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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