PSZ 19:16 (Pind. 1/97)

UNIVERSITI TEKNOLOGI MALAYSIA

BORANG PENGESAHAN STATUS TESIS

JUDUL: SIMULATION OF MRAS BASED SPEED SENSORLESS ESTIMATION TECHNIQUES

FOR INDUCTION MACHINE DRIVES USING MATLAB/SIMULINK

SESI PENGAJIAN: 2005/2006

SAYA AHMAD RAZANI BIN HARON (HURUF BESAR)

mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut: 1. Tesis adalah hakmilik Universiti Teknologi Malaysia. 2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan pengajian

sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara institusi

pengajian tinggi. 4. ** Sila tandakan ( 9 ) (Mengandungi maklumat yang berdarjah keselamatan atau

kepentingan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972)

(Mengandungi maklumat TERHAD yang telah ditentukan

oleh organisasi/badan di mana penyelidikan dijalankan) Disahkan oleh (TANDATANGAN PENULIS) (TANDATANGAN PENYELIA) ALAMAT TETAP: KG. ALOR PASIR

17500 TANAH MERAH PROF. MADYA DR. NIK RUMZI NIK IDRIS

KELANTAN DARUL NAIM

SULIT

TERHAD

TIDAK TERHAD9

TARIKH: 14 APRIL 2006 TARIKH: 14 APRIL 2006

CATATAN: * Potong yang tidak berkenaan. ** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi

berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagaiSULIT atau TERHAD.

Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara penyelidikan,atau disertasi bagi pengajian secara kerja kursus dan penyelidikan, atau Laporan Projek SarjanaMuda (PSM).

I hereby declare that I have read this thesis and in my opinion this thesis

is sufficient in terms of scope and quality for the award of the degree of

Master of Engineering (Electrical Power)

Signature :

Name of Supervisor : Assoc. Prof. Dr. Nik Rumzi Nik Idris

Date : 14 April 2006

SIMULATION OF MRAS BASED SPEED SENSORLESS ESTIMATION

TECHNIQUES FOR INDUCTION MACHINE DRIVES USING

MATLAB/SIMULINK

AHMAD RAZANI BIN HARON

A project report submitted in partial fulfilment of the

requirements for the award of the degree of

Master of Engineering ( Electrical-Power )

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

MAY, 2006

ii

I declare that this thesis entitled Simulation of MRAS Based Speed Sensorless

Estimation Techniques for Induction Machine Drives using MATLAB/Simulink is

the result of my own research except as cited in the references. The thesis has not

been accepted for any degree and is not concurrently submitted in candidature of any

other degree.

Signature :

Name of Author : Ahmad Razani Bin Haron

Date : 14 April 2006

iii

For you,

My dearest mother and father,

My brothers and sisters,

My lovely wife, son and daughter

iv

ACKNOWLEDGEMENT

Alhamdullilah, praise be to Allah S.W.T., the Most Merciful and the Most

Compassionate. Peace be upon him, Muhammad, the messenger of God.

To engage into this research was an experience to gain, knowledge to dig,

friendships to build and passion to achieve

Firstly, I would like to express deepest gratitude, appreciation and thanks to

my supervisor, Assoc. Prof. Dr. Nik Rumzi Nik Idris, for his guidance, critics and

friendship. His longing for knowledge really aspire me.

Appreciation and thanks also should go to my friends for their encouragement

and motivation.

My highest appreciation also dedicated to my mother, father and siblings for

they are part of my life, always supporting me all the time.

Finally I would like to express my special thanks to my wife, Norah for her

love and never ending support, and our kids, Ahmad Aeman Danial and Nur

Batrisyia for theirs big hugs and smiles!

v

ABSTRACT

This thesis is about the study of the speed sensorless estimation techniques of

the induction machine drives. Large variations of techniques are available depending

on the estimation requirement. MRAS based speed sensorless estimation is one of the

most versatile techniques available due to its good performance and straightforward

stability approach. This technique uses two different models (the reference model

and the adjustable model) which has made the speed estimation a reliable scheme

especially when the motor parameters are poorly known or having large variations.

Rotor flux based MRAS (RF-MRAS) and back e.m.f based MRAS (BEMF-MRAS)

are two variants of MRAS based speed estimation techniques which differ in terms

of quantity used but share almost the same structure realization. These facts give a

good platform for comparison. The tracking capability and sensitivity to parameters

variation are two key criteria of comparison in assessing the performance of the

estimators. Implemented in the direct torque control (DTC) structure and simulated

in the MATLAB/Simulink, the results obtained justify the dynamic performance of

the RF-MRAS and BEMF-MRAS estimators.

vi

ABSTRAK

Tesis ini berkenaan dengan kajian teknik-teknik anggaran laju tanpa penderia

di dalam pemacu mesin aruhan. Pelbagai variasi teknik-teknik boleh didapati

bergantung kepada kehendak anggaran. Anggaran laju tanpa penderia berasaskan

MRAS adalah salah satu daripada teknik-teknik yang sangat berkebolehan yang

boleh didapati kerana prestasinya yang baik dan menggunakan pendekatan kestabilan

secara terus. Teknik ini menggunakan dua model berbeza (model rujukan dan model

boleh laras) yang menjadikan anggaran laju satu skim yang bolehharap terutamanya

bila parameter-parameter motor kurang diketahui atau mempunyai variasi yang

besar. MRAS berasaskan fluks pemutar (RF-MRAS) dan MRAS berasaskan d.g.e

balik (BEMF-MRAS) adalah dua varian teknik-teknik anggaran laju berasaskan

MRAS yang berbeza dari segi kuantiti yang digunakan tetapi berkongsi struktur

yang hampir sama. Fakta-fakta ini memberikan platform yang baik untuk

perbandingan. Kemampuan untuk menjejak dan kepekaan kepada variasi parameter-

parameter adalah dua kriterium utama perbandingan dalam menilai prestasi kedua-

dua penganggar. Kedua-dua penganggar menggunakan struktur kawalan terus daya

kilas (DTC) untuk tujuan simulasi. Keputusan-keputusan yang diperolehi dari

MATLAB/Simulink mengesahkan prestasi kedua-dua penganggar RF-MRAS dan

BEMF-MRAS.

vii

CONTENTS

SUBJECT PAGE

TITLE i

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

CONTENTS vii

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF SYMBOLS xiv

LIST OF ABBREVIATIONS xvi

CHAPTER TITLE PAGE

1 INTRODUCTION 1

1.1 Overview 1

1.2 Significance of study 3

1.3 Objectives 4

1.4 Scope of study 4

1.5 Work methodology 5

1.6 Literature review 6

1.7 Thesis organization 8

viii

2 INDUCTION MACHINE DYNAMIC 10

2.1 Introduction 10

2.2 Dynamic equations of induction machine 12

2.3 Induction machine control strategies 15

2.3.1 Scalar control 15

2.3.2 Field oriented vector control 17

2.3.3 Direct torque control 18

2.4 Summary 20

3 THE ART OF SPEED SENSORLESS ESTIMATION

SCHEMES 21

3.1 Introduction 21

3.2 Problems with estimations 22

3.2.1 Parameter sensitivity 23

3.2.2 Pure integration 23

3.2.3 Overlapping-loop problem 24

3.3 Speed sensorless estimation strategies 24

3.3.1 Rotor slot harmonics 25

3.3.2 Open loop estimators 26

3.3.3 Observers 28

3.3.3.1 Luenberger observer 29

3.3.3.2 Kalman filter observer 30

3.3.4 Model reference adaptive system estimators 32

3.4 Advantages and disadvantages of speed sensorless

estimation schemes 34

3.5 Summary 36

ix

4 RF-MRAS VS. BEMF-MRAS BASED SPEED

ESTIMATORS 37

4.1 Introduction 37

4.2 RF-MRAS estimator vs. BEMF-MRAS estimator 37

4.2.1 RF-MRAS estimator 38

4.2.1.1 RF-MRAS stability 40

4.2.2 BEMF-MRAS estimator 43

4.2.2.1 BEMF-MRAS stability 45

4.3 Simulation set up 47

4.3.1 Tracking capability 48

4.3.2 Parameter sensitivity 49

4.4 Summary 49

5 SIMULATION RESULTS AND DISCUSSION 50

5.1 Introduction 50

5.2 Speed response dynamics 51

5.2.1 Tracking capability 53

5.2.1.1 Open loop estimator 53

5.2.1.2 RF-MRAS 54

5.2.1.3 BEMF-MRAS 55

5.2.2 Effect of parameters variation 56

5.2.2.1 Effect of incorrect Rr setting 57

5.2.2.2 Effect of incorrect Rr setting 59

Effect of incorrect J setting 62

5.4 Summary 66

x

6 CONCLUSION AND FUTURE WORKS 67

6.1 Conclusion 67

6.2 Recommendation for future work 68

REFERENCES 70

xi

LIST OF TABLES

TABLE NO. TITLE PAGE

3.1 Trends and tradeoffs of speed estimation schemes 34

4.1 IMs parameters 48

xii

LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 A cut-away view of a squirrel cage induction motor 11

2.2 Induction machine d-q equivalent circuit in arbitrary

reference frame 14

2.3 Scalar control scheme 16

2.4 A typical FOC structure 17

2.5 DTC structure 19

3.1 Type of speed sensorless estimation strategies 22

3.2 Open loop speed calculation scheme structure 28

3.3 Luenberger based speed estimation structure 30

3.4 Extendend Kalman filter scheme block diagram 32

3.5 General structure of MRAS based estimator scheme 33

4.1 Speed estimation using rotor-flux based MRAS 39

4.2 MRAS equivalent nonlinear feedback system 40

4.3 Simulink implementation of RF-MRAS estimator 42

4.4 Back e.m.f based MRAS structure 44

4.5 Simulink implementation of BEMF-MRAS estimator 46

4.6 Estimator and DTC implementation in Simulink 47

5.1 Comparison of rotor speed response 51

5.2 Factors leading to instability of BEMF-MRAS based44

speed estimator 52

5.3 Open loop estimators speed tracking capability with

different speed reference 54

5.4 RF-MRAS estimators speed tracking capability with

different reference speed 55

xiii

5.5 BEMF-MRAS estimators speed tracking capability with

different reference speed 56

5.6 Effect of incorrect setting of Rr value to RF-MRAS

estimators speed response 58

5.7 Effect of incorrect setting of Rr value toBEMF-MRAS

estimators speed response 59

5.8 Effect of incorrect setting of Rs value to RF-MRAS

estimators speed response 60

5.9 Variation in RF-MRAS rotor flux linkages due to

changes in stator resistance setting 61

5.10 Effect of incorrect setting of Rs value to BEMF-MRAS

estimators speed response 62

5.11 Effect of incorrect setting of J value to RF-MRAS

estimators speed response 63

5.12 Effect of incorrect setting of J value to BEMF-MRAS

estimators speed response 64

5.13 Effect of incorrect setting of J value to RF-MRAS

estimators torque response 65

5.14 Effect of incorrect setting of J value to BEMF-MRAS

estimators torque response 65

xiv

LIST OF SYMBOLS

B - Motor friction constant

dsi - d-axis stator current expressed in stationary reference frame

qsi - q-axis stator current expressed in stationary reference frame

dri - d-axis rotor current expressed in stationary reference frame

qri - q-axis rotor current expressed in stationary reference frame

Lm - Magnetizing self-inductance

J - Motor moment of inertia constant

Lr - Rotor self-inductance

Ls - Stator self-inductance

P - Pair of poles

Rr - Rotor resistance

np - Number of pole pairs

Rs - Stator resistance

Te - Instantaneous value of electromagnetic torque

TL - Load torque

Tr - Rotor time constant

dsv - d-axis stator voltage expressed in stationary reference frame

qsv - q-axis stator voltage expressed in stationary reference frame

drv - d-axis rotor voltage expressed in stationary reference frame

qrv - q-axis rotor voltage expressed in stationary reference frame - Angular speed Vs - Stator voltage

r - Rotor speed

xv

r - Estimated rotor speed e - Stator voltage angle e - Synchronous speed ds - d-axis stator flux linkage expressed in stationary reference frame qs - q-axis stator flux linkage expressed in stationary reference frame dr - d-axis rotor flux linkage expressed in stationary reference frame qr - q-axis rotor flux linkage expressed in stationary reference frame

- Total leakage reactance

xvi

LIST OF ABBREVIATIONS

IM Induction machine/motor

IGBT Insulated Gate Bipolar Transistor

DC Direct Curent

AC Asynchronous Current

V/F Volts per Hertz

FOC Field Oriented Control

DTC Direct Torque Control

PWM Pulse Width Modulated

DSP Digital Signal Processor

MRAS Model Reference Adaptive System

E.M.F Electromotive Force

RF-MRAS Rotor Flux Based Model Reference Adaptive System

BEMF-MRAS Back E.M.F Based Model Reference Adaptive System

ANN Artificial Neural Network

OLS Ordinary Least-Square

BPN Backpropagation Network

CHAPTER 1

INTRODUCTION

1.1 Overview

Induction motor (IM) can be considered as the workhorse of the industry

because of its special features such as low cost, high reliability, low inertia,

simplicity and ruggedness. Even today IMs especially the squirrel cage type, are

widely used for single speed applications rather than variable speed applications due

to the complexity of controlling algorithm and higher production cost of IM variable

speed drives. However, there is a great interest on variable speed operation of IM

within the research community mainly because IMs can be considered as a major

industrial load of a power system. On the other hand the IMs consume a considerable

amount of electricity generated. The majority of IMs are operated at constant speed,

determined by the pole pair number and the stator supply frequency.

It is well known fact that electric energy consumption of the appliances can

be reduced by controlling the speed of the motor. The three phase variable speed IM

drives are therefore encouraged to be used in the industry today as an attractive

solution forever increasing electricity generation cost.

2

During the last decade, with the advancement of power electronics

technology, a high speed switching devices such as IGBTs were introduced and a

more precise motor control strategies, such as vector control techniques, were

developed. As a result, today IMs can be used in any kind of variable speed

applications, even as a servomechanism, where high-speed response and extreme

accuracy is required.

Vector control technique is used for high performance variable drive systems.

In the vector control scheme, a complex current is synthesized from two quadrature

components. One of which is responsible for the flux level in the motor and another,

which controls the torque production in the motor. In actual fact the control problem

is reformulated to resemble control of a DC motor. Vector control offers attractive

benefits including wide range of speed control, precise speed regulation, fast

dynamic response, operation above based speed and etc. The principals of vector

control are now well established at high performance IM drives.

In order to implement the vector control technique, the motor speed

information is required. Tachogenerators, resolvers or incremental encoders are used

to detect the rotor speed. However, these sensors impair the ruggedness, reliability

and simplicity of the IM. Moreover, they require careful mounting and alignment and

special attention is required with electrical noises. Speed sensor needs additional

space for mounting and maintenance and hence increases the cost and the size of the

drive system. However, in one aspect, the speed sensor elimination reduces the total

cost of the drive system. On the other hand the sensorless drive system is more

versatile due to the absence of the numerous problems associated with the speed

sensor as discussed previously. Therefore it is encouraged to use the sensorless

system where the speed is estimated by means of a control algorithm instead of

measuring. However eliminating the speed sensor without degrading the

performance is still a challenge for engineers.

3

In this thesis, the speed sensorless estimation concept via implementation of

Model Reference Adaptive System (MRAS) schemes was studied. It is a well known

fact that the performance of MRAS based speed estimators is beyond par from other

speed estimators with regards to its stability approach and design complexity.

Although this thesis is all about MRAS based speed estimators, but it is also the aim

of this project to investigate several speed sensorless estimation strategies for IMs.

Explanations on the type of control strategies also were briefly discussed. As far as

simulation works is concerned, the MRAS based speed sensorless estimation

schemes chosen in this thesis has been implemented in the direct torque control

structure (DTC) to evaluate the estimators performance.

1.2 Significance of study

With the maturing technology of the vector-controlled drives, the need for

speed information is crucial for control purposes and traditionally, this information

can be extracted using mechanical sensor mounted on the motor shaft. However, the

presence of such sensor has reduced the system reliability and increases the drives

systems size and the overall cost. These problems have attracted the interest of

many researchers to develop techniques that can eliminate the use of shaft sensor.

This effort has lead to growth of various speed sensorless estimation schemes based

on the simplified motor models.

Therefore, it is the intention of this work to share the motivation of the

previous researchers to study the speed sensorless estimation strategies. Though it

has gone through a maturing period of over 20 years, improvement and enhancement

of such system is still required. This effort might become a first step to the author to

involved into detail researches of the speed sensorless control in future.

4

The reason behind adopting the MRAS based speed sensorless estimation

strategies in this research is so obvious because it has been proclaimed as one of the

best methods available, especially when the motor parameters are poorly known or

have large variations. Though the performance of MRAS based estimators is

considerably good at high speed but operation at low and zero speed is still a

problem to overcome.

1.3 Objectives

The objectives of this research are outlined as follows:

1) To study the various speed estimation schemes available with main focus

will be on the MRAS based schemes.

2) To model and simulate rotor flux based MRAS (RF-MRAS) and back

e.m.f based MRAS (BEMF-MRAS) speed estimators for IM drives using

toolboxes available in MATLAB/Simulink.

3) To evaluate and compare the performance of the selected MRAS based of

speed estimators in terms of tracking capability and parameters

sensitivity.

1.4 Scope of study

The works undertaken in this project are limited to the following aspects to

ensure the scopes of study are within the anticipated boundary.

5

1. Sensorless estimation of rotor speed using open loop, RF-MRAS and

BEMF-MRAS estimators only.

2. IM parameters are known or readily available.

3. Simulation of MRAS based speed estimators will consider the effect

of parameters variation.

4. Speed estimators are implemented in the direct torque control (DTC)

structure.

5. Simulation in MATLAB/Simulink.

1.5 Work methodology

The research methodology is undertaken according to these stages:

1. Study of the IM dynamic equations related to RF-MRAS and BEMF-

MRAS speed estimators structure.

2. Construct the RF-MRAS and BEMF-MRAS using Simulink blocks.

3. Implementation in direct torque control scheme.

4. Examine the estimated and actual rotor speed response, with and

without effect of parameters variation in MATLAB/Simulink.

5. Evaluate performance of RF-MRAS and BEMF-MRAS based on

simulation results.

6

1.6 Literature review

Speed sensorless estimation has greatly evolved from an open loop, low

performance strategy to closed loop, high performance strategy over the past

decades. The need of developing such technique is essential to adapt to the

advancement in the control strategy, especially the vector control techniques.

Looking back into the past, Abbondanti [1] has become the first to propose

calculating of rotor speed based on the motor model. His innovation has been further

improved by Nabae [2], Jotten and Maeder [3], and Baader [4] and they had used it

in some practical AC drive systems. The fact is that, the real time calculating of the

speed has difficulties for the realization because it is largely dependent on the

motors parameters.

Tamai [5] and Schauder [6] had opened a new horizon to speed sensorless

field for which they had introduced the MRAS to identify the rotor speed. Their

contribution is widely used and referred because identification of speed is more

robust than calculation of speed. Shauder [6] in his paper has proposed a RF-MRAS

technique to estimate the rotor speed based on comparison between the outputs of

two estimators known as the reference model and the adjustable model. The

performance is acceptably good but effect of parameter variation and drift problem is

a drawback to be carefully study.

Peng and Fukao [7] has proposed a new technique of MRAS based speed

estimation to overcome the problem in RF-MRAS proposed by Schauder [6]. The

scheme which is based on back e.m.f, shows a better performance and robustness due

to elimination of pure integrators in the reference and adjustable model. Another

scheme which an extension of BEMF-MRAS also has been proposed. This scheme

uses reactive power information as the tuning signal rather than the back e.m.f or

rotor flux quantity. This scheme is further investigate by M. Ta-Cao et al. [8] which

shows superior robustness compared to previous MRAS schemes.

7

A more powerful and robust estimator based on artificial neural network

MRAS has been proposed by Ben-Brahim et al. [9] which exploit the classical

backpropagation network (BPN) algorithm for the online training of the neural

network to estimate the rotor speed. It is experimentally verified at the lowest speed

limit and even at zero-speed operation. Cirrincione and Pucci [10] proposed an

improvement of the MRAS artificial-neural-network (ANN)-based speed observer

presented by Ben-Brahim et al. [9]. In spite of using BPN algorithm, it uses the

ordinary least-square (OLS) algorithm to solve the problem associated with linearity.

From the study, it is observed that the OLS MRAS outperforms the BPN MRAS

proposed previously.

Although there are various techniques available for speed sensorless

estimation, but not enough effort has been put to review the schemes comparatively.

Illas et al. [11] have investigated and compared several speed sensorless estimation

schemes for field oriented control of IM drives. Speed estimations using speed

estimator, MRAS, speed observer, Kalman filter and rotor slot ripple have been

review and simulated to evaluate the performance based on some figures of merit.

Marwali and Kehyani [12] have performed a comparative study of the RF-MRAS

and BEMF-MRAS evaluated in indirect vector control system. The studies focus on

the level of the difficulty in tuning the adaptive gains and the speed tracking

performances. From the simulation and experimental studies, they have shown that

the BEMF-MRAS is better compared to RF-MRAS. Bodson and Chiasson [13] have

considered three representative approaches such as the adaptive method, least-square

method and nonlinear method for speed estimation. The methods are compared in

terms of their sensitivity to parameters variation, their ability to handle load and their

speed tracking capability.

Some studies related to parameter variation effects in sensorless vector

controlled drives are already available [14][15]. For example, impact of rotor

resistance variation on transient behavior of the drive was studied by Ilas et a1. [11]

and by Griva et a1. [16] through simulation. Viorel and Hidesiu [17] and Armstrong

et al. [18] have studied impact of rotor resistance, stator resistance and mutual

8

inductance variation in low speed region experimentally. The only available

comprehensive investigations of steady-state speed estimation errors caused by

parameter variation effects appear to be works by Gimenez et a1. [19] and Jansen

and Lorenz [20]. However, in both cases structure of the drive dealt with is direct

rotor flux oriented control that combines a MRAS based speed estimator with a

closed loop flux observer and includes a mechanical system model. The validity of

results obtained by Gimenez and Jansen is thus restricted to that specific drive

structure.

1.7 Thesis organization

Speed sensorless estimation is a vast subject of research. MRAS speed

estimators constitute one part of it which significantly influence the maturing of this

field. To study such a vast subject at one time is almost possible; therefore, only

MRAS framework will be studied thoroughly in this work. For that reason, the

organization of the materials in this thesis is indeed intentionally to make available

all the information related to the subject of study. The organization of this thesis is

outlined as follows:

Chapter 2 presents the general theory of the IM dynamics. The IM dynamics

equations extensively used for estimation algorithm were explained. Brief

explanation on IM control strategy also was included.

Chapter 3 gives an overview of speed sensorless estimation strategies

available in literature. Speed estimation techniques are briefly reviewed to give an

idea of the concept and the need for a robust and stable speed estimator. Since the

estimators are uniquely best in its own class, therefore, their trends and trade off

were highlighted at the end of this chapter.

9

Chapter 4 presents the rotor speed estimation using MRAS based strategy; the

RF-MRAS and the BEMF-MRAS. All the schemes were described thoroughly in

terms of mathematical equations, construction, implementation and performance.

The simulation setup for selected schemes i.e. the RF-MRAS and BEMF-MRAS

were presented.

Chapter 5 discusses the simulation results for the two estimators. Estimators

response at different values of speed reference was studied. The performance of the

estimators with effect of parameters variation was also examined. Analysis and

discussion were made to critically evaluate the performance of the two estimators.

In Chapter 6, a thorough conclusion of the research was presented. Some

suggestions for future works also were highlighted.

CHAPTER 2

INDUCTION MACHINE DYNAMICS

2.1 Introduction

The two names for the same type of motor, induction motor and

asynchronous motor, describe the two characteristics in which this type of motor

differs from DC motors and synchronous motors. Induction refers to the fact that the

field in the rotor is induced by the stator currents, and asynchronous refers to the fact

that the rotor speed is not equal to the stator frequency. No sliding contacts and

permanent magnets are needed to make an IM work, which makes it very simple and

cheap to manufacture. As motors, they rugged and require very little maintenance.

However, their speeds are not as easily controlled as with DC motors. They draw

large starting currents, and operate with a poor lagging factor when lightly loaded.

The IM can be operated directly from the mains, but variable speed and often

better energy efficiency are achieved by means of a frequency converter between the

mains and the motor. A typical frequency converter consists of a rectifier, a voltage-

stiff DC link, and a pulse-width modulated (PWM) inverter. The inverter is

controlled using a digital signal processor (DSP).

11

The majority of IMs are used in constant speed drives, but during the last

decades the introduction of new semiconductor devices has made variable speed

drives with IMs available. Variable speed IMs are usually fed by open loop

frequency inverters. The rotor speed of the machine is not measured and a change in

load torque will result in the speed to change.

The control and speed sensorless estimation of IM drives is a vast subject.

Traditionally, the IM has been used with constant frequency sources and normally

the squirrel-cage machine is utilized in many industrial applications, from chemical

plants and wind generation to locomotives and electric vehicles. A typical

construction of a squirrel cage IM is illustrated in Figure 2.1. Its main advantages are

the mechanical and electrical simplicity and ruggedness, the lack of rotating contacts

(brushes) and its capability to produce torque over the entire speed range.

Figure 2.1: A cut-away view of a squirrel cage IM.

12

With the development and maturing of the field-oriented or vector control

theory that started about three decades ago, researchers have considered the IM as a

good candidate for variable speed and servo applications. The objectives are related

to either process control or energy savings. Generally, control and estimation of IM

drives are more difficult than that of DC drives. The main reasons are the complex

dynamic behavior and the need to execute relatively complicated calculations for

estimation and control using microprocessors with limited cost, speed and accuracy.

2.2 Dynamic equations of induction machine

Generally, an IM can be described uniquely in arbitrary rotating frame,

stationary reference frame or synchronously rotating frame. For transient studies of

adjustable speed drives, it is usually more convenient to simulate an IM and its

converter on a stationary reference frame. Moreover, calculations with stationary

reference frame are less complex due to zero frame speed. For small signal stability

analysis about some operating condition, a synchronously rotating frame which

yields steady values of steady-state voltages and currents under balanced conditions

is used.

IM equations can be described in arbitrary frame rotating with angular speed

by the following d-q voltages and fluxes equations:

qsds

dssds dtdiRv += (2.1)

dsqs

qssqs dtd

iRv += (2.2)

13

( ) qrrdrdrrdr dtdiRv += (2.3)

( ) drrqrqrrqr dtd

iRv ++= (2.4)

drmdssds iLiL += (2.5)

qrmqssqs iLiL += (2.6)

drrdsmdr iLiL += (2.7)

qrrqsmqr iLiL += (2.8)

( dsqsqsdspe iin23T = ) (2.9)

Lrr

e TBdtdJT ++= (2.10)

In the general form presented, the above equations are not very helpful for either

estimation or control of the machine. However, by particularizing =0, the IM

representation in the stationary reference frame is obtained. The d-q voltage

equations of the IM in the stationary reference frame are:

dtdiRv dsdssds+= (2.11)

dtd

iRv qsqssqs+= (2.12)

qrrdr

drr dtdiR0 ++= (2.13)

14

drrqr

qrr dtd

iR0 += (2.14)

Equations (2.11)-(2.14) describe the machine behavior as seen from the

stationary reference frame. The flux equations are unchanged. These equations are

extensively used and manipulated in the design of speed estimation techniques to

achieved satisfactory performance of the system The stator voltage equations are

useful since they allow computation of the stator fluxes. The IM dynamic equivalent

circuit in stationary reference frame is illustrated in Figure 2.2 which is constructed

from the voltages and fluxes equations described earlier.

Figure 2.2: IM d-q equivalent circuit in stationary reference frame.

15

2.3 Induction machine control strategies

A brief explanation on the IM drives control strategies are presented in this

section. It can be divided into two major types which are the scalar control (or volts

per hertz, V/F) and vector control, the latter is superior to the former in the speed

accuracy and speed response. The scalar has a very simple control structure and has

been used broadly in industry. However, the traditional scalar control cannot

maintain the air-gap flux constant because the stator resistance voltage drops when

the IM works in the low frequency [21]. In addition, the scalar control scheme

belongs to the open loop control, when the load varies, the system cannot maintain

the speed accuracy due to the absence of the feedback loop [21].

Recently, sensorless control of the IM has been focused on and developed.

Many sensorless vector control schemes were proposed [22] and these control

methods heavily depend on the observed speed. If the observed speed has much

error, it will deteriorate the system performance and the motor cannot normal work at

worse condition. Afterward, all the control schemes described above will require the

information such as speed and position. Therefore, this information must be made

available during control process. For speed control cases, the speed information can

be obtained through estimation rather than measurement with the help of various

sensorless speed estimation techniques.

2.3.1 Scalar control [21][23]

The scalar control scheme has been used broadly in industry because of its

simplicity [21]. The method is based on the control of the stator frequency. The

objective is to control the machine speed while keeping constant the magnitude of

the stator flux. As a result, the machine retains its torque/ampere capability at any

16

speed. By neglecting the stator resistance drop, the stator flux is kept constant if

e

ss

V = and the name of the method comes from this equation.

Early approaches assume that the rotor speed r is approximately equal to the

synchronous speed e (slip speed is neglected). For speed control, the speed

reference r* is set and the stator voltage Vs is computed to maintain the desired

stator flux. Integration of the reference speed gives the angle of the stator voltage

(e). Finally, the space vector described by Vs and e is used as command voltage for

the three-phase inverter that powers the machine. The control scheme is presented in

Figure 2.3.

Figure 2.3: Scalar control scheme.

The major disadvantage of the V/Hz method is its sluggish dynamic response

since the method disregards the inherent machine coupling. A step change in the

speed command produces a slow torque response. During the transient, the

magnitude of the stator flux is not maintained (the magnitude decreases) and the

machines torque response is not sufficiently fast. In addition, there is some amount

of under damping in the machines flux and torque responses that increases at lower

frequencies. In some operating regions, the system may become unstable.

17

2.3.2 Field oriented or vector control [24]-[26]

The modern approach for IM control is based on vector or field-oriented

control (FOC). The invention of vector control in early 1970s has brought a new

beginning in the high-performance control of AC drives. The principle of FOC

combines both speed and torque to determine the required stator currents for the IM.

With FOC, in spite of coupled and nonlinear machine model, the IM emulates a

separately excited DC motor in two ways [25]: (1) independent control of both

magnetic field and torque is achieved. (2) optimal conditions for the production of

torque occur in both steady state and transient operations. The basic structure of FOC

is depicted in Figure 2.4.

The FOC can be classified as direct or indirect. In direct FOC methods, the

magnitude and angle of the rotor flux are measured or estimated with a flux

estimator. In the indirect FOC, a feedforward path determines the rotor flux position.

The most popular class of the successful controllers uses the vector control technique

because it controls both the amplitude and phase of AC excitation. This technique

results in an orthogonal spatial orientation of the electromagnetic field and torque.

Figure 2.4: A typical FOC structure.

18

Some advantages of FOC regarding to scalar control are given below [26]:

true de-coupling between torque and flux control, authorizing dynamical performances similar to the ones obtained with DC motors;

flux level imposition in a wide range of speed, including at standstill; phase currents magnitude is kept moderate, regarding nominal values, during

high torque transients;

effective torque control either in motor or regenerative operations and in the field weakening modes

Drawbacks of FOC are [26]:

rotor flux observation is sensitive to the rotor time constant, which is typically difficult to estimate with good accuracy and may vary as a function

of temperature, frequency and etc.;

the optimal tuning of the PI regulators may be laborious to carry out, and their performance is dependent on the good knowledge of the motor model

parameters;

it still a linear control method, which does not take advantage from the discrete and non-linear natures of the static converter.

2.3.3 Direct torque control [4][27][28]

Takahashi, Depenbrock and Baader [4][27][28] proposed a high performance

scalar control method which is popularly known as direct self control (DSC) or direct

torque control (DTC). The structure of a classical DTC scheme is illustrated in

Figure 2.5. In principle classical DTC selects one of the six voltage vectors and two

zero voltage vectors generated by a VSI in order to keep stator flux and torque within

the limits of two hysteresis bands. The right application of this principle allows a

decoupled control of flux and torque without the need of coordinate transformations,

19

PWM pulse generation and current regulators [29]. However, the presence of

hysteresis controllers leads to a non-constant switching frequency operation.

The time discretization, due to the digital implementation, and the limited

number of available voltage vectors determine the presence of current and torque

ripples. In order to overcome these problems, different methods have been presented,

allowing constant switching frequency operation. They achieve a substantial

reduction of current and torque ripples using, at each cycle period, the calculation of

the stator voltage space vector to exactly compensate the flux and torque errors. In

order to apply this principle, the control system should be able to generate the desired

voltage vector, using the Space Vector Modulation technique (SVM). These methods

require more complex control schemes than basic DTC scheme and present motor

parameters dependence [29].

Figure 2.5: DTC structure.

20

2.4 Summary

Dynamic equations of IM have been manipulated extensively for control and

estimation purposes. The evolution of IM control began with the development of the

scalar-controlled method allowing variable speed control. However, the scalar-

controlled IM failed to match the dynamic performance of a comparable DC drive.

The next step was the introduction of the vector-controlled methods. The goal of

these methods is to make the IM emulate the DC machine by transforming the stator

currents to a specific coordinate system where one coordinate is related to the torque

production and the other to rotor flux.

The FOC methods provide excellent dynamic response, matching that of the

DC machine. The main disadvantage of such controls is the computational overhead

required in the coordinate transformation. The latest development in IM control is the

DTC method. DTC does not rely on coordinate transformation, but rather controls

the stator flux linkage in the stationary reference frame. Despite its control

simplicity, the DTC method provides possibly the best dynamic response of any of

the methods.

CHAPTER 3

THE ART OF SPEED SENSORLESS ESTIMATION SCHEMES

3.1 Introduction

Estimation can be defined as the determination of constants or variables for

any system, according to a performance level and based in the measurements taken

from the process. Speed sensorless estimation as its name implies, is the

determination of speed signal from an IM drive system without using rotational

sensors. It makes use the dynamic equations of the IM to estimate the rotor speed

component for control purposes. Estimation is carried out using the terminal voltages

and currents which are readily available using sensors.

There are various rotor speed estimation schemes available in the market

[9][30]. These schemes were based on different algorithms with the purpose to

improve the performance of the speed estimation process. The schemes range from

open loop basis to closed loop basis with its own advantages and disadvantages. To

estimate the speed of the IM, type of scheme chosen is a factor to consider which at

the end will determine the design complexity, feasibility and performance of the

selected scheme. In this section, an overview of the speed sensorless estimation

schemes available will be discussed.

22

In general, speed sensorless estimation can be divided into two common

groups; estimation based on direct synthesis from IM dynamic equations and

estimation based on rotor slot harmonics as illustrated in Figure 3.1.

Figure 3.1: Type of speed sensorless estimation strategies.

3.2 Problems with estimation [31]

Before looking into individual approaches, the common problems of the

speed and flux estimation are discussed briefly for general field-orientation and state

estimation algorithms [31].

23

3.2.1 Parameter sensitivity

One of the important problems of the sensorless control algorithms for the

sensorless IM drives is the insufficient information about the machine parameters

which yield the estimation of some machine parameters along with the sensorless

structure. Among these parameters, stator resistance, rotor resistance and rotor time-

constant play more important role than the other parameters since these values are

more sensitive to temperature changes.

The knowledge of the correct stator resistance Rs is important to widen the

operation region toward the lower speed range. Since at low speeds the induced

voltage is low and stator resistance voltage drop becomes dominant, a mismatching

stator resistance induces instability in the system. On the other hand, errors made in

determining the actual value of the rotor resistance Rr may cause both instability of

the system and speed estimation error proportional to Rr. Also, correct Tr value is

vital decoupling factor in the sensorless control scheme.

3.2.2 Pure integration

The other important issue regarding many of the topologies is the integration

process inherited from the IM dynamics where an integration process is needed to

calculate the state variables of the system. However, it is difficult both to decide on

the initial value, and prevent the drift of the output of a pure integrator. Usually, to

overcome this problem a low-pass filter replaces the integrator.

24

3.2.3 Overlapping-loop problem

In a sensorless control system, the control loop and the speed estimation loop

may overlap and these loops influence each other. As a result, outputs of both of

these loops may not be designed independently and in some bad cases this

dependency may influence the stability or performance of the overall system. The

algorithms, where terminal quantities of the machine are used to estimate the fluxes

and speed of the machine, are categorized in two basic groups. First one is "the open-

loop observers" in a sense that the on-line model of the machine does not use the

feedback correction. Second one is "the closed-loop observers" where the feedback

correction is used along with the machine model itself to improve the estimation

accuracy.

3.3 Speed sensorless estimation strategies

As being explained in previous section, the speed estimation schemes based

on the direct synthesize of the IM equations can be broadly group into two groups

[30]. The first one is the open loop observer which does not have the feedback

correction and the other one is the closed loop observer which make use of the

feedback correction to improve the estimation accuracy. The open loop calculation

method is simple to implement but prone to error because of high dependency on the

machine parameters. The closed loop group observers for speed estimation are much

more versatile in terms of performance such as the Luenberger observers, Kalman

Filter observers, MRAS estimators and rotor slot harmonics estimator. Each of these

speed estimation schemes differ from each other in terms of equations and structure

used but they share the same objective to provide the speed information and to

improve the performance of the IM drive system. Uniquely, the difference exhibits

their own trends and tradeoffs which will be explained in section 3.4 of this chapter.

25

3.3.1 Rotor slot harmonics [22][30]

The space harmonics of the air-gap flux-linkage in a symmetrical three-phase

IM are generated because of the non-sinusoidal distribution of the stator windings

and the variation of the reluctance due to stator and rotor slots, which are called

m.m.f. space harmonics, stator slot harmonics, and rotor slot harmonics, respectively.

The rotor slot harmonics can be utilized to determine the rotor speed of IMs. The

rotor slot harmonics can be detected by using two different techniques; utilizing

either the stator voltages or the stator currents.

When the air-gap m.m.f. contains slot harmonics, slot-harmonic voltages are

induced in the primary windings when the rotor rotates. The magnitude and the

frequency of the slot-harmonic voltages depend on the rotor speed, so they can be

utilized to estimate the slip frequency and rotor speed. Generally we only use the

frequency of the slot-harmonic voltages since the magnitude depends not only on the

rotor speed, but also on the magnitude of the flux-linkage level and the loading

conditions.

In general, the stator voltage and frequency of dominant component

(fundamental slot-harmonic frequency) of the slot harmonic voltages are given by the

following equations.

++=k

shk3sshs uuuu (3.1)

( )1

r

slr1

1rrsh

f1P

s1ZfNNf3

ffNf

===

(3.2)

where . 1N3N r m=

26

The rotor speed can be obtained by the following equation.

PN

ff2r

1shr

m = (3.3)

3.3.2 Open loop estimators [1][6][30]

Open loop estimators, in general, use different forms of the IM differential

equations. Current model based open-loop estimators use the measured stator

currents and rotor velocity. The speed dependency of the current model is very

important since this means that although using the estimated flux eliminates the flux

sensor, the position sensor is still required. On the other hand, voltage model based

open loop estimators use the measured stator voltage and current as inputs. These

types of estimators require a pure integration that is difficult to implement for low

excitation frequencies due to the offset and initial condition problems. Cancellation

method open loop estimators can be formed by using measured stator voltage, stator

current and rotor velocity as inputs, and use the differentiation to cancel the effect of

the integration. However, it suffers from two main drawbacks. One is the need for

the derivation which makes the method more susceptible to noise than the other

methods. The other drawback is the need for the rotor velocity similar to current

model.

A full order open-loop observer, on the other hand, can be formed using only

the measured stator voltage and rotor velocity as inputs where the stator current

appears as an estimated quantity. Because of its dependency on the stator current

estimation, the full order observer will not exhibit better performance than the

current model. Furthermore, parameter sensitivity and observer gain are the problems

to be tuned in a full order observer designs. These open loop estimator structures are

all based on the IM model, and they do not employ any feedback. Therefore, they are

27

quite sensitive to parameter variations, which yield the estimation of some machine

parameters along with the sensorless structure.

Simplifying and modifying the IM equations in section 2.2 describe a new set

of equations representing the stator voltages and currents in terms of differential

equations represented in matrix form by the following equation [6].

( )( )

+

+

=

q

d

ss

ss

q

d

m

r

q

d

ii

.pLR00.pLR

vv

LL

dtddt

d

(3.4)

The rotor speed equation is given as follows:

(

= dqqd

r

mdq

qd2

rr iiT

Ldt

ddt

d1 ) (3.5)

where, 2q2

d2

r +=

These equations will be used in the construction of an open loop estimator for

simulation purpose. The open loop estimator block diagram is illustrated in Figure

3.2. As can be seen from figure, the open loop estimator imposes no feedback for

rotor speed correction and hence it is easily liable to lower accuracy of speed

estimation.

28

Figure 3.2: Open loop speed calculation scheme structure [6].

3.3.3 Observers

In section 3.3.2, an open loop speed estimator has been described. In open

loop estimator, especially at low speeds, parameters variation has significant

influence on the performance of the drive both at steady state and transient state.

However, it is possible to improve the robustness against parameters mismatch and

also signal noise by using closed loop observers. The most commonly used observers

are Luenberger and Kalman filter types.

29

3.3.3.1 Luenberger observer [30][31]

The scheme is based on the fact that one observer estimates the rotor flux and

the speed is derived by the stator current error and the estimated rotor flux. In terms

of classification, the scheme that adopts an observer could be also treated as MRAS,

where the motor is considered as the reference model and the observer is considered

as the adjustable model.

The IM model in terms of state variables in stationary reference frame is

given as follows:

sr

ss

1

r

s

2221

1211

r

s vBi

Av0B

i

AAAA

i

dtd +

=

+

=

(3.6)

[ ]

=s

ss

iCi (3.7)

where A is the motor parameters matrix, B is the input matrix, C is the output matrix,

[ Tssi ] is the state variables vector, and sv (stator voltage) is the command. The stator current and the rotor flux are estimated by the full order Luenberger state

Observer described by the following equation:

( )ssss

s

s

s iiGvBiA

i

dtd ++

=

(3.8)

The motor speed can be estimated by:

( ) ( ) rirpT0

driqsqridsIdriqsqridsPr dtKK +=+= (3.9)

30

where ( )dsdsids ii = and ( )qsqsiqs ii = are the current errors calculated as the difference between the measured and the estimated currents. The block diagram for

Luenberger observer is represented in Figure 3.3. The basic Luenberger observer is

applicable to a linear, time-invariant deterministic system.

Figure 3.3: Luenberger based speed estimation structure.

3.3.3.2 Kalman filter observer [30][32][33]

The Kalman filter is basically an observer for linear systems, but the gain

matrix is chosen to have an optimum filtering when both inputs and outputs are

corrupted by noise. The noise affecting the system can be taken into account by:

G(t)u(t)B(t)v(t)A(t)x(t)dt

dx(t) ++= (3.10)

y(t) = C(t)x(t) + w(t) (3.11)

where x(t), v(t), y(t) represent, respectively, the state variables (stator and rotor

currents), the commands variables (the stator voltage) and the output variables (the

stator current components), u(t) and w(t) are the input noise and the output noise,

31

respectively. Usually u(t) and w(t) are considered to be white noises (and thus

uncorrelated with inputs and states), although this is not a necessary restriction . Thus

their covariance matrices, denoted as Q(t) and, respectively, R(t), are diagonal.

Kalman filters can be implemented in either continuous or discrete form. In

most cases, the discrete form is used, because the control is digital. For non-linear

systems, as it is the case of IMs where the rotor speed can be regarded as a time

varying parameter, a linearized model must be derived to use the Kalman filter

algorithm, which is referred as the Extended Kalman Filter (EKF). The structure for

EKF scheme is depicted in Figure 3.4. The parameter to be estimated (the rotor

speed) can be introduced as a new state variable. The linearization is done by

assuming that the speed is constant during the sampling time. The system equations

in the discrete time domain are:

x(k+1) = Ad x(k) + Bd v(k) + Gd u(k) (3.12)

y(k) = Cd x(k) +w(k) (3.13)

The EKF equations for the estimation of stator and rotor currents and of the rotor

speed is:

(3.14) ( )( ) Cx(k))1)K(k)(y(k1)(k)v(kB(k)

x(k)(k)A

1k1kx

der

der

++++

=

++

where and

=100)k(A

)k(A dde

=0

)k(B)k(B dde

32

Figure 3.4: Extended Kalman filter scheme block diagram.

3.3.4 Model reference adaptive system estimators [5]-[8][30]

Tamai [5] has proposed one speed estimation technique based on the Model

Reference Adaptive System (MRAS) in 1987. Two years later, Schauder [6]

presented an alternative MRAS scheme which is less complex and more effective.

The MRAS approach uses two models. The model that does not involve the quantity

to be estimated (the rotor speed, r) is considered as the reference model. The model that has the quantity to be estimated involved is considered as the adaptive model (or

adjustable model). The output of the adaptive model is compared with that of the

reference model, and the difference is used to drive a suitable adaptive mechanism

whose output is the quantity to be estimated (the rotor speed). The adaptive

mechanism should be designed to assure the stability of the control system. A

successful MRAS design can yield the desired values with less computational error

(especially the rotor flux based MRAS) than an open loop calculation and often

simpler to implement.

33

Figure 3.5 illustrates the basic structure of MRAS. Different approaches have

been developed using MRAS, such as rotor flux based MRAS (RF-MRAS), back

e.m.f based MRAS (BEMF-MRAS), reactive power based MRAS (RP-MRAS) and

artificial intelligence based MRAS (ANN-MRAS). In the following a basic

description of these schemes will be discussed.

(a)

(b)

Figure 3.5: General structure of MRAS based estimator scheme. (a) Basic scheme

using space vector notation. (b) Basic scheme using space vector components [30].

34

3.4 Advantages and disadvantages of speed sensorless estimation schemes

In the past, researchers have developed various estimators or observers by

manipulating the IM equations in the effort to eliminate the shaft sensors and

increase the drives system reliability. Therefore they are distinct in their own ways.

This part highlights some of the advantages and disadvantages of the available speed

estimation schemes.

Table 3.1: Trends and tradeoffs of speed estimation schemes.

Open Loop Estimator Advantages

Simple in construction Disadvantages

Estimators accuracy depends greatly on the accuracy of machine parameters used.

Suitable for low speed operation. The need for the derivation makes the method more susceptible to noise.

Kalman Filter (Observer) Advantages

Kalman filter algorithm and its extension are robust and efficient observers for linear and nonlinear systems, respectively.

A major advantage of the Kalman filtering approach is its fault tolerance which permits system parameter drifts. Therefore, exact models are not required.

The developments in the real time computational speed of digital signal processing chips makes the Kalman filter a powerful approach to sensorless

vector control.

Disadvantages

Robustness and sensitivity to parameter variation still unsatisfied.

35

Model Reference Adaptive System (MRAS) Advantages

A potential solution for implementing high performance control systems, especially when dynamic characteristics of a plant are poorly known, or have

large and unpredictable variations.

Disadvantages

The implementation of the two models in different reference frames affects the complexity and robustness of the MRAS scheme.

The speed adaptive algorithm used affects the stability and dynamic performance of the closed-loop MRAS.

High Frequency Signal (Rotor Slot) Advantages

Have the potential for wide-speed and parameter insensitive sensorless control, particularly during low speed operation, including zero speed.

Disadvantages

Due to measurement bandwidth limitation, it has not been directly used for rotor speed estimation.

Artificial Intelligent Scheme Advantages

Neural networks have learning capability to approximate very complicated nonlinear functions, and therefore considered as universal approximation.

Disadvantages

Requirement of much training or knowledge base to understand the model of a plant or a process.

36

3.5 Summary

It is well acknowledge that so many efforts have been put in the past to

extract speed or position signal of an IM. The speed information which is important

for control purposes could be extracted using sensor. However, the present of sensor

itself has reduced the drive reliability as well as increased the drives size. This

situation has put the IM drive at disadvantage when talking about its good dynamic

response and performance for variable speed control. Its predecessor, the dc machine

is always a good choice but with the development of several new methods to extract

the speed or position signal, it has put the IM drive as a better choice for variable

speed control. This technique is called speed sensorless technique, which refers to

the elimination of the shaft sensor used to obtain the speed information.

For the past 20 years, the researchers have developed many strategies for

speed sensorless estimation. All the techniques differ from one to another but they

complement to each other in terms of objectives and performances. The strategies

range from open loop to closed loop structure and hence indicates the later has better

performance. Although the list of speed sensorless estimation strategies is bulky in

literature, some problem associated with low speed performance and parameters

mismatch still need careful attention by the researchers. Nevertheless the invention

of speed sensorless estimation strategies has greatly increased the popularity and

performance of the IM drives.

CHAPTER 4

RF-MRAS VS. BEMF-MRAS BASED SPEEDESTIMATORS [6][7][30]

4.1 Introduction

Model reference adaptive system (MRAS) based speed sensorless estimation

has numbers of variant with rotor flux based, back e.m.f based, reactive power based

and artificial intelligent based being the most common approach as being discussed

in the previous chapter. The first three schemes use the calculation from the IM

equations to estimate the rotor speed whereas the later did not involve with adaptive

mathematical equations [30]. In this section, two types of MRAS based speed

estimators have been chosen for study. The estimators are the RF-MRAS and the

BEMF-MRAS based speed estimators. Details explanations were provided in the

next section.

4.2 RF-MRAS estimator vs. BEMF-MRAS estimator [5]-[8][19][30]

This research decided to use the RF-MRAS and BEMF-MRAS based

estimators to perform the simulation and evaluation on the performance of the

38

estimators as mentioned earlier in the objectives of study. These two estimators have

been chosen intentionally since they uniquely differ in terms of the quantity used in

the reference model and the adjustable model but they share almost the same

realization in terms of structure. Both structure also have been widely referred in

literature. Hence, a fair comparison of the estimators can be performed without bias

and the results from this study will enrich the materials available for references in

future. Therefore, this chapter will discussed in detail the realization of the two

estimators from the IM dynamic equations up to the construction of the estimators in

the MATLAB/SIMULINK.

4.2.1 RF-MRAS [6][30]

The RF-MRAS estimator was initially proposed by Shauder in 1989 [6] as an

improvement to the drawbacks incurred in the open loop estimator. As being

discussed in chapter 3, it is possible to estimate the rotor speed by using two

estimators (the reference-model-based and the adjustable-model-based estimators)

which independently estimate the rotor flux linkage components in the stationary

reference frame and by using the difference between these flux linkage estimates to

drive the speed of the adjustable model to that of the actual speed [30]. The

expressions for the rotor flux linkages in the stationary reference frame can be

obtained from the stator voltage and rotor voltage equations of the IM as described

in chapter 2. Stator voltage and flux equations of (2.1)-(2.2) and (2.5)-(2.6) have

been manipulated and simplified to obtain the rotor flux linkages as given by the

following equations:

( )[ = sqsssqssqsm

rsqr iLdtiRvL

L ] (4.1)

( )[ = sdsssdssdsm

rsdr iLdtiRvL

L ] (4.2)

39

where rs

2m

LLL1=

Whereas, the rotor voltage and flux equations of (2.13)-(2.14) and (2.7)-(2.8) have

been rearranged and simplified to give the derivatives of rotor flux linkages in the

stationary reference frame as given by the following equations:

sqs

r

msdrr

sqr

r

sqr i

TL

T1

dtd ++= (4.3)

sds

r

msqrr

sdr

r

sdr i

TL

T1

dtd += (4.4)

Equations (4.1) and (4.2) were implemented as the reference model since it is

independent of rotor speed and the equations (4.3) and (4.4) were implemented as

the adjustable model as it is speed dependent. The tuning signal driving the

adaptation mechanism of this structure is the error output due to comparison of both

models. It varies the rotor speed in order to force to zero the error vector. The block

diagram of the RF- MRAS structure is shown in Figure 4.1.

Figure 4.1: Speed estimation using RF-MRAS [6].

40

4.2.1.1 RF-MRAS stability [6]

It is important to design the adaptation mechanism of the MRAS based

estimators according to the hyperstability concept. This will results in a stable and

quick response system where the convergence of the estimated value to the actual

value can be assured with suitable dynamic characteristics. As being described by

Landau, when designed according to these rules, the state error equations of the

MRAS are guaranteed to be globally asymptotically stable [6]. The adaptation

mechanism can be derived from the following state error equations which is obtained

by subtracting equations (4.3) and (4.4) from the corresponding reference model

equations (4.1) and (4.2).

( rrqqrdr

d T1

dtd ) = (4.5)

( rrdqr

drq

T1

dtd ) += (4.6)

or in matrix form, [ ] [ ][ ] [ ]WAdt

d = . Since r is a function of the state error, these equations describe a nonlinear feedback system as illustrated in Figure 4.2.

Figure 4.2: MRAS equivalent nonlinear feedback system [6] [7].

41

According to Landau [34], to ensure the hyperstability of the system can be

achieved, two criterions must be established. Firstly, the linear time-invariant

forward path transfer matrix, ( ) 1AsI must be strictly positive real and secondly, the nonlinear feedback (which includes the adaptation mechanism) must satisfies

Popovs criterion for stability. Popovs criterion for stability requires a finite

negative limit on the input or output inner product of the nonlinear feedback system.

A candidate adaptation mechanism which satisfies the criterion can be obtained as

given in the following explanation [6]. Let

[ ] [ ] d t0

12r += (4.7)

Popovs criterion requires that:

for all (4.8) [ ] [ ] 1t

0

20

T dtW 0t1

where is a positive constant. Substituting for 20 [ ] , [ ]W and r in this inequality, Popovs criterion for the present system becomes;

[ ] [ ]( ) [ ]( )

t

0

20

t

012rdqqd dtd (4.9)

The following relation can be used to solve the this inequality:

( ) >1t

0

2 0k,)0(f.k21dt)t(f)t(f.pk (4.10)

Using this expression, it can be shown that Popovs inequality is satisfied by the

following functions:

( ) ( )qddqIqddqI1 KK == (4.11)

42

( ) ( )qddqPqddqP2 KK == (4.12)

Substituting equations (4.11) and (4.12) into equation (4.7) yields the estimated rotor

speed as follows:

( qddqIPr .pKK

+= ) (4.13)

The MRAS speed identification based on this adaptation mechanism is

illustrated in Figure 4.3 as being implemented in the MATLAB/Simulink. This

Simulinks blocks will be used in the simulation to examine the performance of the

estimator. The factors m

r

LL in (4.1)-(4.2) and

r

m

TL

in (4.3)-(4.4) have conveniently

been incorporated into the adaptation mechanism gains constants KP and KI.

Figure 4.3: Simulink implementation of RF-MRAS estimator.

43

Although the structure is quite simple in construction, the performance of this

system is the poor at close to zero speed, due to the presence of pure integration and

the stator resistance effect. In order to solve the problems with initial conditions and

drift, modification of the pure integration in the voltage model by a low pas filter is

used. Another way is by inserting a linear transfer function in form of high pass filter

in both the reference and the adjustable model [6]. Tajima and Hori [24] improved

Schauders work by proposing a robust flux observer of which the poles are designed

in function of rotor speed and rotor time constant. As a result, the system is

completely robust to the rotor resistance variation.

4.2.2 BEMF-MRAS [7]

The problem at low speed region can be somehow resolved by replacing the

pure integration of the stator voltage with a filter. However, the natural delay related

to a filter is still present. To avoid completely the integration, the back e.m.f quantity

is used instead of the rotor flux linkage. This MRAS technique was originally

proposed by Peng and Fukao [7] to provide an improvement to the RF- MRAS

technique. The BEMF-MRAS based technique as depicted in Figure 4.4, does not

require any pure integration in its reference model. The estimator uses the induced

back e.m.f in its reference and adjustable models instead of rotor flux linkages as

applied in the RF-MRAS. The equations for the direct-and quadrature-axis back

e.m.f in the reference and adjustable models follow from equations (4.1)-(4.4), as

given by these equations:

(1) Reference model

+=dt

diLiRve dssdssdsmd (4.14)

44

+=

dtdi

LiRve qssqssqsmq (4.15)

(2) Adjustable model

+= sds

rmd

rmqr

r

2m

md iT1i

T1i

LLe (4.16)

+= sqs

rmq

rmdr

r

2m

mq iT1i

T1i

LLe (4.17)

sr

mr

mrm i

T1i

T1i

dtdi += (4.18)

Figure 4.4: BEMF-MRAS structure [7].

45

4.2.2.1 BEMF-MRAS stability [7]

As far as the design of the adaptation mechanism is concerned, hyperstability

approach is important to ensure the stability of the system and the estimated quantity

will converge to the actual value [7]. Referring to Figure 4.2, instead of using the

rotor flux, the design considers the back e.m.f as it input. The design of BEMF-

MRAS adaptation mechanism is almost the same as carried out for RF-MRAS.

Differentiating both sides of equations (4.16) and (4.17), the following

equations can be obtained.

dtdi

TLLe

T1e

dtde s

rr

2m

mr

mrm += (4.19)

Letting mm ee = and subtracting (4.19) for the adjustable model and from (4.19) for the reference model giving the appropriate state error equation:

( ) mrrr

r eT1

dtd = (4.20)

or in matrix form, [ ] [ ][ ] [ ]WAdt

d = . Since r is produced by the adaptation mechanism, these equations describe a nonlinear feedback system as shown in Figure

4.2. To ensure stability of the system, Popovs criterion for hyperstability as given in

equation (4.21) must be satisfies.

for all t (4.21) 01

Letting

(

+= mIPr e.p

KK ) (4.22)

46

and substituting for W in equality (4.21) gives the following simplified equation.

(4.23)

Using the same inequality equation as in (4.10), inequality in (4.23) has been

satisfied. Rewriting equation (4.22) yields the estimated rotor speed of the estimator.

( mmIPr ee.pKK

+= ) (4.24)

The MRAS speed estimation system based on this adaptation mechanism can

be obtained as depicted in Figure 4.5. The factor 2m

r

LL has been conveniently

incorporated into the adaptation mechanism gain constants KP and KI. The structure

is constructed in the MATLAB/Simulink for simulation and evaluation purposes.

Figure 4.5: Simulink implementation of BEMF-MRAS estimator [7].

47

As being mentioned earlier, these two estimators were chosen as candidates

for comparison because of its similarity (almost similar) in terms of structure

realization (refer Figure 4.3 and 4.5). Whereas parts that differentiate them are only

the quantity used in the models and the presence of pure integrator in the RF-MRAS.

Those criteria should give the clear stand on the reason for choosing these two

estimators. Therefore a fair comparative assessment of the estimators performance

can be evaluated and conclusion made applied to both estimators.

4.3 Simulation set up

It is the aim of this research to study the response of the estimators in terms

of its tracking performance and sensitivity to parameters variation. Hence the

estimators were implemented in the DTC structure as illustrated in Figure 4.6 for

simulation in the MATLAB/Simulink.

Figure 4.5: MRAS estimators and DTC implementation in MATLAB/Simulink.

48

As to ensure a fair comparison on the estimators performance, the

parameters of a 3-phase, 4-poles squirrel cage type induction motor have been used

as given in Table 4.1. Knowledge of motors parameter is important for this

simulation since the estimators are highly parameters dependent. Since the estimators

are highly parameters dependent, they are exposed to inaccuracy in estimation as the

parameters vary.

Table 4.1: IMs parameters.

Parameter Value Stator resistance 5.5

Rotor resistance 4.51

Stator self inductance 306.5 mH

Rotor self inductance 306.5 mH

Mutual inductance 291.9 mH

Moment of inertia 0.01 kgm2

Number of poles 4

Rated speed 1410 rpm

Vdc 654 V

Load torque 1 Nm

4.3.1 Tracking capability [35][36]

Tracking capability is one of the key criteria of the comparison. The

performance of an estimator is evaluated in terms of convergence of the estimated

rotor speed to the actual speed. An estimator is said to have good tracking capability

if the estimated value can track the actual value at high and even at close to zero

speed. Using the same parameters in the IM and the MRAS estimator, the tracking

performance of the estimator can be examined by changing the speed reference of the

system.

49

4.3.2 Parameter sensitivity

It is understood that the estimators performance are highly dependent on the

IM parameters since it structure realization is directly extracted from the IM dynamic

equations. The IM parameters are affected by variations in the temperature and the

saturations levels of the machine [35]. Incorrect setting of parameters in the motor

and that instrumented in the vector controller and estimators will results in the

deterioration of performance in terms of steady state error and transient oscillations

of rotor flux and torque [35]. As a consequence, parameter sensitivity has been

treated as a secondary issue in a vector controlled IM drives system [36].

Some of the parameters detuning effect being studied are the stator resistance,

rotor resistance, stator self-inductance, rotor self-inductance and motor moment of

inertia. Amongst these parameters, stator resistance variation has been reported to

have large influence on the estimators performance [30]. Others parameters has

minimum effects but as the variations becomes larger, the effect to the estimators

performance also becomes significant.

4.4 Summary

The estimation of the rotor speed quantity from the IM dynamic equations

was discussed. Two variants of the MRAS based speed estimators have been

explained in detail in terms of the mathematical equations and construction wise.

Using MATLAB/Simulink, the estimators were implemented for study. The

performance of the two estimators can be evaluated based on two criteria of

comparison which are the tracking capability and parameter sensitivity.

CHAPTER 5

SIMULATION RESULTS AND DISCUSSION

5.1 Introduction

It is common nowadays that the response of a system is analyzed using

simulation packages such as MATLAB platform. This software is so helpful in

examining the different conditions of the plant. In this study, the simulation of the

MRAS based speed estimators constructed using Simulink toolboxes have been

performed in the MATLAB 6.5 environment. Each of the estimators was

implemented in the DTC structure using the same motors parameters as shown in

Table 4.1 in the previous chapter. From the simulations results, the performance of

the RF-MRAS and BEMF-MRAS speed estimators were critically compared. Since

the scope of work includes the open loop estimator as part of the scheme under

study, therefore the simulation has been extended to examine the response of rotor

speed for this estimator. The reason to include the open loop estimator in the

simulation is to provide a baseline of comparison between the open loop estimator

and closed loop observers in terms of overall dynamic response, and thus verified the

theoretical analysis explained in the previous chapter.

51

5.2 Speed response dynamics

The speed response dynamics of an estimator is judged based on the tracking

capability of the system. A good estimator will require the estimated speed to track

correctly the actual speed. To show that the MRAS based speed estimators

outperform the open loop estimator as being explained in chapter 3, then it is

necessary to show the simulations results for this type of estimator as compared to

the MRAS based speed estimators. As shown in Figure 5.1, at reference speed of

100rad/s, the speed response dynamics for both MRAS based speed estimators are

much better than open loop estimator. The sluggish response of the open loop

estimator during transient and steady state with an average of 20rad/s (during steady

state) in speed error is due to its high dependency on the motors parameter and the

absence of feedback for correction as incorporated in the closed loop observers.

The MRAS based speed estimator shows a significant improvement from the

open loop estimator with speed error of 4rad/s (during steady state) for the RF-

MRAS and 0.5rad/s (during steady state) for BEMF-MRAS at reference speed of

100rad/s. However, for BEMF-MRAS during the reversal operation, the estimated

speed tends to deviate as high 40rad/s from the actual speed due to instability of back

e.m.f quantity and stator current at low speed operation as shown in Figure 5.2.

(a) (b)

52

(c)

Figure 5.1: Comparison of rotor speed response. (a) Open loop estimator. (b) RF-

MRAS estimator. (c) BEMF-MRAS estimator.

(a) (b)

Figure 5.2: Factors leading to instability of BEMF-MRAS based speed estimator.

(a) Back e.m.f quantity. (b) d-q axis stator currents.

The remaining parts of this section will analyze the speed dynamics response

of the open loop estimator, RF-MRAS and BEMF-MRAS based speed estimators in

terms of tracking capability and sensitivity to parameters variation. Simulation

results will be presented based on condition set during the simulation.

53

5.2.1 Tracking capability

It is always crucial to assess the performance of an estimator based on the

ability of the estimated speed to converge to the actual value, especially during

transient state. This criterion has been well accepted as a primary indicator when

benchmarking the performance of the estimators. To examine the ability of the open

loop, RF-MRAS and BEMF-MRAS based speed estimators to accurately estimate

the rotor speed, simulation at various reference speed has been performed. Reference

speed of 100rad/s, 70rad/s, 50rad/s and 30rad/s has been chosen to investigate the

tracking capability of the estimators.

5.2.1.1 Open loop estimator

The tracking capability of an open loop estimator is acceptable since no

feedback signal for speed correction is available as in closed loop estimator. The

estimated speed can track the actual speed quite well even at low speed. However as

being described by Shauder [6], this estimator is highly parameters dependent and

therefore is bounded to error of estimation if there are parameters variations.

Nevertheless, a much better performance of the open loop estimator is possible as

proposed by M. Zerbo et al. [37]. As shown in Figure 5.1, the tracking capability is

fairly good at high speed but deteriorate as the speed decrease.

(a) (b)

54

(c) (d)

Figure 5.3: Open loop estimators speed tracking capability with different reference

speed. (a) 100rad/s. (b) 70rad/s. (c) 50rad/s. (d) 30rad/s.

5.2.1.2 RF-MRAS

RF-MRAS and BEMF-MRAS based speed estimators show a better

performance in terms of tracking capability when compared to the open loop

estimators. RF-MRAS based speed estimator, when it was first proposed has

successfully improved the speed tracking performance of the open loop estimator.

However, as being mentioned earlier, the intention of this work is to compare the

performance of RF-MRAS and BEMF-MRAS based speed estimators. Therefore the

advantage against the open loop estimator would not be considered. The remaining

parts of this chapter will only focus on the RF-MRAS and BEMF-MRAS estimators

only.

RF-MRAS estimator shows a considerably good tracking performance at high

speed and even at low speed. This is depicted in Figure 5.4. The speed error response

shows a small deviation (approximately 4rad/s during transient state and 1rad/s

during steady state) in the estimated speed and the actual speed values at reference

speed of 30rad/s. Hitherto, speed estimation below reference speed of 20rad/s and

zero speed operation is not applicable due to presence of pure integration and

variation in the motors parameters especially the stator resistance.

55

(a) (b)

(c) (d)

Figure 5.4: RF-MRAS estimators speed tracking capability with different reference

speed. (a) 100rad/s. (b) 70rad/s. (c) 50rad/s. (d) 30rad/s.

5.2.1.3 BEMF-MRAS

The speed tracking performance of BEMF-MRAS shows an improvement as

compared to RF-MRAS. As depicted in Figure 5.5, the estimator shows better

tracking capability at high and even at low speed. This trend is due to elimination of

pure integration process in the reference model as discussed in Chapter 4. The

BEMF-MRAS estimator also has less parameter dependent compared to RF-MRAS.

The speed error response shows a small deviation of 5rad/s during transient state and

about 1rad/s during steady state at reference speed of 30rad/s. Like RF-MRAS, the

BEMF-MRAS operation at reference speed below 20rad/s is not applicable due to

instability of the back e.m.f quantity.

56

(a) (b)

(c) (d)

Figure 5.5: BEMF-MRAS estimators speed tracking capability with different

reference speed. (a) 100rad/s. (b) 70rad/s. (c) 50rad/s. (d) 30rad/s.

5.2.2 Sensitivity to parameters variation

High dependency on motors parameter is one of the characteristics of the

MRAS estimators. The construction of the RF-MRAS and BEMF-MRAS estimators

which are directly extracted from the IM dynamic equations has major influence on

the accuracy of the estimation process. The motors parameters which normally

prone to variations such as temperature rise, magnetic saturation and skin effects will

also vary the estimated speed from the actual value. This section will examine the

estimators response towards variation in the motors parameter by changing the

57

value of parameters in the motor one at a time and concurrently the values

instrumented in the estimators is kept unchanged. The respective parameters are the

rotor resistance (Rr), stator resistance (Rs) and motor moment of inertia (J). However

due to stability factors, effect of incorrect setting of other motors parameters (stator

self-inductance, rotor self-inductance and magnetizing self-inductance) cannot be

carried out.

5.2.2.1 Effect of incorrect Rr setting

Rr is one of the variables that exist explicitly in the equations used to

construct the structure of the MRAS estimators. Variation in the Rr will directly vary

the rotor time constant value, Tr. Incorrect value of Tr affected the accuracy