
Hardware Description Language (VHDL) codes to generate the control signals for
the related controller. Normally, MATLAB SIMULINK Package does not provide
an interface for the VHDL needed for the controller to be embedded in the FPGA
chip. However, the Xilinx System Generator Tool provides such an interface; i.e., a
control algorithm developed Xilinx System Generator Tool convenient to be used
with traditional Simulink blocksets can be translated to the VHDL codes needed
for the controller to be embedded in the FPGA chip. The following section briefly
introduces system modeling using the Xilinx System Generator Tool.
U2.12 System Modeling Using the Xilinx System Generator
The formation of a DSP design begins with a mathematical description of the
operations needed for the controller and ends with the hardware realization of the
algorithm. The hardware implementation is rarely faithful to the original functional
description, instead it is faithful enough. The challenge is to make the hardwarearea and speed efficient, while still producing acceptable results. In a typical
design flow supported by System Generator, the following steps are followed:
1. Describe the algorithm in mathematical terms;
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2. Realize the algorithm in the design environment, initially using double
precision;
3. Trim double precision arithmetic down to fixed point;
4. Translate the design into efficient hardware .
U2.14 Integration in Xilinx Environment
The experimental application presents certain problems caused by the external
noise interference and the appearance of constant offsets at the waveforms. The
flux estimation is achieved by the integration of the stationary voltage and the
current waveforms. However, if there is an offset at the input of the integrator, a
ramp error occurs at the output of the integration [53] .
The implementation of the integral operator1+1 in real time application is yet
another problem to be sorted out. In general, the digital implementation includes
several hardware limitations, such as limited memory, finite precision, and limited
speed execution. Operations that require a finite amount of data and make the
algorithm computable are necessary.
According to the Euler approximation technique, a transfer function in the
differential operator (s) can be transformed into a discrete time transfer function in
the time delay operator (z) by substituting :
s = 1−z
T (2.46)
In Equation (2.46) ,Ts is the sampling interval. Let the clock frequency of the
FPGA be 0.2 MHz and consequently the sampling interval be 5* 10P-6
P sec.
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Chapter Two Direct Torque Control Technique and Xilinx System Generator
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By substituting Equation (2.46) in the integral operator 1+1 , it is obtained:1+1 = 1 +1 = 1+1 =
5x101.000005−z = 4.999975x101−0.999995z (2.47)In time domain, Equation (2.47) is implemented by the difference equation:
[
] = 0.999995y[n
1] + 4.99x10−6
[
] (2.48)
Equation (2.48) yields the following block diagram realization:
Figure 2.17: Block diagram realization of equation (2.48) [22].
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Chapter Three System Implementation and Simulation Results
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Chapter Three
System Implementation and Simulation Results
3.1 Introduction
This chapter deals with the implementation of DTC and examination of the
performance of DTC using differen