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HYBRID PI-FUZZY SPEED CONTROLLER FOR INTERIOR PERMANENT MAGNET SYNCHRONUS MOTOR
A
DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF REQUIREMENTS FOR THE AWARD
OF THE DEGREE OF
MASTER OF TECHNOLOGY IN
ELECTRICAL ENGINEERING
BY
MANISH KUMAR CHANDAN
Univ. Roll No. 2200374
UNDER THE GUIDANCE OF
Mr. CHETAN PRAVEER
(Assistant Professor, EE Dept.,)
To
DEPARTMENT OF ELECTRICAL ENGINEERING
CBS Group of Institutions, Fatehpuri, Jhajjar
M.D. UNIVERSITY ROHTAK, HARYANA (INDIA)
(July 2018)
CBS Group of Institutions, Fatehpuri, Jhajjar
Department of Electrical Engineering
DECLARATION
I hereby declare that the work being presented in the dissertation entitled, “HYBRID PI-
FUZZY SPEED CONTROLLER FOR INTERIOR PERMANENT MAGNET SYNCHRONUS
MOTOR” as partial fulfilment of the requirements for the award of degree of M. Tech.
(Electrical Engg.) in CBS Group of Institutions, Fatehpuri, Jhajjar. This is an authentic record
of my own work carried out under the supervision of Mr. Chetan Praveer, Assistant Professor,
EE, CBS Group of Institutions, Fatehpuri, Jhajjar
Date: - _____________ MANISH KUMAR CHANDAN
Place: - _____________ Roll No. 2200372
Department of Electrical Engineering
CBS Group of Institutions, Fatehpuri, Jhajjar, Haryana
CERTIFICATE
This is to certify that the dissertation entitled “HYBRID PI-FUZZY SPEED CONTROLLER
FOR INTERIOR PERMANENT MAGNET SYNCHRONUS MOTOR” being submitted by
MANISH KUMAR CHANDAN (Roll No: 2200374), for the partial fulfillment of the
requirement for the award of the degree of Master of Technology in Electrical Engineering,
from CBSGI, Fatehpuri (Jhajjar, Haryana), embodies work carried out by him under my
supervision and guidance at Department of EE, CBSGI, Fatehpuri (Jhajjar, Haryana) during
the period of January, 2018 to June, 2018.
During the period of his study at the university, he was found to be a sincere, hardworking
and well behaved person.
Mr. Chetan Praveer
Assistant Professor
Dept. of EE
ACKNOWLEDGEMENT
It is both an elevating and humbling experience to acknowledge all the people
involved in this assignment.
First of all, I sincerely acknowledge my gratitude to Almighty for his compassion and
bountiful of blessings, which made me to see this wonderful moment.
I am lacking words to express my deep sense of gratitude and regards to my revered guide
Mr. Chetan Praveer, Assistant Professor in EE, for providing me inspiration,
encouragement, kind co-operation and esteemed guidance. His innovative ideas, admirable
dedication, commitment to the subject at all phases of the research combined with his
research experience created a unique learning environment in which learning while working
has been a privilege and a joy. Without his motivating guidance and co-operation, this work
would not have possible.
I wish to extend my sincere thanks to all faculty members and non-teaching staff of
the department for their constructive comments and suggestions to improve the quality of
research work from time to time.
Warmest regards are tendered to my classmates for their co-operation, valuable
suggestions and encouragement.
Last, but not the least, the love given by my parents is beyond of any thanks. This
work could be completed only because of them and I will never be able to repay them ever.
MANISH KUMAR CHANDAN
Roll No: 2200374
ABSTRACT
Interior Permanent Magnet Synchronous Motors (IPMSM’s) are used for fast torque
response and for better performance of the machine. IPMSM's are used in low and mid
power applications such as computer peripheral equipments, robotics, adjustable speed
drives and electric vehicles and in servo applications. Simulation tools capable of handling
motor drive simulations are in demand due to growth of PM motor drives. Simulation tools
have the capabilities of performing dynamic simulations of motor drives in a visual
environment so as to facilitate the development of new systems by reducing cost and time.
In this thesis a simulation model has been developed for speed control and
improvement in the performance of a closed loop vector controlled IPMSM drive which
employ two loops for better speed tracking and fast dynamic response during transient as
well as steady state conditions by controlling the torque component of current. The outer
loop employ Hybrid PI Fuzzy logic controller (PI-FLC) while inner loop as Hysteresis Current
Controller designed to reduce the torque ripple. Despite proportional plus Integral (PI)
controller are usually preferred as speed controller due to its fixed gain (Kp) and Integral
time constant (Ki), the performance of PI controller is affected by parameter variations,
speed change and load disturbances in PMSM, due to which it results to unsatisfied
operation under transient conditions. The drawbacks of PI controller are minimized using
fuzzy logic controller (FLC).
A fuzzy control technique has been designed. PI-FLC has also been designed for
effective speed control under transient and steady state conditions. This thesis gives the
detailed modeling of an Interior Permanent Magnet Synchronous Motor drive system in
Simulink. Simulation results are presented to help analyze the system performance and PI
controller parameters influence on the system performance. The analysis has also been
performed with fuzzy logic controller as well. Finally analysis has been carried out by Hybrid
PI Fuzzy logic controller (PI-FLC) under no load, variable speed condition and variable load
conditions separately to show the results.
ORGANIZATION OF THE THESIS
The complete project thesis is divided in to five chapters as follows.
The dissertation is organized as follows:
Chapter 1 introduces the background for this dissertation research, motivation and the
research objectives.
Chapter 2 includes the comprehensive literature review in related areas is given.
Chapter 3 includes the mathematical modeling of interior permanent-magnet synchronous
machines in rotor reference frame. Moreover, basic vector control operation principles of PM
synchronous machines are briefly discussed.
Chapter 4 includes brief analysis and design of different Speed and Current controllers
which include PI, Fuzzy and Hybrid PI-FLC as speed controllers and conventional hysteresis
and Adaptive hysteresis band controller as current controllers along with their advantages
and disadvantages. Finally it describes the whole system operation by considering Hybrid
PI-FLC and AHBCC as speed and current controller respectively for their superior
performance.
Chapter 5 includes the simulation results. A comparative study of PI, Fuzzy and Hybrid PI-
FLC used separately has been made showing their superior performance during transient
and steady state period. Also a comparison study of conventional Hysteresis and adaptive
Hysteresis current controllers has been made in terms of torque ripple, current error and
switching frequency to achieve better current controller for required drive operation.
Finally,
Chapter 6 presents general conclusions and recommendations for future work.
CONTENTS
Detail of Contents Page No.
Acknowledgement
Certificate
Candidate’s Declaration
Abstract
Organization of Thesis
Table of Contents
List of Figures
List of Tables
Abbreviations
Nomenclature
Chapter 1: INTRODUCTION 1-8
1.1 Overview 1
1.2 Surface Mounted Magnet Type (SPMSM) 4
1.3 Interior Magnet Type (IPMSM): 4
1.4 Description of the Drive System 6
1.4.1
Permanent Magnet Synchronous Motor Drive
System
6
1.4.2
Permanent Magnet Synchronous Motor 6
1.4.2.1
Permanent Magnet Materials 7
1.5 Objective 8
Chapter 2: LITERATURE REVIEW
9-14
Chapter 3: THE MATHEMATICAL MODEL OF PMSM
15-19
3.1: Introduction 15
3.2: Transformations 15
3.2.1 Clarke's Transformation 15
3.2.2: Park's Transformation 16
3.3: The Model 16
3.4: Equivalent Circuit of Permanent Magnet Synchronous
Motor
18
3.5: Vector Control or Field Oriented Control Analysis 19
Chapter 4: IMPLEMENTATION OF CURRENT AND SPEED
CONTROLLER
20-32
4.1 Current Controllers 20
4.1.1 Current Controlled Inverter 20
4.1.1.1 Inverter 21
4.1.2 Hysteresis Current Controller 22
4.1.2.1 Advantages of fixed Band Hysteresis current controller 23
4.1.2.2 Disadvantages of fixed Band Hysteresis current controller 23
4.2 Speed Controllers 24
4.2.1 PI Controller 24
4.2.2: Fuzzy Logic Controller 25
4.2.3 Hybrid PI-Fuzzy Logic Controller (PI-FLC) 27
4.3 Description of Proposed PI-Fizzy Hybrid Model 31
4.4 Summary of the Chapter 32
Chapter 5: SIMULATION RESULTS AND DISCUSSION
33-41
5.1: Introduction 33
5.2: Hysteresis Current Pulse Generator 33
5.3 Performance Comparison Using Different Speed
Controllers
34
5.3.1 Result during No-load Condition for Conventional PI
Controller
34
5.3.2 Result during No-load Condition for Fuzzy Logic Controller 35
5.3.3 Result during No-load Condition for Hybrid PI-FLC 36
5.3.4 Result during Variable Load Condition for Hybrid PI-FLC 38
5.3.5 Result during Variable Speed Condition for Hybrid PI-FLC 39
5.4 Summary 41
Chapter 6: CONCLUSION AND FUTURE SCOPE 42-43
7.1: Conclusion 42
7.2: Future Scope 42
References 44
APPENDIX 46
LIST OF FIGURE
Figure Detail of Figures Page no.
Figure 1.1: Classification of Permanent Magnets Machines 3
Figure 1.2: Surface PM (SPM) Synchronous Machine 5
Figure 1.3: Interior PM (IP) Sync. Machine 5
Figure 1.4: Drive System Schematic diagram 6
Figure 1.5: Flux Density Vs Magnetizing Field of PM Materials 7
Figure 3.1: Permanent Magnet Motor Electric Circuit without Damper Windings
18
Figure 3.2: Vector Diagram Of Different Reference Frame 19
Figure 4.1: Voltage Source Inverter Connected to a Motor 21
Figure 4.2: Inverter with IGBTs and Antiparallel Diodes 22
Figure 4.3: Schematic diagram of Hysteresis controller 23
Figure 4.4: Block diagram of speed loop 25
Figure 4.5: Basic diagram of fuzzy control system 26
Figure 4.6: Actual Block diagram of the fuzzy controller in Simulink 27
Figure 4.7: Schematic model of Hybrid PI-Fuzzy speed controller 30
Figure 4.8: PI-Fuzzy Hybrid Speed control model for IPMSM 31
Figure 4.9: Upper layer of Simulink of Hybrid PI-Fuzzy Speed Controller 32
Figure 5.1: Fixed band hysteresis current pulse generator 34
Figure 5.2: PI controller response under No Load condition 35
Figure 5.3: FLC Block diagram 36
Figure 5.4: Electromagnetic Torque, Rotor speed and response of fuzzy logic controller
36
Figure 5.5: Block diagram of Hybrid PI-Fuzzy controller 37
Figure 5.6: Hybrid Torque, Rotor Speed and ripple factor response at No
Load
37
Figure 5.7: Hybrid model variable load fuzzy rule viewer 38
Figure 5.8: Results for variable load on Hybrid model 39
Figure 5.9: Hybrid model variable speed fuzzy rule viewer 44
Figure 5.10: Hybrid model variable speed results 45
List of Tables
Table Detail of Tables Page no.
Table 4.1 Fuzzy logic Control Rules 28
ABBREVIATIONS
AHCC -Adaptive Hysteresis Current Control
Back-EMF Back-Electromotive Force
BLDCM -Brushless DC Machine
CCCP Constant Current Constant Power
CPSR Constant Power Speed Range
EV Electric Vehicle
FLC - Fuzzy Logic Controller
FIS - Fuzzy Inference System
FW Flux-Weakening
HB -Hysteresis Band
HEV -Hybrid Electric Vehicle
HPI-FLC -Hybrid PI- Fuzzy Logic Controller
IPM Interior Mounted Permanent Magnet
IPMSM -Interior Permanent Magnet Synchronous Machine
MF - Membership Function
MMF Magneto-Motive Force
MTPA Maximum Torque per Ampere
PI -Proportion Integral
PM -Permanent Magnet
PMAC -Permanent Magnet Alternating Current
PMDC -Permanent Magnet Direct Current
PMSM -Permanent Magnet Synchronous Machine
PWM -Pulse Width Modulation
SPWM Sinusoidal Pulse Width Modulation
SMPM -Surface Mounted Permanent Magnet
SMPMSM -Surface Mounted Permanent Magnet Synchronous Machine
VSI -Voltage Source Inverter
NOMENCLATURE
Symbols
B friction
BDCM Brushless DC Motor
CSI Current Source Inverter
d Direct o polar axis
fc crossover frequency
ia,ib,ic Three phase currents
id d-axis current
if equivalent permanent magnet field current
iq q-axis current
Im Peak value of supply current
IGBT Insolate Gate Bipolar Transistor
IPM Interior Permanent Magnet
J inertia
L self inductance
Ld d-axis self inductance
Lls stator leakage inductance
Ldm d-axis magnetizing inductance
Lqm q-axis magnetizing inductance
Lq q-axis self inductance
Ls equivalent self inductance per phase
P number of poles
PI proportional integral
PM Permanent Magnet
PMSM Permanent Magnet Synchronous Motor
q Quadrature or interpolar axis
Rs stator resistance
SPM Surface Permanent Magnet
Te develop torque
TL load torque
Va,Vb,Vc Three phase voltage
Vd d-axis voltage
Vq q-axis voltage
VSI Voltage Source Inverter
ρ derivative operator
λd flux linkage due d axis
λf PM flux linkage or Field flux linkage
λq flux linkage due q axis
θr rotor position
ωm rotor speed
ωr electrical speed
ω rated motor rated speed
1
CHAPTER 1
INTRODUCTION
1.1 Overview
The AC machine drives are becoming more and more popular, specifically the Induction
Motors and Permanent Magnet Synchronous Motor (PMSM), but the PMSM drives are meeting
the requirements with a fast dynamic response, high power factor and wide operating speed
range in high performance applications. Some of the PMSM advantages includes high
efficiency, small volume, high power density, fast dynamics, large torque to inertia ratio, and low
maintenance costs. Their applications is found in machine tools, servo and robots, in textile
machines, electric vehicle etc.
In a permanent magnet synchronous motor, the dc field winding of the rotor has been
replaced by a permanent magnet to produce the air-gap magnetic field. By putting the magnets
on the rotor, some of the electrical losses due to the field windings get reduced and the absence
of the field losses improve the thermal characteristics of the Permanent Magnet machines along
with its efficiency. The lack of some mechanical components such as brushes and slip rings
makes the motor much lighter, high power to weight ratio which assures a higher efficiency and
reliability. The permanent magnet synchronous generator is a viable solution for wind turbine
applications as well. PM machines also have some disadvantages, at high temperature, the
magnet gets demagnetized, difficulties to manufacture and high cost of PM material.
Among the synchronous motor types the permanent magnet synchronous motor
(PMSM) is one possible design of the three phase synchronous machines. The stator of a
PMSM has conventional three phase windings. In the rotor, PM materials have the same
function of the field winding in a conventional synchronous machine. Their development was
possible by the introduction of new magnetic materials, like the rare earth materials. The use of
a PM to generate substantial air gap magnetic flux makes it possible to design highly efficient
PM motors. With fast and accurate speed responses, quick recovery of speed from load
disturbances and insensitivity to parameter variation is the important criteria of high
performance drive system. The conventional PI and proportional integral derivative controllers
have been broadly used as speed controllers in PMSM drives.
2
Permanent Magnet Machines are such electromechanical devices which are using
magnets to produce a magnetic flux in the air gap. There are two major classifications of ac
motors. The first one is induction motors that are electrically connected to power source through
electromagnetic coupling, the rotor and the stator fields interact, creating rotation without any
other power source. The second is synchronous motors that have fixed stator windings that are
electrically connected to the ac supply with a separate source of excitation connected to field
windings when the motor is operating at synchronous speed.
The permanent magnet synchronous motor (PMSM) has a number of advantages over
other machines used for ac servo drives. The stator current of an induction motor (IM) contains
magnetizing as well as torque producing components. The use of the permanent magnet in the
rotor of the PMSM makes it unnecessary to supply magnetizing current through the stator for
constant air gap flux; the stator current need only to be torque-producing. Hence for the same
output, the PMSM will operate at a higher power factor (because of the absence of magnetizing
current) and will be more efficient than the IM. The conventional wound-rotor synchronous
machine (SM), on the other hand, must have dc excitation on the motor, which is often supplied
by brushes and slip rings. This means that the rotor losses and regular brush maintenance, are
less. The key reason for the development of the PMSM was to remove the foregoing
disadvantages of the SM by replacing its field coil, dc power supply, and slip rings with a
permanent magnet. The PMSM, therefore, has a sinusoidal induced EMF which requires
sinusoidal currents to produce a constant torque just like the SM. Current research in the design
of the PMSM indicates that it has a higher-torque-to-inertia ratio and power density when
compared to the IM or the wound-rotor SM, which makes it preferable for certain high-
performance applications like robotics and aerospace actuators. The PMSM which is smaller in
size and lower in weight makes it preferable for high performance applications.
The model of PMSM is however non-linear. This paper applies the concept of vector
control that has been extensively applied to derive a linear model of the PMSM for the controller
design purposes. The speed and current controllers are then designed. The nonlinear equations
of the PMSM, current and speed controller equations and real time model of the inverter
switches and vector control are used in the simulation. The switches are assumed to be ideal.
PM electric machines are classified into two groups: PMDC machines and PMAC
machines. The PMDC machines are similar with the DC commutator machines; the only
difference is that the field winding is replaced by the permanent magnets while in case of PMAC
the field is generated by the permanent magnets placed on the rotor and the slip rings, the
brushes and the commutator does not exist in this type of machine. For this reason the
3
machine is simpler and more attractive to use instead of PMDC. PMAC can be classified
depending on the type of the back electromotive force (EMF): Trapezoidal type and Sinusoidal
type. Sinusoidal type PM machine can further be classified as Surface mounted PMSM and
Interior PMSM. The classification can be shown as below:
Figure.1.1 Classification of Permanent Magnets Machines
The trapezoidal PMAC machines also called Brushless DC motors (BLDC) has a
trapezoidal-shaped back EMF and can develop trapezoidal back EMF waveforms with following
characteristics:
Rectangular current waveform
Rectangular distribution of magnet flux in the air gap
Concentrated stator windings.
While the sinusoidal PMAC machines, called Permanent magnet synchronous machines
(PMSM) has a sinusoidal-shaped back EMF and develop sinusoidal back EMF waveforms with
following characteristics:
Sinusoidal current waveforms
Sinusoidal distribution of magnet flux in the air gap
Sinusoidal distribution of stator conductors.
Based on the rotor configuration the PM synchronous machine can be classified as:
4
1.2 Surface Mounted Magnet Type (SPMSM):
In these type of machines the magnets are mounted on the surface of the rotor. The
magnets can be presumed as air because the permeability of the magnets is close to unity (μ =
1) and the saliency is not present due to same width of the magnets. Therefore the inductances
expressed in the quadrature coordinates are equal (Lq = Ld). In the case of SPMSM the
saliency is not present, making this machine easier to design, becoming an attractive solution
for wind turbine application.
1.3 Interior Magnet Type (IPMSM):
In this type of motors, the magnets are placed inside the rotor. In this type the saliency
is available and the air gap of d-axis is greater as compared with the q axis gap resulting that
the q axis inductance has a different value other than the d axis inductance. There is inductance
variation for this type of rotor because the permanent magnet part is equivalent to air in the
magnetic circuit calculation. These types of motors are considered to have saliency with q axis
inductance greater than the d axis inductance (Lq>Ld). Due to saliency IPMSM is a good choice
for the high-speed operations such as PCB manufacturing, spindle drives and hybrid electric
vehicles (HEV) etc.
Among Interior Permanent Magnet Synchronous Motor (IPMSM) and Surface Mounted
Permanent Magnet Synchronous Motor (SMPMSM), IPMSM is preferably used for many
application due to its constructional features along with higher demagnetizing effect to enhance
the speed above the base speed. Although IPMSM demand gradually increasing in various
industrial applications with veracious speed control and fast dynamic response, there still exists
a great challenge to control its speed more accurately under various conditions.
Vector control (or Field Oriented Control) principle makes the analysis and control of
Permanent Magnet Synchronous Motor (PMSM) drives system simpler and provides better
dynamic response. It is also widely applied in many areas where servo-like high performance
plays a secondary role to reliability and energy savings. To achieve the field-oriented control of
PMSM, knowledge of the rotor position is required. Usually the rotor position is measured by a
shaft encoder, resolver, or hall sensors.
In the type Permanent Magnet Synchronous Motor, the excitation flux is set-up by
magnets. So no magnetizing current is needed from this type of supply. So it enables the
5
application of the flux orientation mechanism by forcing the d-axis component of the stator
current vector (id) to be zero. As a result, the electromagnetic torque will be directly proportional
to the q-axis component of the stator current vector (iq), hence better dynamic performance is
obtained by controlling the electro-magnetic torque separately. This thesis presents the field
oriented vector control scheme for permanent magnet synchronous motor (PMSM) drives which
regulates the speed of the PMSM and is provided by a quadrature axis current command
developed by the speed controller. PI controller may preferably be used for outer speed control
loop but because of its fixed proportional gain constant and integral time constant, the behavior
of the PI controllers are affected by parameter variations, load disturbances and speed
fluctuation [23] [24]. To overcome the problem of PI controller, a Fuzzy controller has been
designed and implemented. Finally taking the superior performances of PI and Fuzzy controller,
a Hybrid PI-Fuzzy controller has been designed and implemented as outer speed loop which
provides the reference quadrature axis current to the current controller.
Fig.1.2 Surface PM (SPM) Synchronous Machine Fig.1.3 Interior PM (IP) Sync. Machine
The conventional hysteresis band current controller has proved that it is most suitable for
current controller VSI fed ac drives due to its simplicity and fast speed tracking. However it has
certain limitations like large current ripple in steady state and a variable switching frequency
operation during motor load changes. So here an adaptive hysteresis current controller has
been implemented in which the hysteresis band is programmed as a function of variation of the
6
motor speed and load current. The proposed current control strategy is applied to the inner loop
of the vector controlled permanent magnet synchronous motor (PMSM) drive system in order to
reduce the torque ripple during load variation.
1.4 Description of the Drive System
The description of different components such as permanent magnet motors, position
sensors, inverters and current controllers of the drive system. A review of permanent magnet
materials and classification of permanent magnet motors is also given.
1.4.1 Permanent Magnet Synchronous Motor Drive System
The motor drive consists of four main components, the PM motor, inverter, control unit
and the position sensor. The components are connected as shown in figure 2.1.
Figure 1.4 Drive System Schematic diagram
Descriptions of the different components of Permanent Magnet Synchronous Motor drive are
explained follows:
1.4.2 Permanent Magnet Synchronous Motor:
A permanent magnet synchronous motor (PMSM) is a motor that uses permanent magnets
to produce the air gap magnetic field rather than using electromagnets. These motors have
significant advantages, attracting the interest of researchers and industry for use in many
applications.
7
1.4.2.1 Permanent Magnet Materials
The properties of the permanent magnet material will affect directly the performance of the
motor and proper knowledge is required for the selection of the materials and for understanding
PM motors. The earliest manufactured magnet materials were hardened steel. Magnets made
from steel were easily magnetized. However, they could hold very low energy and it was easy to
Demagnetize. In recent years other magnet materials such as Aluminum Nickel and Cobalt
alloys (ALNICO), Strontium Ferrite or Barium Ferrite (Ferrite), Samarium Cobalt (First
generation rare earth magnet) (SmCo) and Neodymium Iron-Boron (Second generation rare
earth magnet) (NdFeB) have been developed and used for making permanent magnets. The
rare earth magnets are categorized into two classes: Samarium Cobalt (SmCo) magnets and
Neodymium Iron Boride (NdFeB) magnets. SmCo magnets have higher flux density levels but
they are very expensive. NdFeB magnets are the most common rare earth magnets used in
motors these days. A flux density versus magnetizing field for these magnets is illustrated in
figure 1.5.
Figure 1.5 Flux Density Vs Magnetizing Field of PM Materials [21]
8
1.5. Objective:
The main objective of this research is to improve the performance of an IPMSM drive system
by achieving more precise speed tracking and smooth torque response by implementing a
Hybrid PI-FLC and an adaptive hysteresis band current controller respectively by employing
their superior performance.
The overall objectives to be achieved in this study are:
To design the equivalent d-q model of IPMSM for its vector control analysis and closed loop
operation of drive system.
Analysis and implementation of PI, Fuzzy and Hybrid PI-Fuzzy logic controller separately as
outer speed loop in steady state and transient condition (step change in load and speed) in
MATLAB/Simulink environment.
Analysis and implementation of conventional hysteresis current controller and adaptive
hysteresis band current controller as inner current controller in MATLAB/Simulink environment
to compare their performances so as to consider better controller for our system application.
Comparison of system performance using PI, Fuzzy and Hybrid PI-FLC separately as speed
controller and adaptive hysteresis current controller as controller during steady state and
transient condition in MATLAB/Simulink environment.
9
CHAPTER 2
LITERATURE REVIEW
Magnetic motor drives have been a topic of interest for the last twenty years. Different
authors have carried out modeling and simulation of such drives.
In 1986 Sebastian, T., Slemon, G. R. and Rahman, M. A. [1] reviewed permanent
magnet synchronous motor advancements and presented equivalent electric circuit models for
such motors and compared computed parameters with measured parameters. Experimental
results on laboratory motors were also given.
In 1986 Jahns, T.M., Kliman, G.B. and Neumann, T.W. [2] discussed that interior
permanent magnet (IPM) synchronous motors possessed special features for adjustable speed
operation which distinguished them from other classes of ac machines. They were robust high
power density machines capable of operating at high motor and inverter efficiencies over wide
speed ranges, including considerable range of constant power operation. The magnet cost was
minimized by the low magnet weight requirements of the IPM design. The impact of the buried
magnet configuration on the motor’s electromagnetic characteristics was discussed. The rotor
magnetic saliency preferentially increased the quadrature-axis inductance and introduced a
reluctance torque term into the IPM motor’s torque equation. The electrical excitation
requirements for the IPM synchronous motor were also discussed. The control of the sinusoidal
phase currents in magnitude and phase angle with respect to the rotor orientation provided a
means for achieving smooth responsive torque control. A basic feed forward algorithm for
executing this type of current vector torque control was discussed, including the implications of
current regulator saturation at high speeds. The key results were illustrated using a combination
of simulation and prototype IPM drive measurements.
In 1988 Pillay and Krishnan, R. [3], presented PM motor drives and classified them into
two types such as permanent magnet synchronous motor drives (PMSM) and brushless dc
motor (BDCM) drives. The PMSM has a sinusoidal back emf and requires sinusoidal stator
currents to produce constant torque while the BDCM has a trapezoidal back emf and requires
rectangular stator currents to produce constant torque. The PMSM is very similar to the wound
rotor synchronous machine except that the PMSM that is used for servo applications tends not
10
to have any damper windings and excitation is provided by a permanent magnet instead of a
field winding. Hence the d, q model of the PMSM can be derived from the well known model of
the synchronous machine with the equations of the damper windings and field current dynamics
removed. Equations of the PMSM are derived in rotor reference frame and the equivalent circuit
is presented without dampers. The damper windings are not considered because the motor is
designed to operate in a drive system with field-oriented control. Because of the non sinusoidal
variation of the mutual inductances between the stator and rotor in the BDCM, it is also shown
in this paper that no particular advantage exists in transforming the abc equations of the BCDM
to the d, q frame.
As an extension of his previous work, Pillay, P. and Krishnan, R. in 1989 [4] presented
the permanent magnet synchronous motor (PMSM) which was one of several types of
permanent magnet ac motor drives available in the drives industry. The motor had a sinusoidal
flux distribution. The application of vector control as well as complete modeling, simulation, and
analysis of the drive system were given. State space models of the motor and speed controller
and real time models of the inverter switches and vector controller were included. The machine
model was derived for the PMSM from the wound rotor synchronous motor. All the equations
were derived in rotor reference frame and the equivalent circuit was presented without dampers.
The damper windings were not considered because the motor was designed to operate in a
drive system with field-oriented control. Performance differences due to the use of pulse width
modulation (PWM) and hysteresis current controllers were examined. Particular attention was
paid to the motor torque pulsations and speed response and experimental verification of the
drive performance were given.
A torque production at low speeds along with the system practical limitation in the high
speed regions were investigated by Dhaouadi R. and Mohan N. [5] by using ramp type,
hysteresis type and space vector type controller and performances of these different types of
controllers were noticed. Traditional Hysteresis control method is used due to its simplicity in
implementation, fast control response, and inherent current(peak) limiting ability.
The paper in 1997 by Wijenayake, A.H. and Schmidt, P.B. [6], described the
development of a two-axis circuit model for permanent magnet synchronous motor (PMSM) by
taking machine magnetic parameter variations and core loss into account. The circuit model
was applied to both surface mounted magnet and interior permanent magnet rotor
configurations. A method for on-line parameter identification scheme based on no-load
11
parameters and saturation level, to improve the model, was discussed in detail. Test schemes
to measure the equivalent circuit parameters, and to calculate saturation constants which
govern the parameter variations were also presented.
In 1997 Jang-Mok, K. and Seung-Ki, S. [7], proposed a novel flux-weakening scheme
for an Interior Permanent Magnet Synchronous Motor (IPMSM). It was implemented based on
the output of the synchronous PI current regulator reference voltage to PWM inverter. The on-
set of flux weakening and the level of the flux were adjusted inherently by the outer voltage
regulation loop to prevent the saturation of the current regulator. Attractive features of this flux
weakening scheme included no dependency on the machine parameters, the guarantee of
current regulation at any operating condition, and smooth and fast transition into and out of the
flux weakening mode. Experimental results at various operating conditions including the case of
detuned parameters were presented to verify the feasibility of the proposed control scheme.
Bose, B. K., in 2001 [8], presented different types of synchronous motors and compared
them to induction motors. The modeling of PM motor was derived from the model of salient pole
synchronous motor. All the equations were derived in synchronously rotating reference frame
and was presented in the matrix form. The equivalent circuit was presented with damper
windings and the permanent magnet was represented as a constant current source. Some
discussions on vector control using voltage fed inverter were given.
Bowen, C., Jihua, Z. and Zhang, R. in 2001 [9], addressed the modeling and simulation
of permanent magnet synchronous motor supplied from a six step continuous inverter based on
state space method. The motor model was derived in the stationary reference frame and then in
the rotor reference frame using Park transformation. The simulation results obtained showed
that the method used for deciding initial conditions was very effective.
In 2002 Mademlis, C. and Margaris, N. [10], presented an efficiency optimization method
for vector-controlled interior permanent-magnet synchronous motor drive. Based on theoretical
analysis, a loss minimization condition that determines the optimal q-axis component of the
armature current was derived. Selected experimental results were presented to validate the
effectiveness of the proposed control method.
In 2004, Jian-Xin, X., Panda, S. K., Ya-Jun, P., Tong Heng, L. and Lam, B. H. [11]
applied a modular control approach to a permanent-magnet synchronous motor (PMSM) speed
control. Based on the functioning of the individual module, the modular approach enabled the
12
powerfully intelligent and robust control modules to easily replace any existing module which did
not perform well, meanwhile retaining other existing modules which were still effective. Property
analysis was first conducted for the existing function modules in a conventional PMSM control
system: proportional-integral (PI) speed control module, reference current-generating module,
and PI current control module. Next, it was shown that the conventional PMSM controller was
not able to reject the torque pulsation which was the main hurdle when PMSM was used as a
high-performance servo. By virtue of the internal model, to nullify the torque pulsation it was
imperative to incorporate an internal model in the feed-through path. This was achieved by
replacing the reference current-generating module with an iterative learning control (ILC)
module. The ILC module records the cyclic torque and reference current signals over one entire
cycle, and then uses those signals to update the reference current for the next cycle. As a
consequence, the torque pulsation could be reduced significantly. In order to estimate the
torque ripples which might exceed certain bandwidth of a torque transducer, a novel torque
estimation module using a gain-shaped sliding-mode observer was further developed to
facilitate the implementation of torque learning control. The proposed control system was
evaluated through real-time implementation and experimental results validated the
effectiveness.
Araujo, R.E., Leite, A.V. and Freitas, D.S. in 1997 [12], mentioned the different
simulation tools available and the benefits that were obtained by accelerating the process for
the development of visual design concepts. Among various software packages for simulation of
electronic circuits, like SPICE and SABER, EMTP, EUROSTAG, or for specialized simulations
tools for power electronics system like SIMPLORER, POSTMAC, SIMSEN, ANSIM, and
PSCAD, they had chosen MATLAB/Simulink. MATLAB/Simulink had user-friendly environment,
visual design, Real-Time Workshop and libraries of models for the various components of a
power electronic system.
Ong, C in 1998 [13], explained the need for powerful computation tools to solve complex
models of motor drives. Among the different simulation tools available for dynamic simulation he
had chosen MATLAB/SIMULINK® as the platform for his book because of the short learning
curve required to start using it, its wide distribution, and its general purpose nature.
Macbahi, H. Ba-razzouk, A. Xu, J. Cheriti, A. and Rajagopalan, V. in 2000 [14],
mentioned that a great number of universities and researchers used the MATLAB/SIMULINK
software in the field of electrical machines because of its advantages. such as user friendly
13
environment, visual oriented programming concept, non-linear standard blocks and a large
number of toolboxes for special applications. In 1997 Reece, J.H., Bray, C.W., Van Tol, J.J. and
Lim, P.K. [15], discussed three possible computer simulation tools such as PSpice, HARMFLO
and the Electromagnetic Transients Program (EMTP) in their project on power systems
containing adjustable speed drives. They selected EMTP as the primary simulation tool because
of its broad range of capabilities, which were well matched to their problem.
French, C.D., Finch, J.W. and Acarnley, P.P. in 1998 [16], had found that in recent
years the increase in desktop computing power has lead to an increase in the sophistication of
both design and simulation tools available to the design engineer. One such tool becoming
more wide spread amongst academia and industry was Mathwork’s Simulink / Matlab package.
This paper described how Simulink could be used as an integrated development environment
for simulation and real time control of electric motor drive systems. This was carried out with the
aid of motor models together with simulation and real time control circuits. It was demonstrated
how such a set-up could be used as a cost effective control system rapid prototyping scheme.
Onoda, S. and Emadi, A. in 2004 [17], had developed a modeling tool to study
automotive systems using the power electronics simulator (PSIM) software. PSIM was originally
made for simulating power electronic converters and motor drives. This userfriendly simulation
package was able to simulate electric/electronic circuits.
Venkaterama, G. [18]; had developed a simulation for permanent magnet motors using
Matlab/simulink. The motor was a 5 hp PM synchronous line start type. Its model included the
damper windings required to start the motor and the mathematical model was derived in rotor
reference frame. The simulation was presented with the plots of rotor currents, stator currents,
speed and torque.
Simulink PM Synchronous Motor Drive demo circuit (2005) [19] used the AC6 block of
Simulik Power Systems library. It modeled a permanent magnet synchronous motor drive with a
braking chopper. The PM synchronous motor was fed by a PWM voltage source inverter, which
was built using a Universal Bridge Block. The speed control loop used a PI regulator to produce
the flux and torque references for the vector control block. The vector control block computed
the three reference motor line currents corresponding to the flux and torque references and then
fed the motor with these currents using a three-phase current regulator. Motor current, speed,
and torque signals were available at the output of the block.
14
In the above works, none of them have considered a real drive system simulation in
Simulink operating at constant torque and flux weakening regions. In this thesis, a combination
of PI-Fuzzy controllers has been used for speed control and improvement in performance of the
IPMSM drive system.
15
CHAPTER 3
THE MATHEMATICAL MODEL OF PMSM
3.1 Introduction
A three phase PMSM is constructed with sinusoidally distributed phase windings, with a 120
degree angle phase shift between the three windings. In a stator frame of reference coordinate
system the phase vectors abc can be seen as they are fixed in angle, but with time varying
amplitudes. This three vector representation makes calculation of machine parameters
unnecessarily complex. Transformation of the system into a two vector orthogonal system,
makes the necessary calculations much simpler.
3.2 Transformations
A 3-phase machine can be described by a set of differential equations in time dependent
coefficients. By the transformation of the motor parameters, the complexity of machine
calculations can be reduced. According to the definitions the transforms give a 3rd component,
zero-sequence. But since a motor normally is a balanced load, the zero-sequence not of
importance.
The two transformations presented below are not the exact Clarke and Park, but in a slightly
modified form to make power invariance.
3.2.1 Clarke's Transformation
The Clarke transformation changes a 3-phase system into a 2-phase system with orthogonal
axes in the same stationary reference frame. The ABC parameters are transformed into
parameters by equation and in reverse by it’s inverse equation.
16
3.2.2 Park's Transformation
The Park transformation changes a 2-phase system in one stationary reference frame into a
2- phase system with orthogonal axes in a different rotating reference frame. The 2 new phase
variables are denoted d and q, and are referred to as the motors direct and quadrature-axis.
Q r is the position angle between stator and rotor reference frame
3.3 The Model
A surface-mounted SM is used in this research work, hence it’s mathematical model of the
PMSM is presented. The d-q model has been developed on rotor frame of reference. Stator
mmf rotates at the same speed as that of the rotor.
The model of PMSM without having damper winding has been developed on rotor reference
frame using the following assumptions:
1. The induced EMF is sinusoidal.
2. Eddy currents and hysteresis losses are negligible.
3. There are no field current dynamics.
4. The stator windings are balanced with sinusoidally distributed magneto-motive force (mmf).
The stator flux linkage, voltage, and electromagnetic torque equations in the dq reference
frame are as follows:
17
18
3.4 Equivalent Circuit of Permanent Magnet Synchronous
Motor
For analysis purpose equivalent circuits of the motors are used for study and simulation
of motors. From the d-q modeling of the motor using the stator voltage equations the equivalent
circuit of the motor can be derived. Assuming rotor d axis flux from the permanent magnets is
represented by a constant current source as described in the following equation λf= Ldmif ,
following figure can be obtained from shown as fig 2.1
The equivalent circuits are
1. Dynamic stator q-axis equivalent circuit
2. Dynamic stator d-axis equivalent circuit
Figure 3.1 Permanent Magnet Motor Electric circuit without Damper Windings
19
3.5 Vector Control or Field Oriented Control Analysis
This control strategy was developed prominently in the1980s to meet the challenges of
transient condition analysis and oscillating flux with torque responses in inverter fed induction
and synchronous motor drives during transient as well as steady state condition. The
inexplicable dynamic behavior of large current transients and the resulting failure of inverters
was a curse and barrier to the entry of inverter fed ac drives into the market. Compared to these
ac drives, the separately excited dc motor drives were excellent dynamic control of flux and
torque. The key to the dc motor drives performance is its ability to independently control the flux
and torque. Vector diagram of different frames is given below:
Figure 3.2 Vector Diagram of Different Reference Frame
20
CHAPTER 4
IMPLEMENTATION OF CURRENT AND SPEED
CONTROLLERS
4.1 Current Controllers:
The behavior of proposed PMSM drive system predominantly depends on the
characteristics of type of current control technique that we employ for the current control of
Voltage Source Inverter (VSI). So, the current control of VSI is again another subject that we
have to concern seriously for better performance of motion control drive applications. In this
proposed system, the current controller has implemented in inner loop which generates the
control gate signals for control of inverter output which in spite control output torque of IPMSM.
Appropriate selection of controllable switches and current controller play an important role for
the better efficacy of the VSI as well as drive system.
Now going through the characteristics of various controllers that have been previously
used as current controller for the speed control of IPMSM drive [5-7] [11], it has been found that
Adaptive Hysteresis Band Current Controller (AHBCC) can be used to achieve a better and
satisfying control for the current controller. Although fixed band hysteresis current controller is
simple in implementation with less complexity but prior to it AHBCC has been preferred due to
its some advantages over fixed band hysteresis current controller. So in this section,
conventional fixed band hysteresis and adaptive hysteresis band current control technique has
been discussed along with their design and implementation of adaptive hysteresis band current
controller in the drive system.
4.1.1 Current Controlled Inverter
The motor is fed form a voltage source inverter with current control. The control is performed by
regulating the flow of current through the stator of the motor. Current controllers are used to
generate gate signals for the inverter. Proper selection of the inverter devices and selection of
the control technique will guarantee the efficacy of the drive.
21
4.1.1.1 Inverter
Voltage Source Inverters are devices that convert a DC voltage to AC voltage of variable
frequency and magnitude. They are very commonly used in adjustable speed drives and are
characterized by a well defined switched voltage wave form in the terminals. Figure 3.1 shows a
voltage source inverter. The AC voltage frequency can be variable or constant depending on the
application.
Figure 4.1 Voltage Source Inverter Connected to a Motor
Three phase inverters consist of six power switches connected as shown in figure 4.1 to a
DC voltage source. The inverter switches must be carefully selected based on the requirements
of operation, ratings and the application. There are several devices available today and these
are thyristors, bipolar junction transistors (BJTs), MOS field effect transistors (MOSFETs),
insulated gate bipolar transistors (IGBTs) and gate turn off thyristors (GTOs). The devices list
with their respective power switching capabilities are shown in table 2.1 MOSFETs and IGBTs
are preferred by industry because of the MOS gating permits high power gain and control
advantages. While MOSFET is considered a universal power device for low power and low
voltage applications, IGBT has wide acceptance for motor drives and other application in the
low and medium power range. The power devices when used in motor drives applications
require an inductive motor current path provided by antiparallel diodes when the switch is turned
off. Inverters with anti parallel diodes are shown in figure 4.2.
22
Fig 4.2 Inverter with IGBTs and Antiparallel Diodes
4.1.2. Hysteresis Current Controller:
Among the different PWM techniques, hysteresis-band current control PWM technique is
popularly used due of its simplicity of implementation. Hysteresis band current controller is a
current control technique in which controller will try to keep the input current error within a range
which is fixed by some width of band gap defined by upper and lower band. In this technique,
the reference current of any phase is summed with the negative of the measured current value
of that phase which will give the current error. The current error is then provided as the input of
the controller which then compare it with its defined fixed band and gives the output as per its
characteristics as required gate drive signal. The characteristics of hysteresis band can be
defined as “when the error crosses the lower limit of the hysteresis band, the upper switch of the
inverter leg (one at a time) is turned ON and when the current attempts to become more than
the upper limit of band, the bottom switch (one at a time) is turned ON”. So, the switching logic
can be formulated as follows:
Suppose current error (δ) is given by,
δ = Reference Current (Iref) – Actual current (Iact), then
If δ >HB upper switch of any single leg of VSI is ON (say Q1=1) and lower switch of same leg
is OFF (say Q4=0).
If δ <-HB upper switch of any single leg of VSI is OFF (say Q1=0) and lower switch of same
leg is ON (say Q4=1).
For symmetrical operation of three phases, above logic is same but only band profile of other
phases will be displaced with 1200.
23
The logic based upon which this controller generates the required gate drive signal can
be easily understood from fig. 4.3
Figure.4.3: Schematic diagram of Hysteresis controller.
Here we can observe that the current error has restricted in between the defined band gap
which in other view trying to follow the reference current with less current error which we can
achieve by decreasing the defined band gap and as a result it producing the required gate drive
signal as per its behavior. But on the other hand we also have to take care of better
performance of drive system during fixing up the upper and lower hysteresis band such that it
should be optimum and it would not lead to poor operation of drive system.
4.1.2.1 Advantages of fixed Band Hysteresis current controller:
The conventional fixed band hysteresis current control technique has been suitable for
current controlled voltage source inverters due to some of its advantages as follows:
1. Simple implementation.
2. Inherent current peak limitation.
3. Good transient response.
4. Unconditioned stability.
5. Robust against system parameters variation.
4.1.2.2 Disadvantages of fixed Band Hysteresis current controller:
Despite of above advantages of the fixed band hysteresis band current control, there are
some unavoidable drawbacks in the technique as follows:
1. Switching frequency is not constant i.e. variable switching frequency.
24
2. Greater current ripple in steady- state.
3. The modulation process generates undesired sub-harmonic components resulting in higher
machine heating.
4. No intercommunication between each hysteresis controller of other phases and hence no
strategy to generate zero-voltage vectors. Due to which the switching frequency increases at
lower modulation index and the signal will leave the hysteresis band whenever the zero vector is
turned on.
4.2. Speed Controllers:
The design of the speed controller is important from the point of view of imparting
desired transient and steady-state characteristics to the speed-controlled PMSM drive system.
The purpose of a motor speed controller is to take a signal representing the demanded speed,
and to drive a motor at that speed.
4.2.1. PI Controller:
A proportional plus integral controller is sufficient for many industrial applications and
hence, it is considered in this section. The speed error between the speed and its reference,
given by (ωr *- ωr), is processed through a proportional plus integral (PI) type controller
(hereafter known as the speed controller) to nullify the steady-state error in speed. The output of
this speed controller constitutes the electromagnetic torque reference, T*, because the speed
error can be nulled and minimized only by increasing or decreasing the electromagnetic torque
in the machine, depending on whether the speed error is positive or negative, respectively.
The operation of the controller must be according to the speed range. For operation up
to rated speed it will operate in constant torque region and for speeds above rated speed it will
operate in flux-weakening region. In this region the d-axis flux and the developed torque are
reduced. Speed controller calculates the difference between the reference speed and the actual
speed producing an error, which is fed to the PI controller. PI controllers are used widely for
motion control systems. They consist of a proportional gain that produces an output proportional
to the input error and an integration gain to minimize the steady state error zero for a step
change in the input. The design of the speed loop assumes that the current loop is at least 10
times faster than speed loop. The PI controller can be integrated as outer speed loop in system
is shown in fig.3.4.
25
Fig.4.4: Block diagram of speed loop
For our IPMSM; kt = (3/2) (P/2) λf = 0.816; where: λf = 0.272; P = 4; J = 0.000179
4.2.2. Fuzzy Logic Controller:
Fuzzy logic is a logic having many values, approximate reasoning and have a vague
boundary. The variables in fuzzy logic system may have any value in between 0 and 1 and
hence this type of logic system is able to address the values of the variables (called linguistic
variables) those lie between completely truths and completely false. Each linguistic variable is
described by a membership function which has a certain degree of membership at a particular
instance. The human knowledge is incorporated in fuzzy rules. The fuzzy inference system
formulates suitable rules and based on these rules the decisions are made. This whole process
of decision making is mainly the combination of concepts of fuzzy set theory, fuzzy IF-THEN
rules and fuzzy reasoning. The fuzzy inference system makes use of the IF-THEN statements
and with the help of connectors present (such as OR and AND), necessary decision rules are
constructed. The fuzzy rule base is the part responsible for storing all the rules of the system
and hence it can also be called as the knowledge base of the fuzzy system. Fuzzy inference
system is responsible for necessary decision making for producing a required output. The fuzzy
control systems are rule-based systems in which a set of fuzzy rules represent a control
decision mechanism for adjusting the effects of certain system stimuli. The rule base reflects the
human expert knowledge, expressed as linguistic variables, while the membership functions
represent expert interpretation of those variables. The block diagram of a fuzzy control system
is shown in Fig. 4.5 and 4.6. A fuzzy logic controller is composed of the following four elements:
26
Fig. 4.5 Basic diagram of fuzzy control system
1. A rule-base (a set of If-Then rules), which contains a fuzzy logic quantification of the expert’s
linguistic description of how to achieve good control.
2. An inference mechanism (also called an “inference engine” or “fuzzy inference” module),
which emulates the expert’s decision making in interpreting and applying knowledge about how
best to control the plant.
3. A fuzzification interface, which converts controller inputs into information that the inference
mechanism can easily use to activate and apply rules.
4. A defuzzification interface, which converts the conclusions of the inference mechanism into
actual inputs for the process.
27
Fig 4.6: Actual Block diagram of the fuzzy controller in Simulink
The crisp inputs are applied to the input side of fuzzification unit. The fuzzification unit
converts the crisp input into fuzzy variable. The fuzzy variables are then passed through the
fuzzy rule base. The fuzzy rule base computes the input according to the rules and gives the
output. The output is then passed through defuzzification unit where the fuzzy output is
converted into crisp output.
Now there are mainly two types of Fuzzy Inference System which are used for
evaluation of individual rules. The difference between two fuzzy inference systems based on
their fuzzy rules and their aggregation. These two types of FIS are:
1. Mamdani Max-Min composition scheme: In this scheme aggregation used is Maximum
operation and implication is Minimum operation.
2. Mamdani Max-Prod composition scheme: In this scheme aggregation used is Maximum
operation and implication is Product operation.
Here in this FLC, a rule base is defined to control the output variable. This fuzzy rule is
a simple IF-THEN rule with some condition and conclusion which relates the input variables to
the required output variables properties. The FLC converts a linguistic control strategy into an
automatic control strategy, and fuzzy rules are constructed by an expert knowledge and human
experience with understanding. Initially, the speed error ‘e’ and the rate of change in speed error
‘Δe’ have been placed as input variables of the FLC. Then the output variable of the FLC
generates the controlled q-axis reference current iq *. The fuzzy rules are expressed in English
28
like language with syntax such as, If {error speed ‘e’ is X and rate of change of error speed ‘Δe’
is Y} then {control output variable iq *is Z}. To convert these numerical variables into linguistic
variables, here the following five fuzzy levels or sets has been chosen as: NB (Negative big),
NS (Negative small), ZE (Zero), PS (Positive small), and PB (positive big) are used and
summarized in Table 1. Each of the inputs and the output contain membership functions with all
these three linguistics with 5*5 Triangular MFs.
So for the proposed system, Type-1 Fuzzy Logic controller has been chosen along with
its following characteristics:
Triangular based 5×5 Membership Function [MF] for both inputs as well as output variables of
FLC.
Fuzzy implication using Mamdani’s min operators.
Defuzzification using Centroid method for getting required output from the FLC.
Fuzzy logic control rules are shown in the Table 1 below:
Table 4.1: Fuzzy logic Control Rules
29
4.2.3. Hybrid PI-Fuzzy Logic Controller (PI-FLC):
As it is important to achieve a smooth and improved performance of outer speed loop in
vector controlled PMSM drive during transient as well as steady state condition, the combined
advantages of proportional plus integral (PI) and fuzzy controllers were selected and a Hybrid
PI-Fuzzy controllers are designed in which the output can either be the outputs of the two, i.e.
the PI or fuzzy units being switched during a particular period as per the predetermined speed
errors. PI controller has rarely superior performance as compared to the fuzzy controller under
steady state conditions when speed error is very less while the FLC has superior performance
mainly under transient condition and sometimes steady state condition also. So combining the
superior performances of the fuzzy and PI controllers, a hybrid PI-fuzzy controller can be
obtained. This can be implemented as an outer speed controller where the PI controller is rarely
active near steady state conditions when the speed error found to be very less and the fuzzy
controller is active during transient conditions and when the speed error is greater than some
minimum predefined value.
Hybrid PI-Fuzzy speed controller has been used for the control of the induction motor,
where the fuzzy controller is active during speed overshoot or undershoot only. Alike in a
permanent magnet brushless dc (PMBLDC) motor or PMSM also Hybrid PI-Fuzzy speed
controller can be implemented where the fuzzy logic controller is activated under the condition
of overshoot and oscillations, otherwise the output of the fuzzy logic controller is null and hence
inactive and in contrast, the PI controller is activated during steady state condition with very less
error. Here, the selection between the fuzzy and the PI speed controllers is carried through a
logical switch which is based on a set of simple rules; oscillations have to be detected by
comparing the sum of errors over a period of time with the sum of absolute errors over the same
period. A schematic model which can describe the function of Hybrid PI-Fuzzy speed controller
is shown in fig.4.7:
30
Fig.4.7: Schematic model of Hybrid PI-Fuzzy speed controller
The actual motor speed is sensed and compared with the commanded reference speed
value. The speed error is processed by the hybrid PI-Fuzzy speed controller, where the FLC
and PI controller are operated through a conditional switch and either of one from two
controllers performs its function during a particular period which determines the reference value
of the q-axis current. The condition that is provided to the conditional switch is set from the
knowledge of speed error oscillation or rate of change in speed error that we can measure from
our system response such that during the transient conditions the output of the fuzzy logic
controller has the prominent effect on the output of the hybrid controller and during the steady
state conditions with very less error, the PI controller will have the prominent effect. The
condition for the conditional switch should be set as a “minimum” value of Δe such that the FLC
will switch mainly when Δe will greater than a minimum set value of Δe which will mostly occurs
under transient periods and PI controller will rarely switch when Δe will less than that minimum
set value of Δe that is during steady state periods with very less speed ripple.
So for the comparative analysis of behaviour of conventional PI controller, FLC and
Hybrid PI-Fuzzy controller, we designed the whole IPMSM drive system in MATLAB/Simulink
environment and all three controllers were implemented separately as outer speed loop. The
result and comparison of performance of these controllers were presented and analyses in later
31
chapter where we can distinguish between their performances during different conditions and
accordingly we can select our required controller as per our requirement and whole condition of
drive system operation.
4.3. Description of Proposed PI-Fizzy Hybrid Model:
After analyzing the performances of different current and speed controllers, Hybrid PI-FLC
integrated as speed controller and hysteresis band current controller integrated as current
controller to achieve better performance for the designed PMSM drive system. The block
diagram of proposed PMSM drive system based on Hybrid PI-FLC and HBCC is shown in
fig.4.8.
Fig 4.8: PI-Fuzzy Hybrid Speed control model for IPMSM
Fig. 4.9 shows the schematic diagram of a vector controlled IPMSM drive system with
Hybrid PI-FLC controller as speed controller in the outer loop and an Adaptive Hysteresis Band
Current Controller (AHBCC) as current controller in the inner loop. The actual speed is
compared with the reference speed and error speed (e) fed to the hybrid PIFLC controller which
32
gives reference torque component of current iq* . A conditional If-else switch is used inside
Hybrid PI-FLC to select either FLC or PI controller to function as speed controller during a
particular period according to preset change in speed error (Δe) value.
Fig 4.9 Upper layer of Simulink of Hybrid PI-Fuzzy Speed Controller
Now using Inverse Park’s transformation, the stator reference current is generated from
iq* considering id*=0. The actual currents are sensed and compared with the generated
references current and the error current are fed to the current controller which will generate the
required gate drive signal such a way that it will results a ripple less smooth performance for
IPMSM drive system.
4.4. Summary of the Chapter:
In this chapter some current controllers such as Conventional fixed band hysteresis current
controller and adaptive hysteresis band current controller has been discussed along with their
mathematical model. Their advantages and disadvantages were also discussed. Further some
speed controller such as PI, FLC and Hybrid PI-FLC also discussed along with their designing.
Their performances under different condition also analyzed. Finally description about proposed
model with its block diagram and operation has been described.
33
CHAPTER 5
SIMULATION RESULTS AND DISCUSSION
5.1 Introduction
The conventional and proposed MATLAB/Simulink models were developed for 100 kW
PMSM and the rest system parameters values are tabulated. The motor is operated in constant
torque mode. In the designed model for performance improvement of IPMSM drive system, two
controllers have been integrated: One as outer speed controller and other as inner current
controller. Here our main aim is to analyze and compare the performances of PI, Fuzzy and
Hybrid PI-FLC as different speed controllers but before that we require to select an excellent
current controller which can provide smooth and ripple free responses of current and torque
developed. So for selection of current controller first we compares the responses of drive
system using conventional hysteresis band current controller and based on their performance
we choose the better current controller for required operation of PMSM drive system. For this
purpose PI controller is used as speed controller tuning its constants as Kp= 5 & Ki= 100.
5.2. Hysteresis Current Pulse Generator:
In this section, diagram of Hysteresis current pulse generator has been shown which generates
pulses. In this section, diagram of fixed band Hysteresis current pulse generator has been
shown which generates pulses. The Power is 100 kW for its operation. The Hysteresis band
value is 0.1. The value of Kp= 5 & Ki= 100. This type of Hysteresis has been used in this
model. Hysteresis band current controller is a current control technique in which controller will
try to keep the input current error within a range which is fixed by some width of band gap
defined by upper and lower band. In this technique, the reference current of any phase is
summed with the negative of the measured current value of that phase which will give the
current error. The current error is then provided as the input of the controller which then
compare it with its defined fixed band and gives the output as per its characteristics as required
gate drive signal. The characteristics of hysteresis band can be defined as “when the error
crosses the lower limit of the hysteresis band, the upper switch of the inverter leg (one at a time)
34
is turned ON and when the current attempts to become more than the upper limit of band, the
bottom switch (one at a time) is turned ON”.
Figure 4.1: Fixed band hysteris current pulse generator
4.3. Performance Comparison Using Different Speed
Controllers:
In this section, performance of drive system using PI, Fuzzy and Hybrid PI-FLC as
different speed controller has been demonstrated at no-load, variable load & variable speed
conditions. For all condition operation Adaptive hysteresis band current controller has been
integrated as inner current controller. The MATLAB/Simulation is focused on minimization of the
ripple contents of stator current, torque and improving the motor speed response under
transient and steady state operating conditions.
4.3.1. Result during No-load Condition for Conventional PI Controller:
For this case the gain constants are set as Kp= 5 & Ki= 100 and the reference speed to
be track is 1350 rad/sec. Fig.4.2 shows the 3-phase stator current which does not contains any
disturbances, smooth response of electromagnetic torque and rotor speed where the ripple
contents of the rotor speed are 200 and settling time is 0.5 sec. The response of the PI
controller is under No-load condition.
35
Fig.4.2: PI controller response under No Load condition
5.3.2. Result during No-load Condition for Fuzzy Logic Controller:
For this case a 5×5 triangular MF for both inputs as well as output variables of FLC,
Fuzzy implication using Mamdani’s min operators and Defuzzification using Centroid method
has been implemented for designed FLC. Fig.5.3 shows the Fuzzy Logic Control Block diagram.
Figure 5.4 shows the 3-phase stator current, shows response of electromagnetic torque and
rotor speed where the ripple content is 200 and the rotor speed are 1350 rad/sec and settling
time is 0.1 sec.
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Fig 5.3.: FLC Block diagram
Fig 5.4: Electromagnetic Torque, Rotor speed and response of fuzzy logic controller
5.3.3. Result during No-load Condition for Hybrid PI-FLC:
Figure 5.5 shows the block diagram of Hybrid PI-Fuzzy Logic Controller. Fig.5.6 shows the 3-
phase stator current, response of electromagnetic torque and rotor speed where the ripple
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contents are 100 and the rotor speed is 1350 rad/sec and settling time is 0.1 sec. So the
responses obtained in this case are little improved as compared to Conventional PI and FLC.
Fig.5.5: Block diagram of Hybrid PI-Fuzzy controller
Fig:5.6: Hybrid Torque, Rotor Speed and ripple factor response at No Load
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5.3.4. Result during Variable Load Condition for Hybrid PI-FLC:
The figure 5.7 shows the Hybrid model variable load fuzzy rule viewer. Fig.5.8 shows
the 3-phase stator current, response at torque 60 Nm and 63 Nm , variable Load and rotor
speed responses. Here also it can be observed that the notches in speed response get smaller
than response using conventional PI controller and ripple contents in torque is 0.05 Nm.
Fig: 5.7: Hybrid model variable load fuzzy rule viewer
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Fig:5.8: Results for variable load on Hybrid model
5.3.5. Result during Variable Speed Condition for Hybrid PI-FLC
Fig.4.9 shows the Hybrid model variable speed fuzzy rule viewer and the figure 4.10 shows
the 3-phase stator current, response of electromagnetic torque and rotor speed responses with
lesser ripple and notches in the stator current and torque response than the PI & FLC. The
ripple content in torque under load condition is 0.05 Nm. So it can be revealed that the
performance of IPMSM drive system gets improved using Hybrid PI-FLC model.
40
Fig 5.9: Hybrid model variable speed fuzzy rule viewer
Fig 5.10: Hybrid model variable speed results
41
5.4. Summary:
In this chapter a comprehending results and responses of proposed IPMSM drive
system using two integrated control strategy has been presented which is modeled and verified
in the MATLAB/ Simulink environment. From the given responses of speed control of IPMSM
drive system using a current controller and different speed controller techniques, we come to
the conclusion that the hysteresis band current controller reduces the torque ripple, minimizes
the current error and maintains the switching frequency. While among different speed controller,
Hybrid PI-FLC is giving better response than others during both steady state and transient
conditions.
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CHAPTER 6
CONCLUSIONS AND FUTURE SCOPE
6.1. Conclusion:
This dissertation is mainly emphasized on the study of performance of IPMSM drive
system using different current controllers in inner loop and speed controllers in outer loop. In
order to run IPM motor at the desired speed, a closed loop with vector control IPMSM drive was
successfully designed and operated in constant torque mode. The feasibility of the above
mentioned integrated control strategy is modeled and verified in the MATLAB/Simulink
environment for effectiveness of the study.
From the obtained results we observed that, during both steady-state and transient
conditions hysteresis current controller reduces the torque ripple, minimize the current error and
maintain the switching frequency. While comparing with the PI controller, the FLC and hybrid PI-
FLC techniques, It is proved that PI-FLC controller has superior performance. The ripple
contents of stator current, flux and torque are minimized considerably and the dynamic speed
response is also improved with the proposed control technique under transient and steady state
operating conditions. The simulation results are presented in forward motoring under no-load,
load and sudden change in speed operating conditions.
So the proposed model with Hybrid PI-FLC as speed controller and fixed band
hysteresis current controller has been used as a current controller which is providing smooth
and improved performances as compared to other controllers that have been taken in
consideration in this Thesis.
6.2. Future Work:
Here the focused has been made on the performance enhancement of IPMSM drives
and simulation work has been done for its thorough analysis. However, due to equipment
limitations these methods could not tested practically for all purposes. So in the future work the
results obtained for proposed control techniques from simulation environment may be validated
43
with experimental results. In addition to that, the analysis of performance of PMSM drive
implementing further advanced and intelligent controller like Adaptive fuzzy controller, Adaptive
Hysteresis controller and implementation of such controller in both speed and current loop can
be carried out. The analysis also can be extended to the above rated speed operation i.e. Flux
weakening region also.
44
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46
APPENDIX
Nominal Parameters taken for IPMSM Drive system are:
3-Phase PMSM, 220 V, 2.5 kW, 3 A, 50 Hz,
N=3000 rpm, P = 4, Rs = 4.3 Ω, λf = 0.272Wb, Ld = 27mH, Lq = 67mH,
Vdc = 300V, J= 0.000179 kg m2, B = 0.05 N-m/rad/sec, fs = 500 KHz.