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

37

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

38

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

39

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.