thesis design and implementation of a three-phase induction motor control scheme

2001 Thesis Project 1 Gareth S Roberts

Design and Implementation of a

Three-Phase Induction Motor Control Scheme

By Gareth Stephen Roberts

Department of Information Technology and Electrical

Engineering, the University of Queensland

Submitted for the degree of Bachelor of Electrical Engineering (Honours).

October 2001

2001 Thesis Project A2 Gareth S Roberts

34 Tolaga Street,

Westlake, QLD, 4074

October 17, 2001

The Head of School,

School of Information Technology and Electrical Engineering,

University of Queensland,

St. Lucia, Qld, 4072

Dear Professor Simon Kaplan,

In accordance with the requirements of the degree of Bachelor of Engineering (Honours)

in the division of Electrical Engineering, I present the following thesis entitled Design

and Implementation of a Three-Phase Induction Motor Control Scheme. This thesis was

carried out under the supervision of Dr. Geoff Walker.

This thesis project has not been submitted at any other University. I declare that this

work has not been published or written by any other person, except where reference is

made by text.

Yours sincerely,

Gareth Roberts.


Abstract The use of a combustion engine to motivate a car has been questioned in recent times due

to the increasing concern of global warming. As a result of this, the concept of driving

a car with an electric engine has become of particular interest. Dr. Geoff Walker and his

PhD students are working on the creation of the Universitys own electric car.

This thesis project is focused on deriving a control scheme to drive an induction machine

that could be applied to the electric car. Induction machines are universally used in

industry because of their robustness, reliability, low price and high efficiency (up to

80%). However, until recent times, it has been hard to control the torque of the induction

motor.

By using the TMS320F243 DSP controller, which is embedded in an existing hardware

design and a control scheme called Field Orientated Control, we can control the torque

of an induction machine with a high degree of accuracy. Hence, this thesis project

demonstrates how to apply Field Orientated Control with a DSP controller. To do this,

extensive MATLAB analysis was conducted in order to optimize the control system. The

complete physical system is expected to be working on the demonstration day.


Acknowledgements

I wish to thank the following people:

Dr. Geoff Walker, my supervisor, for taking the time through the whole course of the

year for offering clear and enthusiastic explanations. Dr. Walker was always able to

guide the thesis along the right path.

Mr. David Finn for lending me his motor controller board. David also provided the

required information needed to operate this board.

My family, for offering support through my University years; this year in particular.

My fellow occupants in the Power Electronics labs, for putting up with my company for

days on end. To Andrew Gray and Jeffrey Jordan, thank you for the advise you offered

through the course of the year.


Table of Contents

Abstract.. i

Acknowledgements. ii

List of Figures and Illustrations iii

Chapter 1 Need/Basis for the thesis project.. 1

1.1. Project Specification. 1

1.2. Available resources... 1

1.3. What are hyper and electric cars?. 1

1.4. Why do we use an Induction motor?. 3

Chapter 2 Literature Review... 5

2.1. The Hybrid concept... 5

2.2. Induction Motor Theory and Practice 5

2.3. Power Electronics.. 6

2.4. Field-Orientated Control 7

2.5. MATLAB analysis. 8

Chapter 3 The Hardware Design. 9 3.1. The basic control format... 9

3.2. The existing motor controller... 10

3.3. Current sensing module 11

3.4. The speed sensor... 12


Chapter 4 The Induction Motor. 14

4.1. The fundamental operating principles for an

Induction Motor... 14

4.2. The Electrical principles of an Induction Motor.. 14

4.3. Torque/Speed generation for an Induction Motor 16

Chapter 5 Field-Orientated Control (FOC) 19

5.1. An introduction.. 19

5.2. Transformation between reference frames. 20

5.3. The PI controller. 21

5.4. PWM Pulse-Width Modulation... 22

5.5. The Overall Design. 24

5.6. Conclusions drawn from Chapter 5 26

Chapter 6 The MATLAB design 27 6.1. MATLAB An introduction 27

6.2. MATLAB simulation design 27 6.2.1 Field Orientated Control using SIMULINK... 28

6.2.2 The Current Controller 32

6.2.3 The Motor Model 32

6.3. Simulation of the MATLAB design. 34 6.3.1. Speed response analysis. 34

6.3.2. Analysis of the Field-Orientated Section of the

Design.. 38

6.3.3. The significance of feedback... 41

6.4. The conclusions drawn from Chapter 6. 42


Chapter 7 The Software Design 43

7.1. A basic overview of how the software is

organized 43

7.2. The Main Program The Field-Orientated Control

Portion of the Software Design. 44 7.2.1. The torque controller & Field Weakening.. 45

7.2.2. Calculation of iqs, ids, cos(rho) and sin(rho). 48

7.2.3. The Current Controller section of the software design 50

7.3. The PWM Interrupt Service Routine. 51

7.4. The Encoder Interrupt Service Rountine... 55

7.5. A/D conversion. 57

7.6. Concluding remarks. 58

Chapter 8 Final Project Performance and Evaluation 59

8.1. PWM test program... 59

8.2. Encoder test program #1... 61

8.3. Encoder test program #2... 62

Chapter 9 Conclusion. 64

9.1 Summary and Conclusion... 64

9.2 Future work. 64

Bibliography 66

APPENDIX A The proposed software design

APPENDIX B PWM test program


APPENDIX C Encoder detection test program #1

APPENDIX D Encoder detection test program #2

APPENDIX E The schematics for the Motor Controller board


List of Figures

Figure 1.1 The Honda Insight Figure 1.2 The parallel hybrid car Figure 3.1 The basic physical design Figure 3.2 The existing motor controller board Figure 3.3 The current sensing module Figure 4.1 The per phase representation of an Induction motor in steady state Figure 4.2 The torque/speed curve Figure 4.3 Field weakening Figure 5.1 The transformation of the stationary reference frame to the rotating

reference frame Figure 5.2 The PI controller Figure 5.3 Leg A of the full-bridge inverter Figure 5.4 PWM VSI schematic and waveforms Figure 5.5 The complete FO controller design in a block representation Figure 6.1 The Look-up Table Figure 6.2 The complete SIMULINK design Figure 6.3 The FO_controller block Figure 6.4 The dqe2abc block Figure 6.5 The Inverse_Park_Transform Block Figure 6.6 The Inverse_Clarke_Transform Block Figure 6.7 The Current_controller block Figure 6.8 The Induction machine in stationary qd0 Figure 6.9 The MATLAB speed simulation results Figure 6.10 The speed response of the control system where the proportional

gain is increased Figure 6.11 The speed response of the system with a proportional gain of 90 Figure 6.12 cos(rho) and sin(rho) signals Figure 6.13 The ids and iqs signal curves over time Figure 6.14 The applied signal to phase A of the Induction motor and the drawn

current on phase A Figure 6.15 The speed response of the system without feedback Figure 7.1 The flow chart for this thesis project Figure 7.2 The torque controller Figure 7.3 Graphical representation of the trapezoidal rule Figure 7.4 Limiting the integration result Figure 7.5 Calculation of the required rotor flux: Lambdare_r Figure 7.6 The results of using the field-orientated technique Figure 7.7 Overflow prevention of the slip-angle


Figure 7.8 Demonstration of the development of the slip angle over time Figure 7.9 Flow-chart demonstrating how the current controller section works Figure 7.10 PWM waveforms with dead-band Figure 7.11 The PWM infrastructure Figure 7.12 The Peripheral Interrupt Expansion Block Diagram Figure 7.13 The encoder detection infrastructure Figure 7.14 The flow-chart for Encoder detection Figure 8.1 Experimentally measured PWM waveforms on the CRO

2001 Thesis Project 1 Gareth S Roberts

1. Need/Basis for the thesis project

1.1. Project Specification To design a control scheme for a three-phase induction motor drive. This induction

motor drive is proposed to be incorporated into a hybrid car or an electric car.

1.2. Available resources

Motor controller board. This was constructed by 1999 thesis student, Mr.

David Finn and was designed to control a brush-less DC motor. However, by

constructing a feedback loop that can detect the outputs of an induction motor, we

can use this motor controller to control an induction machine.

TMS320F243 DSP controller. This is manufactured by the Texas Instruments Company and is one of the major components on David Finns motor controller.

For this thesis project, a software control design has to be devised that will

correctly control the DSP controller to meet specifications.

DC bus. This DC bus is made available from SUNSHARK battery packs, 12VDC to 140VDC. ~40 VDC is the most compatible voltage supply for the motor

controller that will be used for this thesis.

Induction motor. Three-phase, 0.5kW, 4-pole machine. This induction motor is only used for the prototype design presented in this thesis.

1.3. What are hybrid and electric cars?

Under the supervision of Dr. Geoff Walker, a group of Computer Science and Electrical

Engineering Ph.D. students at the University of Queensland are constructing a hybrid or

an electric car. Both of these types have been inaugurated due to the increasing concerns

of global warming. An electric car simply uses an electric engine as the means of

motivating the car instead of the conventional combustion engine. These cars have not

yet been released in the commercial world because the electric engine system (including


batteries) does not provide the same power per weight as the combustion engine from the

research to date [8].

Figure 1.1. The Honda Insight [14]

Figure 1.2. The internal infrastructure of a parallel hybrid car [14]

A hybrid car was released commercially this year. It combines two or more sources of

power; the gasoline-electric hybrid car, for instance, does just this. The electric engine


boosts acceleration and reduces demand on the petrol engine, saving fuel and improving

performance in the process [14]. While cruising, power comes solely from the petrol

engine. When the vehicle is coasting downhill, or during deceleration and braking, the

electric motor recharges a nickel metal hydride battery pack. During periods when the

vehicle is stationary, the engine automatically shuts down to save fuel, and then starts up

again when the throttle is pressed. The Honda Insight for instance consumes less than

half the fuel of a conventional small car and harmful exhaust emissions are lowered by a

significant 90% [14]. This model features a 10kW electric motor that delivers power to

the front wheels via a five speed manual gearbox.

1.4 Why do we use an Induction motor? For this application, the only external input for the electric motor applied by the user is

the accelerator; which is essentially a variable torque input. There are two existing

options for an electric motor: the Direct current (DC) type or the Induction type.

Induction motors are universally used in industry because of their high robustness,

reliability, low price and high efficiency (up to 80% [15]). However, the brush-less DC

motor has been, traditionally, the more attractive option for variable torque control. This

is because the torque can be controlled by varying the armature current (ia), while the

flux can be controlled by varying the field/exciting current (ix). These two quantities

operate in a decoupled manner, which is highly advantageous from a design perspective.

Also, an induction machine has been difficult to control due to its complex mathematical

model, its non-linear behavior during the saturation effects and the electrical parameter

oscillation that depends on the physical influence of temperature [15].

However, the recent fruition of digital signal processors (DSPs) has swung the

pendulum toward the induction motor for torque control. These high computational

power silicon devices have made it possible to realize far more precise digital control

algorithms. Field Orientated Control (FOC), for instance, is a vector control method that

demonstrates the capability of performing direct torque control. FOC provides an

induction motor every advantage that DC machine control can have, while freeing itself

from mechanical commutation drawbacks [9]. It is anticipated that the application of the


correct control algorithm combined with the inherent efficiency and power potential will

make this design very compatible for use in a hybrid car. Additionally, the induction

machine makes execution of regenerative braking relatively simple. Regenerative

braking is a means of using the induction machine as a brake. It is anticipated that the

outcomes from this thesis project support the claim that an induction motor is a better

means of motivating a hybrid or an electric car.


2 The literature review This section of the thesis report reviews the focal sources of information that were

required to compile this thesis project.

2.1. The Hybrid car concept

Honda and Toyota only released the Hybrid car this year. Knowledge of its operational

principles is not commonly known. The web-site, How Stuff Works, is an educational

site that is written by Mr. Marshall Brain. It provides a basic introduction onto how a

hybrid car works. Within this article, the definition of the hybrid car and its potential

advantages are stated. The concept of the parallel hybrid car is presented. This is a car

design that simultaneously utilizes both the combustion engine and the electric engine to

turn the wheels. Mr. Brain also offers an explanation on how commercially released

hybrid cars (the Toyota Prius and the Honda Insight) work.

2.2 Induction Motor Theory and Practice

Wildi [1] is an excellent source of information on the theory behind the operation of an

induction motor. The three-phase induction machine is presented in Chapter 13. The

electromagnetic and mechanical phenomena that are responsible for the induction

motors many advantages are clearly explained. Wildi also presents the two types of

induction motors: the squirrel cage induction motor and the wound motor. An

explanation of the advantages and disadvantages of each is given. Essential concepts

such as synchronous speed, slip, torque and the rated electrical inputs are presented

and exemplified with example problems. The equivalent electrical circuit for an induction

motor is derived based on the three-phase transformer.

This book also presents the fundamentals of the induction motor from a practical

viewpoint. The small and large motor types are distinguished, where the typical electric

and mechanical characteristics of each are shown. In the later chapters (20 to 23), Wildi

takes the reader through some of the existing methods of driving an induction motor:


Static frequency charges

Static voltage controllers

Rectifier-inverter systems with line commutation

Rectifier-inverter systems with self-commutation

Pulse-width modulation systems

Pulse-width modulation systems are the only control schemes that can be considered for

this thesis as the motor controller is specifically designed for Pulse-width modulation.

The text by Mohan, Undeland and Robbins [2] gives good explanations on the operating

principles of the induction machine. Concepts such as operating the induction motor in

the constant torque region, volts per hertz control, starting up considerations and driving

an induction machine with a three-phase bridge inverter are explained.

2.3. Power Electronics

Operation of the motor controller board requires knowledge of how the power electronic

aspects work. Mohan Undeland and Robbins [2] provides chapters of information on

power electronics; Dr. Geoff Walker utilizes this text to teach his Power Electronics

subject. In chapter two, all the current power-switching devices are presented. These

are: the Diode (the various types of diodes are presented and compared), the Bipolar

Junction Transistor (BJT), the Metal Oxide Field-Effect Transistor (MOSFET) and the

Insulated Gate Bipolar Transistor (IGBT). In this chapter, the requirements of a

switching device are also stated. The general desired characteristics of a power switching

device is to have a high blocking voltage in the reverse direction, to have minimal

switching losses (this is related to fast switching ability) and the power device is required

handle a sufficient amount of average forward current. It is found that the MOSFET

provides the minimal switching losses and is, hence, well suited for voltage switching

purposes.


In chapter eight, the basic switching topologies are outlined. An inverter is an electronic

configuration that transforms a DC signal into an AC signal in a controlled manner. This

is very relevant for this thesis project as we have available a DC supply and the induction

motor requires an AC supply that needs to be controlled to a certain degree of accuracy.

It compares how each topology generates harmonics. It discusses utilization of the

supply voltage. All voltage-switching designs require a modulation chip to generate

Pulse Width Modulated (PWM) signals that are applied to the gate of the power

switching devices. There are two types of PWM outlined: sinusoidal and square-wave.

While square-wave switching utilizes the supply voltage better, the harmonic content of

the output waveform is too high to really be considered an effective solution. Therefore,

sinusoidal PWM is the best option based on the literature provided in this text. Later in

the chapter, they talk about dead-time, which is a time delay that needs to be

introduced to the square-wave to avoid commutation of the power switching devices.

2.4. Field-Orientated Control

Bimal K. Boses book that he edited in 1996 [4] presents extensive explanations on FO

control. Concepts that comprise Field-Orientated (FO) control such as the rotating and

stationary reference frames, Clarke and Park transforms, PI controllers and PWM are

extensively explained. Bose also exemplifies some MATLAB models that can be used to

simulate FO control. In the later stages, self-tuning and sensor-less FO control are

investigated. Bose also offers the reader general explanations on microprocessors and

how they are the central control means of FO control.

The Texas Instruments Literature Document BPRA073 also presents theoretical and

practical clarifications on FO control. However, they present their DSP controller device,

the TMSC320C240. This device is specifically suited to motor control techniques such

as FO control. In BPRA043 [10], example assembler code used to execute FO control is

offered. Texas Instruments Technical Document BPRA076[17] provides an extensive

practical detail of how to apply FO control to an induction motor.


2.5. MATLAB analysis

The book, Control Systems Engineering[7] is dedicated to presenting the concepts of

generating a control design. Furthermore, MATLAB is extensively used through the

course of the book. However, Dynamic Simulation of Electric Machinery using

MATLAB/SIMULINK[6] is a book that specifically presents how to apply FO control

in MATLAB, how to model an induction motor in MATLAB and the control design

aspects of FO control.


3. The Hardware Design 3.1. The basic control format

In essence, we are endeavoring to design a controller that can vary the torque induced in

the rotor of the motor. To do this, the induction motor controller will be configured in

the following format:

Figure 3.1. The basic physical design [16] The user applies an input signal (e.g., the throttle of the car) that will be fed into the

command generator of the DSP controller. The DSP controller will manipulate this

control signal to produce signals that the induction motor can operate off. These signals

will be converted to PWM (Pulse-Width Modulated) signals so that the Full-bridge

MOSFET (Metal-Oxide Silicon Field Effect Transistor) inverter on the motor controller

can amplify these signals to substantial voltage levels. It is anticipated that the amplified

PWM signals will then induce a torque in the rotor of the induction motor that is

proportional to the magnitude of the input signal applied by the user. The design will

utilize an encoder that sends down pulses that can be manipulated to calculate the speed

and position of the rotor. The encoder pulses and the measured currents drawn by the

induction motor form the feedback portion of the design. Hence, the major aim of this

thesis project is to develop a control strategy for the DSP controller that controls the

torque production within the induction machine. However, there is no great emphasis

placed on precise torque control.


3.2. The existing motor controller

David Finns motor controller board can be seen in figure 3.2. There are two main

features that are of particular relevance to this thesis project:

A. TMS320F243 DSP controller: provides several key functions of different nature,

in particular, signal filtering, regulation, drive signal generation, measurement,

monitoring, protection and more. The speed at which we need to execute the control

algorithms and detect signals in the control feedback loop suggests the requirement

for an advanced Digital Signal Processor. The TMS320F243 is specifically designed

for Digital Motor Control. This device combines a 16 bit fixed-point DSP core with

micro-controller peripherals in a single chip solution that is part of a new generation

of DSPs called DSP controllers[15]. This DSP controller is built with a Harvard

architecture, where the data and the instructions occupy separate memories and travel

over separate buses[16]. Because of this dual bus structure, the processor can fetch,

simultaneously, an instruction and a data operand. Pipelined operation of instructions

and data transfer is thus possible, resulting in higher instruction throughput rate[4].

This DSP controller is capable of executing 20 million instructions per second.

This DSP controller offers the following:

12 PWM (Pulse Width Modulation) outputs. Six of these will be utilized to

drive the three-phase MOSFET bridge inverter on the motor controller board.

UART (Universal Asynchronous Receiver and Transmitter), this allows for

communication to occur between the PC and the motor controller. Therefore,

data acquisition, debugging and fault logging are realized.

2 fast A/D (Analogue to Digital) converters with 10-bit resolution make the

computation of accurate, real-time phase current measurements possible.

Many more features that will be mentioned through the course of this report.


Figure 3.2. The existing motor controller board B. The Power Electronics Design: three half-bridge circuits combine to form a

three-phase full-bridge inverter. The semi-conductor switches are high quality

MOSFETs that feature sufficient switching efficiency and blocking voltage for

applications of this nature. Within the DSP controller, the software generates three-

phase sinusoidal signals. These are then converted to 6 PWM signals in the DSP, one

for each MOSFET on the full-bridge inverter. Because the PWM signals are square

waves of varying duty-ratio, we can use the MOSFETs to amplify the PWM

waveform to significant voltage levels that the induction machine can operate off.

PWM generation through the software design is discussed in Chapters 5 and 7.

3.3. Current sensing module

The implemented current-sensing module consists of two current transducers. Because

the stator windings of the motor are a three-phase wye connection, we can use the

following relation to find the other unknown current magnitude:

0 = Ia + Ib + Ic (3.1)

Where Ia, Ib and Ic are the three-phase stator currents.


However, application of an effective current sensing module requires the designer to

consider that the DSP A/D converters operate within a voltage range of 0 to +5V. The

problem with this is that the currents sensed by the transducers are sinusoidally

oscillating between +2.5V and 2.5V. Therefore, a DC offset of +2.5V will have to be

continually added to the current signal to ensure that the current does not drop below 0.

Furthermore, the amplitudes of these signals would be greater than +2.5V.

Consequently, we would need to insert resistors on the bus to attenuate the current signal

appropriately. The existing motor controller applies all of this.

Figure 3.3. The current sensing module [17]

The added 2.5V offset is subtracted from the A/D conversion result in the PWM service

routine of the controllers software (see Chapter 7).

3.4. The speed sensor

On the shaft of the rotor is an encoder. The encoder generates 500 pulses per revolution

in a square-wave format. Furthermore, the encoder generates two pulses, A and B,

which will allow the DSP controller to detect the direction of the rotor; the B pulse lags

the A pulse by 900 in the positive direction. The DSP controller detects rising and falling

pulses on its interrupt pins; therefore, the DSP controller is effectively detecting 2000

pulses per revolution. Based on this, the software section of the design must interrupt the

speed of the rotor based on the number of pulses it receives. The rated speed of the

induction motor used in this thesis project is 1500rpm, which is 25 rps. Therefore, the

DSP controller will receive:


(2000 pulses per revolution) 25 (revolutions per second)

= 50 103 pulses per second at rated speed.

Every time a pulse is detected, the existing integer number in the free-running counter of

the DSP controller is latched into a register that the software design can read (T2CNT).

Therefore, if the software design compares a new count(the current value latched in the

T2CNT register) to an old count (the previous value), the following formula can be

applied to calculate the speed:

Speed = Clock rate (encoder rate (new count old count)) (3.2)

[(revolutions per second) = (counts per second) (revolutions per pulse) (pulse per count)]

If the induction machine was rotating constantly at the rated speed, the count difference

between consecutive encoder pulses will be (the clock speed is 20 MHz):

Count difference = 20 MHz (counts per second) (50 103 pulses per second)

= 400 counts per pulse.

If we now apply formula (3.2):

Speed = 20 MHz / (2000 400) = 25 rps

Also, the detection of a pulse means that the rotor has progressed by:

(3600 per revolution) (2000 pulses per revolution) = 0.180 per pulse.

Considering the rate that pulses are detected, the resultant resolution of the positional

angle of the rotor seems to be more than adequate for torque control for this project. If

the resolution of the rotor angle was not satisfactory, the software design would have to

interpolate between the pulses. This is discussed in the software section (Chapter 7).


4. The Induction Machine

4.1 The fundamental operating principles for an induction motor

An induction motor is an asynchronous AC (alternating current) motor. The least

expensive and most widely used induction motor is the squirrel cage motor. The major

reason why these machines are so robust and inexpensive is that no external current is

required inside the rotor to create the revolving magnetic field. An induction machine

consists fundamentally of two parts: the stator (the stationary part) and the rotor (the

moving part). For a three-phase induction machine (this will be used in this thesis

project), three-phase sinusoidal voltages are applied to the windings of the stator. This

creates a magnetic field. Because the voltages differ in phase by 1200 with respect to

each other, a revolving magnetic field is created that rotates in synchronism with the

changing dominant poles around the cylindrical stator.

The rotor, which, for a squirrel-cage rotor consists of copper bars in a cylindrical format,

follows the created revolving magnetic field. As a consequence, a voltage is induced in

the rotor bars that is proportional to the relative angular speed of the magnetic field (this

is referenced to the angular speed of the rotor). Because a voltage is induced, magnetic

fields are created around the rotor wires. The two generated magnetic fields (in the rotor

and stator) interact to generate a force that is also proportional in magnitude to the

relative angular speed of the magnetic field. Torque is equal to force multiplied by the

radius of the cylindrical stator. Therefore, the resultant torque applied by the rotor is

proportional to the relative speed of the magnetic field with respect to the speed of the

rotor.

4.2 The Electrical principles of an Induction motor

The induction machine is an electrical device. The electrical properties that are of

particular interest to this thesis project are the stator and rotors resistance and

inductance, as well as the magnetizing inductance. During steady state, the induction

motor can be modeled in a per phase representation seen in figure 4.1.


Figure 4.1. The per phase representation of an induction motor in steady state [17]

These parameters are important for the control strategies that will be presented in chapter

5. The induction machine used in this thesis project has the following electrical

parameters:

E = rated phase voltage, 127 Vrms

P = power rating, 500W and 0.67hp

p = Pole pairs, 2

rs = stator resistance, 4.495

rr = rotor resistance, 5.365

xs = stator inductance, 16 mH

xr = rotor inductance, 13 mH

xm = magnetizing inductance, 149 mH

Mnom = rated Torque, 3.41 Nm

J = rotor of inertia, 0.95 10-3 kg m2

Hence, the full-load current for this three-phase motor can be calculated using the

following approximate equation:

IFL = 600 PH / E (4.3)

= 600 0.67 / 220

= 1.82 A


4.3 Torque/Speed generation for an Induction motor

The angular speed at which the magnetic field rotates is called the synchronous speed,

while the angular speed by which the rotor falls behind is called the slip speed.

Synchronous speed, ns = (120f) p (4.1)

= (12050) 4

= 1500rpm in this case

Slip, s = (ns n) ns (4.2)

Where f = the rated frequency of the motor, p = the number of poles and n = the angular

speed of the rotor.

An induction motor never travels at synchronous speed; this is why they are referred to as

asynchronous machines. When no load is applied to the rotor, the induction machine has

a slip of 0.5%. When the rotor is locked, the slip is, of course, 100%. At locked-rotor

conditions, the current can be five to six times the full-load current, making I2R losses 25

to 36 times higher than normal. For this reason, it is not recommended to leave the rotor

locked for more than a few seconds [1]. The torque speed curve for the type of induction

motor used in this thesis project can be seen over-page.


Figure 4.2. The torque speed curve for the induction machine at the rated voltage used in this thesis

As you can see, there is no simple relationship between speed and torque, this is why

inspection of this curve is so important. Breakdown torque represents the maximum

torque that the load can apply before the induction motor is unable to develop speed. The

nominal speed is the angular speed that the induction machine accelerates toward for a

given voltage and frequency. Therefore, by applying different voltages of different

frequency (voltage and frequency have to increase by the same proportion in order to

maintain a constant rotor flux), we can rotate the induction machine at a wide range of

nominal speeds and rated torque values. By changing the developed nominal speed, the

torque speed curve is shifted horizontally along the x-axis.

Usually, the speed operation of the motor has an upper limit that is equal to the rated

speed of the motor. Operation of the induction motor above the rated speed affects the

drive efficiency and torque production due to heat dissipation and magnetic saturation

[17]. Therefore, the rotor flux must be reduced so that the range of high efficiency

operation of the motor drive is extended. Consider the figure seen below:


Figure 4.3. The field weakening operation As can be seen, by maintaining a constant flux, increasing the applied voltage and

frequency can proportionally increase the nominal speed. However, outside the rated

speed operation, the flux has to be decreased like an inverse function of speed. By

weakening the rotor flux, the induction machine can reach speeds that are four times the

nominal speed [4].

In summary, the major design considerations for driving an induction motor are:

The voltage (both magnitude and frequency) applied to the stator windings (is) is

proportional to the created speed/torque of the rotor.

(rotor flux) ! needs to be maintained constant when operating in speeds below

the rated speed. Anything above this, the speed needs to be decreased in an

inverse, non-linear fashion. Hence, we need to develop a control strategy that varies the frequency and voltage of the

signal applied to the windings of the induction motor, while controlling the flux created

in the air-gap of the induction motor. This will be shown in the next chapter.


5. Field-Orientated Control (FOC) 5.1. An introduction

A DC machine has traditionally been a superior choice for torque control. The

commutator of the DC machine holds a fixed, orthogonal spatial angle between the field

flux and the armature MMF, allowing for the torque and flux to be controlled in a de-

coupled manner [4]. Induction machines, via FOC, can emulate this control method.

FOC control is a software algorithm that utilizes the position of the rotor combined with

two-phase currents to generate a means of instantaneously controlling the torque and

flux. Field-orientated controllers require control of both magnitude and phase of the AC

quantities and are, therefore, also referred to as vector controllers. FOC produces

controlled results that have a better dynamic response to torque variations in a wider

speed range compared to other scalar methods. Also, FO control can induce a high

torque at zero speed.

To simplify equations and to provide a control over torque production in a

straightforward manner, both stator and rotor equations are expressed with respect to a

common reference axis. This axis is along the rotor field r, at a rotor flux angle rf with

respect to the stator s1 axis (a axis in figure 5.1). In order to express the torque in terms

of the rotor flux r and the stator current, an orthogonal d-q axes reference frame is

introduced. The direct (d)-axis is always aligned with the rotor flux r, while the

quadrature (q)-axis is always 900 ahead of the d-axis. The current space vector can be

decomposed along the d-q axes as:

is = isd + jisq (5.1)


Figure 5.1. The transformation of the stationary reference frame to the rotating reference frame [9]

Hence, the FOC concept implies that the current control components applied to the

system are in-phase (flux component) and in quadrature (torque component) to the rotor

flux r. By locking the phase of the reference system such that the rotor flux is entirely in

the d-axis (d-axis), the following mathematical constraint eventuates:

qr = 0 (5.2)

The electromagnetic torque developed by the motor can, hence, be shown by

Tem = kt dr isq (5.3)

Therefore, the stator current along the quadrature axis is given by:

isq = Tem (kt dr) (5.4)

Finally, the following relation can demonstrate the rotor-flux along the direct axis:

dr = kr isd (5.5)

The stator current along the direct axis is given by:

isd = dr kr (5.6)

Where kt and kr are constants that depend on the stator and rotors resistance and

inductance. Having equations that are dependent on variables that describe the motor

will consequently result in better control over torque variations. By maintaining dr and,

therefore, isd at a constant value, the electromagnetic torque developed by the rotor Tem is

completely determined by the stator current along the quadrature axis, isq, as seen in

equation (5.3). Therefore, isq becomes the desired torque control command.

5.2. Transformation between reference frames

It was found in the previous section that the DSP chip and the designer require two

current control quantities, isq and isd, that are referenced along a rotating axis.

Furthermore, the induction motor requires three stationary voltage inputs that are each

1200 apart. In order to transform the two rotating input quantities into three stationary

output quantities, we need to perform the Inverse Clarke and Park transformations. See

figure 5.1 for the way this transpires on the vector diagram.


(d,q) ! (, ) the Inverse Park transformation. This projection transforms the d,

q rotating reference frame to a two-phase orthogonal system (, ). It utilizes the

positional angle of the rotor flux () to do this:

The Inverse Clarke transformation, modifies a two dimension orthogonal system

(, ) into a three-phase system (a,b,c):

To obtain the positional angle of the rotor flux we require, firstly, an encoder connected

on the shaft of the rotor; this is used to detect the position of the rotor (with the assistance

of software). Secondly, we need to calculate the slip angle. This is computed by using

Hence, the rotor flux angle is given by:

= (slip + rotor) dt (5.11)

Where: Lm = the magnetizing inductance, Tr = the rotor time constant (= rotor inductance

rotor resistance) and r is the estimated rotor flux.

5.3. The PI controller

The PI controller is an effective means of regulating torque and voltage magnitudes to the

desired values. It also improves the steady state error and the error sensibility [4]. This

is achieved by providing a gain for the error term with an integral component correction.

Kp is the proportional gain and Ki is the integral gain of the feedback loop. The PI

controller will be executed completely in the software section of the design. Via

(5.8)

(5.10) Lm isqTr r

=slip

isaisbisc

=isis

" 0

-# $#

-# -$#

(5.9)

isis

=cos -sinsin cos

isdisq


MATLAB analysis, we have to find the necessary poles and zeros for the design so that

the transient response is quick and steady state errors are minimized.

Figure 5.2. The PI controller

There are four PI controllers used in this design. The first PI controller is called the

torque controller as it calculates the required electromagnetic torque required by the

motor. The other three are used in the current controller section of the design from the

speed error signal. These PI controllers regulate the voltage into the induction machine

by making sure that the induction machine is not drawing too much or too little current.

5.4. PWM Pulse-Width Modulation

The objective of PWM is to shape and control the three-phase output voltages in

magnitude and frequency by utilization of a constant DC voltage. PWM is a process

where three-phase sinusoidal signals are compared with a repetitive switching frequency

triangular waveform. In the software design, the DSP core will cause periodic interrupts

where the three sinusoidal values are fed into 3 compare registers (see Chapter 7). The

TMS320F243 DSP will create the desired symmetrical synchronized PWM through the 6

PWM signal generators. The 6 PWM signals are applied to the 6 MOSFETs on the three-

phase inverter on David Finns motor controller via the MOSFET drivers.

The frequency of the triangular wave is 20 kHz. This is compatible for use with the

MOSFETs existing on David Finns motor controller board. In spite of this, because of

the finite turn-on and turn-off times associated with any type of switch, the design

requires the inclusion of slight time delays when the MOSFETs are switching. A dead

band is the time delay between switching off one MOSFET on a phase of the inverter and

switching on the complementary MOSFET. This ensures that any time delay in

CorrectionError

Error Kp

Error Ki

+

+

Command signal

-

Feedback signal


switching off a device does not lead to a shoot-through short circuit that can damage the

circuit when its partner is switched on.

Figure 5.3. Leg A on the full-bridge inverter If you turn your attention to figure 5.4, when PWM 1 is positive, MOSFET A+ will

conduct. When PWM1 is zero, its compliment, PWM2, will be positive, thereby, turning

MOSFET A- on. This will connect ground to the phase A connection for the duration that

PWM2 is on. From the point of reference of the induction machine, it sees a line-to-line

voltage relationship between phase A and phase B (VAB = VA VB). This is because it is

connected in a three-phase Y format, this can be seen in Figure 5.5. As a consequence of

this, a sinusoidal signal is created (see the figure below).

Figure 5.4. PWM VSI schematic and waveforms [2]


Therefore, the FO control design is essentially applying line-to-line voltages to the

induction machine from its point of reference. The induction machine will draw currents

that are determined by the inductance and the back EMF. The PI controllers that feature

in the current controller section of the design regulate the current drawn by the induction

machine.

5.5. The Overall Design

Following theoretical considerations, a block diagram of the complete FO controller can

be seen over the page.

The design employed here is referred to as Indirect Field Orientation. This is because

this method uses a speed sensor in the feedback loop instead of a hall sensor that the

direct method uses. * is the input applied by the user (the throttle of the car). This is

compared with the attained speed of the rotor that is obtained from the speed sensor.

This is then converted into an electromagnetic torque signal Tem* via the torque controller

(this is a PI controller). The obtained speed of the rotor is also used to set the required

rotor flux r* that is needed to be created in the air-gap induction motor. The Field-

Weakening Block compares the incoming speed value and outputs a desired flux value.

For the most part, the induction motor requires constant rotor flux, however, at high

positive and negative speeds, the Field-Weakening Block will have to decrease the output

flux in a non-linear fashion. The Tem* and dr* signals are then converted into isd and isq

signals using equations (5.4) and (5.6) that were stated above.

These values, that are in the rotating reference frame, are then converted into three-phase

a, b, c values that are referenced in the stationary frame via inverse Clarke and Park

transformations. The inverse Clarke transform requires the quantified positional angle of

the rotor that is obtained from the rotary encoder. This is added to the slip angle to equal

positional angle of the rotor flux, rho. The calculated three-phase sinusoidal current

values are then compared with the measured stator currents. The three-phase error

currents are then fed into current controllers. These are blocks that contain PI controllers

that convert the current signal into a voltage signal. Also, the current controllers contain


saturation blocks that limit the amount of voltage that can be applied to the next stage.

The sinusoidal voltage signals are converted to PWM signals. These PWM signals are

then amplified by the three-phase MOSFET bridge inverter on the existing motor

controller and fed into the stator windings of the induction machine.


Figure 5.5. The complete FO controller design in a block representation


5.6. Conclusions drawn from Chapter 5

It is concluded that FOC provides a reliable and effective means of controlling torque and

flux. For this project, there is basically one variable torque input (the throttle of the car),

which can directly control the torque of the induction motor by means of FOC.

Furthermore, FOC facilitates four-quadrant operation, full motor torque capability at low

speeds and higher efficiency (compared to the traditional Volts/Frequency control

method) for each operation point in a wide speed range [4]. Therefore, FOC is elected as

the means of motion control for this thesis project. This complete design will have to be

tested in a computer simulation program called MATLAB. All of this design discussed

except for amplification of the PWM signals will comprise the C-code design that will be

downloaded into the DSP controller.


6. The MATLAB design

The MATLAB design constructed is used to simulate the final FO control design where

all parameters, processes and variables are modelled mathematically. Furthermore, the

MATLAB program can convert a MATLAB design into a C-code design in a relatively

straightforward manner. Hence, this stage of the thesis project is seen to be of great

importance.

6.1. MATLAB An introduction

MATLAB is a computer simulation program developed by Math Works Inc. Embedded

within MATLAB version 6 is SIMULINK. This is a program that allows the user to

create mathematical blocks with inputs and outputs; highly suited to designing a control

system of this nature. A proper explanation of MATLAB is beyond the scope of this

report. However, one key feature is that it allows you to simulate your design over a

specified period of time. This way, you can analyze the time response of your control

system.

6.2. MATLAB simulation design

A MATLAB control design ultimately allows the designer to check its correctness. All

the blocks that were shown in figure 5.6 can be represented by mathematical formulae.

However, there is a great difficulty in properly simulating an induction machine.

Development of an induction machine SIMULINK model is a quite complex and

extensive process. The problems that can eventuate from this are, firstly, that the

building of a correct model is a long and difficult process. Secondly, if there exists a

problem in the generated induction machine design, trouble-shooting through the

induction machine model is a very long and tedious task; this student experienced this.

Finally, you will never be able to properly model an induction machine. This is because

of unpredictable parameters such as temperature, magnetic flux saturation etc. In spite of

all this, we can get a good general feel for how the device operates and, more

importantly, that it by and large works.


6.2.1. Field Orientation Control using SIMULINK The complete MATLAB model can be seen below in Figure 6.2. This SIMULINK

design essentially employs all the basic principles of indirect field-orientation that was

discussed in the previous section. As mentioned, the speed of the rotor is used to set the

desired rotor flux that will be induced in the air-gap of the induction machine. To do this,

we use a Look-Up Table block called lambdare^r* on this design. The Look-Up

Table matches the desired value of rotor d-axis flux to that of the mechanical speed, rm. For speeds less than the base or rated speed, the rotor flux command is set equal to its no

load value with rated supply voltage, as determined by [6]:

(vqse jvdse) = (rs + jweLs) (iqse jidse) + (Eqs jEds) (6.1)

Beyond the base speed, the flux speed constant is set at the base speed value. The values

of dr* and mechanical speed are generated by an m3 file (this can be seen in Appendix

E).

Figure 6.1. The Look-Up Table block

There are two inputs into this system, * and T_load. The fundamental intention of this SIMULINK design, is that the FO control portion of the design will cause the rotor to

generate a speed profile that follows the commanded speed input, *. To do this, the commanded speed signal is fed into the FO section of the design where it is subtracted

from the measured speed of the rotor. The error generated is then fed into a torque

controller block. The torque controller block is a PI controller that generates a Torque

command, Tem*. This torque command is used to set the electromagnetic torque induced

within the induction motor by calculating an appropriate iqs* command based on the

generated Tem* signal and using equation 5.4.


Figure 6.2. The complete SIMULINK design


Tem*, lambdare_r (the signal produced from the look-up table), along with theta_r

(the integral of the speed of the rotor) are fed into the FO_Controller block.

Figure 6.3. The FO_Controller block

The constants used in this block are equal to:

Gain_G1 = (4*xr)/(3P*xm) = 0.05817

Gain_G2 = 2/P = 0.5

Gain_G3 = 1/xm = 6.711

Gain_G4 = xr/(rr*xm) = 0.0163

Gain_G5 = xm*rr/(lamdare_est*xr) = 177.72

The FO_controller block mathematically calculates iqs^e*, ids^e*, cos_rho

and sin_rho by using equations 5.3 to 5.10. All of these are the outputs of this block

and are the inputs of the next block, the dqe2abc block. The FO_controller and

dqe2abc blocks regulate the sinusoidal currents applied to the current_controller

according to the commanded electromagnetic torque, Tem* and the rotor flux,

lambdare_r. The dqe2abc block can be seen below. It utilizes the inverse Clarke and

Park transformations; methods used to transform values referenced along the rotating

reference frame, into values referenced in the stationary frame, by using equations 5.8

and 5.9. isq and isd, are used to set the magnitude of the current sinusoidal values


produced by the dqe2abc block. rho sets the frequency or angular displacement of the

signals.

Figure 6.4. The dqe2abc block

Figure 6.5. The Inverse_Park_Transform block

Figure 6.6. The Inverse_Clarke_Transform block


6.2.2. The Current Controller The primary purpose of this block is the to regulate the voltage signal applied to the

induction motor. The phase currents measured from the feedback portion of the circuit

(ia, ib, ic) are subtracted from the commanded currents (ia*, ib*, ic*) The

error generated is fed through PI controllers. After this, it is amplified to significant

voltage levels that the induction machine can operate off.

Figure 6.7. The Current_Controller block

6.2.3. The Motor Model We are trying to simulate a three-phase, 4-pole symmetrical induction machine in the

stationary reference frame with winding connections. For small dynamic stability

analysis, a synchronously rotating reference frame yields steady-state values of steady-

state voltages under balanced conditions [6]. We need to build a model that includes the

stator and rotor flux referenced along the d-q axes. This is because these values are used

to calculate the voltages induced in the rotor. Once again, calculations are greatly

simplified when all quantities are referenced along the d-q reference frame, however, in

this case, the d-q reference frame is stationary. Therefore, the angular position of the


2Jb d(r/b) = Tem + Tmech - TdampP dt

rotor is not required to make the transformations. The abc2qds block seen in figure 6.2

performs this transformation. The interior of the induction machine in

stationary qd0 block can be seen below:

Figure 6.8. The Induction machine in stationary qd0

Explanation of the operation of this block is of no great relevance to this thesis. In short,

this block allows the designer to:

By using this equation:

(6.2)

The rotor mechanical speed can be calculated, which is essential for the whole

operation of this SIMULINK design.

Observe the dynamic response of this vector control method

See how well such a control keeps the rotor flux constant during changes in load

torque.


6.3. Simulation of the MATLAB design

Simulation of the proposed MATLAB design is seen in Figure 6.2 is considered to be of

significant importance to the success of this thesis project. While simulation gives an

excellent insight into how well the design works, it also allows the designer to witness

first-hand how all the sub-systems within FO control work together to produce the

desired outputs. Hence, the designer can attain a deeper understanding of how FO

control works. This knowledge is found mainly through the use of Scopes. A scope is

a SIMULINK block that displays signals at nodes during simulation. The displayed

signals from the scopes are the basis for discussion in this section of the report. The

simulation studied occurred over 2 seconds. The integration method used is variable-

step, the Dormand-Prince method with an initial step size of 0.0005s. Indeed, to

effectively use this integration method with sine and cos functions would require a micro-

controller with high processing power. This highlights why the TMS320F243 DSP

controller is used for an application of this nature instead of the conventional Atmel,

HC11 etc. chips.

6.3.1. Speed response analysis The speed response of our designed control system is the outcome that is of the utmost

significance to this section of the thesis project. By feeding an input speed command into

the system, we are going to observe the speed developed by the rotor of the induction

machine over time. The two major criteria that we are trying to fulfill are:

1. That the system develops a speed response that closely resembles the input

speed command.

2. That the system is stable (stability is the most important design

specification for any control system [7]).

Other criteria that we are looking to achieve are a quick transient response (quick

acceleration) and a response that is smooth.


Figure 6.9. The MATLAB speed simulation results

For the simulation conducted, the speed input fed into this system (in figure 6.2) ramps to

200rpm for the first 0.5s and then remains at 200rpm for the remaining 1.5s; this can be

seen in figure 6.9. The other curve, which resembles an over-dampened second-order

control system response, is the actual speed developed by the motor. The major

conclusion that can be drawn from this graph is that our design works and there is no

substantial indication of instability. The speed response curve adequately resembles the

speed command curve. From figure 6.9, it can be seen that when the speed input

command is constant, the speed response is relatively constant. Therefore, it is concluded

this system is acceptably stable. Recalling that this motor control scheme would only be

used to drive a hyper or electric car, it is concluded that this speed response is

satisfactory.

For this simulation, the steady-state error is 8 rpm, which is 4%. Let us say, for argument

sake, that 200 rpm is equivalent to 60 km hr-1 for our electric car. Furthermore, the user

provides the input speed command by applying a force on an accelerator pedal. A


steady-state error of this magnitude is not of any real concern as the user will simply

press the accelerator pedal down until he/she sees that the speed developed by the car is

60 km hr-1 via reading the speedometer on the dashboard of the car. However, inspection

of figure 6.9 would suggest that there is room to speed up the transient response. To do

this, we would have to add more proportional gain to the torque controller (the PI

controller for the speed error signal) [7]. Therefore, an experiment was conducted where

the proportional gain was increased from 30 to 60. The results can be seen below:

Figure 6.10. The speed response of the control system where the proportional gain of the speed

controller is increased

As you can see, the transient response is faster as it follows the speed command slope

more closely. The problem with this speed response is that the ramp response is not very

smooth; instead, it is quite coarse and jagged. This indicates the existence of high

frequency components that have significant voltage magnitudes. This could be either

noise or harmonics. Both of these affect the short-term and long-term performance of the

induction machine. According to Bose [3], harmonics can cause the following to an

induction machine:


Harmonics:

Can cause torque and speed disturbances (cogging and frequency beats)

Can cause motor overheating due to excess iron and copper losses

Causes motor current transients that overtax the inverter commutation ability. Furthermore, these high frequency components would strain mechanical components that

are connected to the rotor. One important point that should be reinforced is that

MATLAB is a program that models all the physical processes involved with this motor

controller mathematically. It does not consider variables such as heat, magnetic

saturation etc. With the presence of high frequency components, we have not seen how

these variables or a rapid speed response may affect the operation of the induction

machine. If we now increase the proportional gain from 30 to 90, the system becomes

unstable as can be seen in Figure 6.11. Our speed control signal has no significant

influence on the speed developed by the motor, therefore, our control design is no longer

adequately controlling the induction machine.

Figure 6.11. The speed response of the system with a proportional gain of 90


Therefore, it is concluded that increasing the proportional gain of the torque controller

will:

Either amplify or introduce high frequency components into the system that will

damage the induction machine.

The system will approach instability that breaches the fundamental design

specification of any control scheme.

Therefore, the proportional gain of the torque controller is elected to be 30. Based on the

MATLAB analysis, we get an adequate transient response from this. Also, the transient

response does not feature rapid, sharp transients of any kind. It seems to be a reliable and

safe option. If one where to optimize the transient response of this system, they would

have to conduct tests physically by trial and error as MATLAB does not truly

demonstrate exactly how the induction machine behaves.

6.3.2. Analysis of the Field-Orientated Section of the Design In the later stages of Chapter 4, it was mentioned that to increase the speed of the rotor,

we have to increase the voltage and frequency by the same proportion. This ensures that

we maintain a constant magnetic flux in the air-gap of the induction motor. In this

section of the report, through the use of scopes placed on nodes of interest, we will see

that FO applies this principle of speed operation. If you turn your attention to figures

6.12 to 6.14, we see how FO control transforms the commanded DC signals applied by

the user and the feedback signals into sinusoidal signals that the induction machine

requires.


Figure 6.12. The top and bottom graphs are the cos(rho) and sin(rho) signals respectively.

Figure 6.13. The ids^e* and iqs^e* curves over time


Figure 6.14. The applied signal to phase A of the Induction motor and the drawn current at phase A

FO control is also referred to as vector control because it controls both the magnitude and

phase of the voltage signal applied to the stator windings of the induction motor. The

manner in which the phase changes over time for the cos_rho and sin_rho signals

(figure 6.12) is very similar to the way the phase voltage signal develops over

time (figure 6.14). Also, the iqs signal ramps for the first 0.5s then it remains constant

(figure 6.13). The amplitude development of the phase voltage signal has a

similar profile. Therefore, the cos_rho and sin_rho signals control the phase, while

the iqs and ids signals control the magnitude. Hence, it is through these signals (all of

which are produced in the FO_controller block) that FO control achieves vector

control. Furthermore, it can be seen that the speed is linearly increased when the

frequency and amplitude of the phase voltage signal are increased by the same

proportion.

The principle of increasing the voltage magnitude and the frequency by the same

proportion in order to maintain a constant rotor flux is the basis for applying scalar volts

per hertz speed control method. However, the equations used to execute FO control

consider the parameters of the motor, therefore, we achieve better control over torque


variations. FO control also has the advantage of extending the speed range of operation

through field weakening. Finally, FO control is a torque control method. This suits the

requirements of the this thesis control design.

6.3.3. The significance of feedback While the MATLAB design shown illustrates the behavior of a working solution, we can

use it to demonstrate how the system would operate if components failed. What speed

profile would the rotor develop without speed feedback? We can answer this question

with MATLAB. By simply removing the feedback path from the design shown in figure

6.2, we can see how the system operates without feedback. This highlights why

MATLAB analysis is an intrinsic stage in the development of a working motor controller.

Observe the figure below:

Figure 6.15. The speed response of the system without feedback i.e. the open-loop response of the

system

As can be seen, there exists no adequate control over the steady-state response of the

system. Hence, it has no stability. Furthermore, the transient response is erratic and


uncontrolled. This simulation highlights the need for feedback in this system. Because

of this, it is very important that the encoder actually works and that we execute the speed

feedback analysis correctly in the software design. If not, the induction motor will travel

to speeds that are higher than we command and the system will become unstable. For an

application such as a hyper or electric car, this would not be very good at all.

6.4. The conclusions drawn from Chapter 6 We saw how FO control on an induction motor can be modelled and tested using

SIMULINK.

By simulating the control system shown in figure 6.2, we found that this

developed a good speed response and there was adequate stability.

It was concluded that the torque controller should have a proportional gain of 30,

as this seems to be the safest and most reliable option based on the simulation

results.

Increasing the proportional gain of the torque controller will either introduce or

amplify noise and/or harmonics. This affects the short-term and long-term

performance of the induction machine. Also, by increasing the proportional gain

of the torque controller, the system approaches unstable regions of operation.

In Chapter 4, it was stated that to increase the speed of the rotor, we have to

increase the magnitude and frequency of the voltage signal by the same

proportion. We found that FO control emulates this principle.

From the simulation results of the system without speed feedback, we witnessed

that the speed response becomes unstable and dangerous.


7. The Software Design

7.1 A basic overview of how the software is organized

This section of the thesis project is concerned with formulating a software design that

will instruct the DSP Controller to the extent that the design can control the torque and

flux of the induction motor in a decoupled manner. The software design is the point of

convergence for this thesis project. This is because it is the point where all theories and

practices presented through the course of this report come to together to form an

appropriate software design. The DSP controller commands the operation of the

hardware by the use of the software design. The constructed software design is a C-code

design. Programming DSPs in a high-level language such as C provides portability and

maintainability. This allows for the program to be prototyped relatively quickly (relative

to producing an assembler design) and the program can be optimized to this particular

Figure 7.1. The flow-chart for this thesis project

Start

Initialize Parameters and ISRs. Write to the registers used for PWM, Encoder detection, ADC and SCI

while (1)

Calculate the desiredspeed input in rps

Calculate the 3 phase currentsdrawn by the induction motor

Calculate the required

electromagnetic torque

Calculate the

required rotor flux

+_

Calculate the commanded iqs^e*, ids^e* and

Calculate the required three phase currentsusing Clarke and Park transforms

+_

Encoder ISR PWM ISR

Pulsedetection onthe QEP pins

Regular interrupttriggered by Timer1

Return

Feed the existingthree-phase voltagevalues into the threePWM compareregisters

Return

Acceleratorinput

A/D results

Calculate the speedand position of therotor.

PI controller +Voltage limitation

Phase voltages


processor architecture.

The flow-chart shown on the previous page is more complex than a standard flow chart

used for a microprocessor. One of the inherent differences between a DSP controller and

other microprocessors is that they have the ability to receive and service multiple

interrupt sources very quickly. This highlights again the need for such a sophisticated

DSP controller like the TMS320F243. The initialization section is where all the variables

and constants that will be used in the program are initialized. The method void

initalise_parm(void) initializes all the variables and constants, as well as calling

the PWM, the ISR, the A/D conversion and the Serial Communication Interface (SCI)

setup methods. In these methods, all the relevant registers associated with these

processes are appropriately written to.

The main program is essentially the Field Orientated control portion of the design. There

are two interrupt routines (this may change by the time the final product is presented).

The PWM Interrupt Service Routine (ISR) is regularly entered into in a real-time fashion.

The PWM time period is set by TIMER1, an internal register within the DSP controller

that can be set to an integer multiple of the clock period. The details of this routine will

be seen in section 7.3. The second ISR is requested when the DSP detects a pulse on

either the QEP1 or QEP2 pins from the encoder. The code embedded within this ISR

will be detailed in section 7.4. At the time this report was complied, the encoder code

was not fully tested. It is anticipated that there will be no need for an encoder ISR and

the code used to calculate the positional angle of the rotor and the speed of the rotor will

be embedded in the PWM ISR.

7.2. The Main Program The Field-Orientated Control Portion of the Software Design

This section of the design essentially emulates the processes presented in Chapter 6 from

the SIMULINK design. Referring back to figure 6.2, we are formulating a software

design that applies the initial summation block, the Torque PI controller, the


FO_Controller block, the dqe2abc block and the current controller block. It was

mentioned earlier that we could generate a C code design from the MATLAB design

using the real-time workshop. When this process was carried out, it was found that the

generated C code was not very efficient in the way it utilized the variables it declared.

Also, the MATLAB generated code used variables called temp1, temp2 etc.; this

impedes the portability and maintainability advantages associated with using C code. By

using temp variables, it is hard to see how FO control develops within the program. As

a result, it makes optimization of the code a difficult process. Hence, it is concluded that

the generated code in the real-time workshop is a good guide as to how to build the

program. However, it should not be used as the final solution to the FO control portion of

the software design.

7.2.1 The torque controller & Field weakening All the constants and variables used in the main program are declared at the start of the

program. The following flow diagram represents the torque controller and how it is used

to generate the commanded electromagnetic torque signal:

Figure 7.2. The speed error signal, wrm, is the input for the torque controller and Tem* is the output

The Speed_input signal is made available by using the SCI interface. The value of the

Speed_feedback variable is updated every time an encoder pulse is detected and the

Encoder ISR (this will be seen in section 7.4) is requested. Hence, the generated speed

error variable, wrm, is used in the torque controller section of this code. The integral gain

section of the torque controller is simply represented by Integrator1. The code used

to generate the Integrator1 value can be found in the Integrator blocks section of the

Tem*Speed error

Speed error Kp

Integrator1

+

+


software design (see Appendix A). The following code is used to generate the

Integrator1 value:

/* The calculation of Integrator1 uses the trapezoidal rule where */ /* it updates its magnitude by integrating over the time period */ /* for timer1. */

Integrator1 = Integrator1 + timer1_period*Gain_Ki*wrm;

As the initial comment suggests, the trapezoidal rule is used to integrate the wrm value. If

you turn your attention to figure 7.3, we can see how the trapezoidal rule works over time

for a constant speed error signal. Every time this portion of the code is processed, the

existing Integrator1 value is added to the TIMER1 period multiplied by the speed

error signal, wrm and the Integral gain of the PI compensator, Ki. Therefore, the software

design is effectively creating a step profile over time. This makes sense when you

consider that the integration of a constant or straight line is a linear slope. The

continuous blue line drawn in between the pink blocks in figure 7.3 demonstrates that by

using the trapezoidal rule, we create a linear slope from a constant wrm value. The

software design only requires the value of Integrator1 every TIMER1 period. Therefore,

this method more than adequately suits the requirements.

Figure 7.3. A graphical representation of how the trapezoidal rule develops the Integrator value over time for a constant speed error signal

Application of the Trapezoidal rule over time

0.00E+002.00E-054.00E-056.00E-058.00E-051.00E-041.20E-041.40E-041.60E-041.80E-042.00E-04

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

TIMER1 interrupts

The

valu

e of

Inte

grat

or1

0

5

10

15

20

25

30

35

40


If the motor controller is used over a long period of time and we do not slow the speed of

the induction motor at any stage of the operation, the Integrator1 value will eventually

reach a relatively large value. We do not want this to happen. This is because the

generated electromagnetic torque command could reach values outside the possible

operation limits of the induction motor. The other possibility is that Tem value could

overflow. Therefore, the value goes from being relatively large to be being very small in

one clock cycle. By using an if-else statement shown below (figure 7.4), we inhibit any

chance of either of these scenarios occurring.

Figure 7.4. Limiting the integration result In Chapter 6, the SIMULINK design used a look-up table to achieve field weakening.

We could create the same in this software design, however, we would have to account for

all the possible speed values. Therefore, the look-up table would be rather large and

would strain the memory limits. By using the if-else statement shown, a constant flux is

maintained below the rated speed limit. The Constant_flux sets the applied flux

signal lambdare_r to be constant at 0.571 Wb. This is fundamental when the induction

motor is operating in the constant torque region. Outside this region (the constant power

region), the DSP CPU will decrease the flux value by setting it equal to the inverse

square of the speed error signal multiplied by one hundred. The result of using this

technique can be seen over the page:

Integrator1 If (Integrator1 > Integrator1_US )

Yes

No

Integrator1 = Integrator1_US

Integrator1

If (Integrator1 > Integrator1_LS )

YesIntegrator1 = Integrator1_LS

Integrator1

No Integrator1


Figure 7.5. Calculation of the required rotor flux: Lambdare_r

Figure 7.6. The results of using the field-weakening technique used in the software design

7.2.2. Calculation of iqs^e*, ids^e*, cos(rho) and sin(rho) This section of the software design is equivalent to the FO_Controller block seen in

the SIMULINK design shown in Chapter 6. The code used to generate the FO control

variables can be seen in Appendix A. These calculated values are strongly dependent on

the rotor and stator resistance values. One design consideration that has not been

exploited by this software design, is that the rotor resistance and stator resistance values

change as the induction machine is operated over time. This is because the induction

motor heats up and the resistance magnitude of the stators windings and the rotors bars

is proportional to heat. While we do not require precise speed control, the effects of heat

Field_weakening using the if-else statement

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80 100 120

Speed error

Com

man

ded

Flux

Speed_feedback If (Speed_feedback > rated_speed )

Yes

No

Field weakening

Lambdare_r = the rated flux value

Lamdare_r

Lamdare_r


may become significant eventually. Therefore, if this software design were to be

optimized in the future, the designer should strongly consider the inclusion of a self-

tuning FO control module.

The methods used to calculate the stator currents along the quadrature and direct axis are

simply employing the formulae seen in Chapter 5. To calculate rho, the software design

uses another Integrator variable. This integrator method again uses the trapezoidal

method; the code used to create this value can be seen below:

/* The magnitude of Integrator2 gets updated over the time period for timer1 */

Integrator2 = Integrator2 + slip_speed *timer1_period;

Figure 7.7. Overflow prevention of the slip angle

This time we do not constrain the Integrator value to upper and lower limits. This is

because the Integrator2 value is essentially the slip angle that was discussed in Chapter 5.

Therefore, in order to ensure that overflow of this value never occurs, if the slip angle is

equal to or greater than 3600, 3600 is subtracted from the current slip angle value. This

will reset the slip angle value to 00 or lower. The result over time can be seen in figure

7.8; it looks like a saw-tooth wave.

After the DSP controller calculates the angle of rho, it calculates the sin and cos of rho.

To do this, it requires the utilization of functions from the maths library. This will

consume some valuable program execution time. All these values are used in the inverse

Park Transform.

Integrator2 (~Slip_angle)

If (Integrator2 => 3600 )

Yes

No

Integrator2 = - 3600

Integrator2

Integrator2


Figure 7.8. Development of the slip angle over time

7.2.3. The Current Controller section of the software design

Figure 7.9. This flow chart demonstrates how the Current Controller section works

At the start of this section of the code, there is a summing junction for the commanded

phase currents and the feedback currents. After this, each phase current error is fed

through their own PI controllers. Once again, Integration methods are employed that

utilize the trapezoidal rule and an if-else statement to limit the values calculated.

Limiting the values is very important because it prevents numbers that are either negative

or greater than the TIMER1s triangular waves amplitude from being sent to the PWM

compare registers. The PI compensators proportional gain is used to scale the current

error value.

Demonstration of the slip angle over time

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100 120 140time

slip

ang

le

Ia_command

Ia_feedback

-

+ Ia_command PI controllerVa_command

TIMER1 ISR request

TIMER1compareregister #1

16


7.3. The PWM Interrupt Service Routine The software design generates symmetrical complementary PWM signals at 20kHz

where TIMER1 is used as a time base. The TIMER1 period is set in the PWM_setup() method to be 500 (20kHz = 20Mhz/(500*2) and 20MHz is the clock speed). By setting

up the relevant registers in continuous up-counting mode, the DSP unit can generate a

triangular wave that is compared to the value placed into the three TIMER1 compare

registers. Because the design requires 6 PWM signals and we only write to 3 compare

registers, we have to set the GP TIMER1 control register into Time Source Symmetric

mode. This means that for the PWM signal on phase A, its complement is also produced.

Hence, three-phase symmetric PWM signals are generated as a consequence.

To illustrate how PWM signals are generated, we will send the following values into the

three compare registers to generate the following waveforms:

TIMER1 period register, TPR = 5h

TIMER1 compare register1, CMPR1 = 3h



Figure 7.10. The PWM waveforms generated with dead-band enabled[11]


As can be seen, the amplitude of the generated triangular wave is 5 and its period is 10.

TIMER1 compare register 3 was sent the largest compare value (4h), however, it had the

smallest duty ratio of all the non-complemented waveforms. Based on this, the PWM

process effectively inverses the number fed into the compare register.

Figure 7.11. Shows the internal infrastructure of the DSP controller that is concerned with PWM

generation (use Figure on page 7 of the dead-time generation) [11]

As can be seen in the diagram above, we have to program the GP Timer 1 register to

provide the correct PWM period. Also, the three compare units will have to be fed the

desired compare values (the three-phase current values) every time the PWM ISR is

requested. The registers associated with generating Symmetric PWM and Dead-Band

Control have to be correctly enabled.

When the GP timer is in this mode, the state of the output of the waveform generator is

determined by the following:

0 before the counting operation starts


Remains unchanged until the first compare match

Toggles on the first compare match

Remains unchanged until the second compare match

Toggles on the second compare match Remains unchanged until the end of the period.

Requesting an interrupt every TIMER1 period is fundamentally important if PWM is to

implemented. There are three steps that must be undertaken to ensure that the interrupt

service routine associated with PWM is requested at regular intervals:

1. Define the interrupt routine in the x.C file. For this software design, the

following code was used to achieve this: #define PWM_ISR c_int2

void PWM_ISR (void) {

2. An initialize interrupt method must be declared before the while (1) statement

starts running. In this initialize interrupt method, the interrupt mask register

(IMR) and the group A i

thesis design and implementation of a three-phase induction motor control scheme

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