Design and Implementation of a Three-Phase Induction Motor Control Scheme

List of FiguresFigure 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 – Th

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

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 University’s own electric car

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

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

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

Company and is one of the major components on David Finn’s motor controller For this thesis project, a software control design has to be devised that will

correctly control the DSP controller to meet specifications

12VDC to 140VDC ~40 VDC is the most compatible voltage supply for the motor controller that will be used for this thesis

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

motor’s 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 exemplifiedwith 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 Bose’s 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 Finn’s 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 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

three-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 controller’s 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 rotor’s 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

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

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 = (120×f) ÷ p (4.1)

= (120×50) ÷ 4

= 1500rpm in this case

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

• Ψ (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 λr, at a rotor flux angle θrf 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 λr and the stator current, an orthogonal d-q axes reference frame is

introduced The direct (d)-axis is always aligned with the rotor flux λr, 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:

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 λr 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:

Where kt andkr are constants that depend on the stator and rotor’s 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 λdr 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) ! (α, β) the Inverse Park transformation This projection transforms the d,

q rotating reference frame to a two-phase orthogonal system (α, β) It utilizes the positional angle of the rotor flux (ρ) to do this:

• The Inverse Clarke transformation, modifies a two dimension orthogonal system

(α, β) 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:

ρ = ∫(ωslip + ωrotor) dt (5.11)

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

÷ rotor resistance) and λr 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

isd

isq

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 Finn’s 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 Finn’s 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

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 ω* 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 λr* 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 λdr* 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, ω rm For speeds less than the base or rated speed, the rotor flux command is set equal to it’s 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 λdr* 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, ω * 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, ω * 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