SIMULATION OF SPEED TRACKING FOR BRUSHLESS DC MOTOR USING

FUZZY LOGIC CONTROLLER

AFIFAH BINTI ALIR

A project report submitted in partial fulfillment of the

requirement for the award of the degree

Master of Electrical Engineering

Faculty of Electrical and Electronic Engineering

University Tun Hussein Onn Malaysia

JULY 2013

vi

ABSTRACT

Brushless DC motors are normally used in an automotive application,

robotics, medical, industrial automation equipment and machine tools due to its

advantages. The advantages are long life operation, easy to construct, noiseless

operation and has a better speed performance. This project presents a simulation

model for BLDC motor using MATLAB/Simulink. Usually, the speed control is

achieved by using PI controller. Then, the dynamic response of the BLDC motor

such as speed, torque as well as current and voltage are observed and been analyzed

using the MATLAB model. It is quite hard and difficult to tune the conventional PI

controller parameters. Therefore, a suitable speed controller is been developed by

using MATLAB Fuzzy Logic tool box. The objectives of this project are to minimize

the maximum overshoot (%OS), settling time (Ts) and also peak time (Tp). Besides,

the purpose is to improve the speed performance of the motor drive system. In order

to verify the effectiveness of the controller, both control algorithms (Fuzzy logic

control and PID) are compared. The simulation results show that the FLC controller

has better performance which has reduced and minimized the percentage of

maximum overshoot, settling time, peak time and rise time compared with the used

of conventional PI controller.

vii

ABSTRAK

Motor arus terus tanpa berus (BLDC) kebiasaanya digunakan di dalam

bidang automotif, robot, perubatan, peralatan automotif industri dan peralatan mesin

disebabkan oleh kelebihan motor tersebut. Antara kelebihannya adalah untuk jangka

hayat operasi yang lama dan panjang, mudah dibina, tidak terlalu bising serta

mempunyai prestasi kelajuan yang baik. Projek ini memaparkan model simulasi

motor arus terus tanpa berus menerusi aplikasi penggunaan MATLAB/Simulink.

Kebiasaannya, kawalan kelajuan dicapai menggunakan kawalan PI. Kemudian tindak

balas dinamik motor arus terus tanpa berus seperti kelajuan, tork, termasuk juga arus

dan voltan diperhatikan dan dianalisa menggunakan modul MATLAB. Bagi melaras

konvensional kawalan PI adalah agak rumit dan sukar. Oleh yang demikian,

kesesuaian kawalan kelajuan telah dibina menggunakan perkakasan MATLAB

pengatur logik kabur. Tujuan projek ini ialah untuk menggurangkan lanjakkan

(%OS), masa tetapan (Ts) dan juga masa puncak (Tp). Selain itu, adalah tujuannya

untuk membaiki prestasi kelajuan system pemajuan motor. Bagi memastikan

keberkesanan kawalan, kedua-dua kawalan algoritma (pengatur logic kabur dan PID)

dibandingkan. Simulasi menunjukkan kawalan FLC mempunyai prestasi yang baik

di mana ianya dapat meminimakan serta mengurangkan peratusan lanjakkan

maksimum, tetapan masa, masa puncak dan masa meningkat jika dibandingkan

dengan penggunaan konvensional kawalan PI.

viii

CONTENTS

TITLE i

DECLARATION iii

DEDICATION iv

ACKNOWLEDGEMENT v

ABSTRACT vi

ABSTRAK vii

TABLE OF CONTENTS viii

LIST OF FIGURES x

LIST OF TABLES xii

LIST OF ABBREVIATIONS xiii

CHAPTER 1 INTRODUCTION

1.1 Research background 1

1.2 Problem statement 4

1.3 Objectives of the project 5

1.4 Scope of project 5

1.5 Thesis outline 6

CHAPTER 2 LITERATURE REVIEW

2.1 Technology developments 7

2.1.1 Speed control of BLDC motor using adaptive 7

Fuzzy PID controller

2.1.2 Simulation of a variable speed brushless DC 8

motor using Neural Network controller

2.1.3 Fuzzy controller in induction motor speed 8

control with constant flux

2.1.4 Real time implementation of DSP based fuzzy 9

logic controller for speed control of BLDC motor

2.2 Operation of BLDC motor 10

2.2.1 BLDC motor construction and operating principles 11

ix

2.2.2 Mathematical equations of BLDC motor 13

2.3 Fuzzy logic controller system 18

2.4 PID controller systems 22

2.4.1 Tuning PID parameters 23

CHAPTER 3 METHODOLOGY

3.1 Introduction 25

3.2 System structure 28

3.2.1 BLDC motor modeling 28

3.2.2 Structure of speed control system for BLDC motor 30

3.3 Proportional-Integral (PI) controller design 33

3.4 Proposed controller 35

3.5 Fuzzy logic controller design 36

3.5.1 Fuzzification interface 38

3.5.2 Fuzzy rule base 42

3.5.3 Fuzzy inference mechanism 44

3.5.4 Defuzzification 44

CHAPTER 4 RESULT AND ANALYSIS

4.1 Introduction 45

4.2 System performance without controller 47

4.3 Motor drive system with PI controller 49

4.4 Motor drive system with Fuzzy logic controller 56

4.5 Discussions 65

CHAPTER 5 CONCLUSION AND RECOMMENDATION

5.1 Conclusion 66

5.2 Recommendations 67

REFERENCES 68

VITA 72

APPENDIX A: BLDC motor system without controller 73

APPENDIX B: BLDC motor system with PI controller 74

APPENDIX C: BLDC motor with Fuzzy logic controller in 75

MATLAB/Simulink

x

LIST OF FIGURES

2.1 BLDC motor transverse section 11

2.2 DC motor model 13

2.3 BLDC motor block diagram 15

2.4 Configuration of BLDC motor and VSI system 15

2.5 Fuzzy logic controller block diagram 19

2.6 Membership function of fuzzy controller 19

2.7 Schematic model of PID controller 22

3.1 Flow chart overall design of research 26

3.2 BLDC motor modeling in MATLAB/Simulink 28

3.3 Block diagram for BLDC motor speed control 30

3.4 Schematic model for BLDC motor with PI controller 33

3.5 Block diagram of proposed controller 35

3.6 Block diagram of fuzzy logic controller 36

3.7 Flow chart of designing FLC 37

3.8 FIS editor 39

3.9(a) First input variable named “error” 40

3.9(b) Second input variable named “change of error” 40

3.9(c) Output variable “output” 40

3.10 Rule editor structure 42

4.1 BLDC motor system without controller 47

4.2 BLDC motor response without controller 48

4.3 BLDC motor system with PI controller 49

4.4 Reference speed of 3000rpm with no load for PI controller 50

4.5 Reference speed of 3000rpm with load for PI controller 51

xi

4.6 Step up speed of 2500-3000 rpm with no load for PI controller 52

4.7 Step up speed of 2500-3000 rpm with load for PI controller 52

4.8 Step down speed of 3000-2500 rpm with no load for PI controller 53

4.9 Step down speed of 3000-2500 rpm with load for PI controller 54

4.10 BLDC motor with fuzzy logic controller in MATLAB/Simulink 56

4.11 Reference speed of 3000 rpm with no load for fuzzy logic 57

controller

4.12 Reference speed of 3000 rpm with load for fuzzy logic 58

controller

4.13 Reference speed of 1500 rpm with no load for fuzzy logic 58

controller

4.14 Reference speed of 1500 rpm with load for fuzzy logic controller 59

4.15 Step up speed of 2500-3000 rpm with no load for fuzzy logic 60

controller

4.16 Step up speed of 1000-1500 rpm with no load for fuzzy logic 60

controller

4.17 Step up speed of 2500-3000 rpm with load for fuzzy logic 61

controller

4.18 Step up speed of 1000-1500 rpm with load for fuzzy logic 62

controller

4.19 Step down speed of 3000-2500 rpm with load for fuzzy logic 63

controller

xii

LIST OF TABLES

2.1 Motor types comparison 10

2.2 Rule base of FLC 21

2.3 Rules for hand-tuning in PID controller 23

2.4 Rules for Zeigler-Nichols 24

3.1 Parameter of BLDC motor drive system 29

3.2 Clockwise rotation 32

3.3 Gate logic to transform electromagnetic forces 32

3.4 Rule base of fuzzy controller (membership 3x3) 43

3.5 Rule base of fuzzy controller (membership 5x5) 43

3.6 Rule base of fuzzy controller (membership 7x7) 43

4.1 Performance result of conventional PI controller 55

4.2 Performance result of fuzzy logic controller 64

xiii

LIST OF ABBREVIATIONS

DC - Direct current

BDCM - Brushed DC Motor

BLDCM - Brushless DC Motor

PMSM - Permanent Magnet Synchronous Motor

EMF - Electromotive Force

PWM - Pulse Width Modulation

PID - Proportional Integral Derivative

PI - Proportional Integral

FLC - Fuzzy Logic Controller

FC - Fuzzy Controller

MP - Maximum Peak overshoot

OS% - Percentage of Overshoot

eSS - Steady state error

Ts - Settling time

Tr - Rise time

Tp - Peak time

xiv

Ia(t) - Motor current

Va - Armature Voltage

Ra - Armature resistance

La - Armature inductance

Tm - Motor torque

Jm - Motor inertia

Bm - Damping ratio / Viscous friction coefficient

Km - Torque constant

KB - Back EMF constant

Θ - Angular speed

ω - Speed

Kp - Proportional gain

K i - Integral gain

Kd - Derivative gain

Ku - Ultimate gain

Tu - Ultimate time

TI - Integral time

TD - Derivative time

u(t) - Control signal

rpm - Revolution per minute

CHAPTER 1

INTRODUCTION

This chapter will focus on the introduction of the project to be carried out. The

important overview or description including the problem statement, objectives of the

project, and project scopes are well emphasized in this part.

1.1 Research background

The system which is used to control the electric motor is called as an electric drive

system. An electric drive system is the electromechanical that converts electrical

energy to the mechanical energy of the driven machine. The main components of a

modern electric drive system are the motors, power processor, control unit and

electrical source. The purpose of using an electric drive system is to control the speed

and torque of the electric motors. Theoretically, there are two mainly types of direct

current (DC) motors used in the industry. The first one is the conventional brushed

dc (BDC) motor. This type of dc motor is produced a flux by the current through the

field coil of the stationary pole structure. The second type is the brushless dc (BLDC)

motor where the permanent magnet provides the necessary air gap flux instead of the

wire wound field poles. BLDC motor is conventionally defined as a permanent

2

magnet synchronous motor (PMSM) with a trapezoidal back EMF (electromotive

force) waveform shape. As the name implies, BLDC motors do not use brushes for

commutation, instead they are electronically commutated [1].

According to the journal that been done by Lee and Pang (1994), a permanent

magnet brushless dc motor is inside out construction of DC motor. The efficiency is

likely to be higher than the DC motor of equal size and the absence of commutator

and brushes, reduces the motor length. Hence, the lateral stiffness of the motor is

increased, allowing for the high speeds. The power electronic converters required in

a brushless dc motor are similar in topology to the Pulse Width Modulation (PWM)

inverter used in induction motor drives.

Recently, BLDC motors are very popular compared with the brushed DC

motors. In short, BLDC motors have some advantages over conventional brushed DC

motors and induction motor. Some of these advantages are better speed versus torque

characteristics, high dynamic response, high efficiency, high power density, long

operating life, noiseless operations and has higher speed ranges. In addition, BLDC

motors are reliable, easy to control, low maintenance and it is inexpensive [2], [3],

[4]. Due to their favourable electrical and mechanical properties, thus they are widely

used in servo applications such as automotive, aerospace, medical instrumentation,

robotics, machine tools, textile, industry automation equipment and many more as

studied by researchers like Lee and Ehsani (2003). The small sized of motors with

external rotors are widely used in visual equipment such as computer disc drives,

tape recorders and digital audio tapes [5]. BLDC motors are one of the motor types

rapidly gaining popularity. Therefore, the motor must be controlled precisely so that

it will give the desired performance in all these applications.

The classical Proportional-Integral-Derivative (PID) controllers are

commonly used in industries due to their simplicity and ease of implementation [6].

The classical controllers need an accurate mathematical model of the system, can

perform well and resulting good control performances only under linear system

model. Since the BLDC motor drive is highly coupled non-linear multivariable

system, it is difficult to obtain its accurate mathematical model. Besides, a control

performance of the PID controller becomes poor and difficult to determine the

3

controller parameters. To tune the PID control parameters are very difficult and poor

robustness [7].

For this reason, an intelligence controller such as fuzzy logic controller is

needed to improve the control performance of the BLDC motor drive. Fuzzy logic

controller (FLC) has many advantages over conventional control. The fuzzy logic

controller is capable of providing the high accuracy required by the high

performance drive system without the need of mathematical model. FLC

accommodates non-linearity without utilization of mathematical modeling [8].

Therefore, it is less sensitive to the changes of the system parameter. Design

objectives that are difficult to express mathematically can be easily incorporated in a

fuzzy controller by using linguistic rules. In addition, its implementation is simple

and straight forward [9]. It is suitable for applications such as the speed control of

DC motor which has nonlinearities.

In this project, a complete simulation model with fuzzy logic control (FLC)

method for BLDC motor drive is proposed using MATLAB/Simulink.

MATLAB/Simulink simulation model is built to study the dynamic response of

speed for the BLDC motor and the performance of proposed controller. Based on the

simulation result, the develop FLC has the ability to adapt its own controller

parameters based on external disturbance and internal variation of the converter by

giving a minimum peak overshoot (Mp), low value of the steady state error (ess),

settling time (Ts) and rise time (Tr) of the output voltage.

4

1.2 Problem statement

Nowadays, an accurate speed control demand is increased due to research for better

and modern intelligent motion applications in the electrical engineering industry. The

conventional control scheme such as proportional (P), proportional integral (PI) and

proportional integral derivative (PID) have been developed to control the speed of

the brushless dc motor. According by Ramesh et al., (2011) has stated that “..Up to

now, over 80% of the controllers are PI (Proportional and Integral) controllers

because they are facile and easy to understand. The speed controllers are the

conventional PI controllers while current controllers are the P controllers to achieve

high performance drive...”.

Usually, speed control is achieved by using proportional-integral (PI)

controller. Although conventional PI controllers are widely used in the industry due

to their simple control structure and ease of implementation, these controllers pose

difficulties where there are some control complexity such as non linearity, load

disturbances and parameter variations. In other word, these controllers fail to yield

better performance when the system becomes nonlinear. Furthermore, the controller

produce more noise and difficult to achieve the optimal state under field conditions

in the actual production.

As the BLDC machine has nonlinear model, the PI controller may no longer

be suitable. So in this project, it will be focused on how to develop the speed control

of BLDC motor by using Mamdani Fuzzy Logic Controller (MFLC). Fuzzy logic

control offers an improvement in the quality of the speed response. By referring to

Sakhtivel (2010), even though the computing time for the FLC is longer than the

conventional PID controller because the complex operations of fuzzification and

defuzzification, but the fuzzy control applications still widely used in many practical

systems such as robot, heat exchanger, elevator, video cameras, train operation, car

parking control and many more.

5

1.3 Objectives of the project

The project attempts to use a simulation model for fuzzy logic controlled BLDC

motor drive by using software package MATLAB/Simulink. Other objectives of this

project are:-

i. To implement fuzzy logic in the speed control system.

ii. To analyze and improve speed performance results of the BLDC motor such as

minimize maximum peak overshoot (%OS), Settling time (Ts) and Rise time

(Tr) between the classical PID controller and Fuzzy Logic Controller.

1.4 Scope of project

There is a lot of researches have been done on BLDC motor, which is related with

the performance of speed motor. The need of intelligent control system is required to

improve the performance of BLDC motor. In this study, there is some limitation that

been set to accomplish the objectives of this study as listed below:

i. Measure the speed of the BLDC motor by using fuzzy logic control method as a

controller. The structure of the FLC will be used in this project consists of input

membership 7 x 7. The reference speed is 3000 rpm.

ii. The PID controller also will be developed to compare the effectiveness of the

proposed controller.

6

1.5 Thesis outline

The thesis is organized into five (5) chapters which are introduction, literature

reviews, methodology, simulations and results analysis, conclusion and

recommendation.

Chapter I In this chapter, background of the study which is

related with the speed brushless DC motor by using fuzzy logic controller, objectives

that been set up to achieve, scope of study and the problem statement or justification

of the study had been stated as well.

Chapter II In this chapter, all the literature review from the

previous study related to the objectives of the study had been gathered. This includes

about the brushless direct current (BLDC) motor, the study of the mathematical

modeling of the BLDC motor, methodology in fuzzy logic controller (FLC) and

classical PID controller.

Chapter III In this chapter, the overall design and methods to apply

in this study had been stated. The main methodology that been stressed out related to

the intelligent control and data collection from the MATLAB simulation.

Chapter IV In this chapter, it presents the simulation results and

analyzes the speed performance of the proposed controller. The simulation results of

the systems performance have been observed.

Chapter V In this chapter, it states the conclusions and

recommendations for future works that can be done to improve the systems.

CHAPTER 2

LITERATURE REVIEW

2.1 Technology developments

These researches that are relevant to this project will discus to demonstrate

continuity from the previous researches.

2.1.1 Speed Control of BLDC Motor Using Adaptive Fuzzy PID Controller Adaptive Fuzzy PID control was introduced by this thesis to control the speed of

regulation system of BLDC motor. The parameter can be adjusted real time by using

Adaptive fuzzy controller capability. The performance of adaptive fuzzy logic

controller can be improved by increase in number of inputs and membership function

when necessary by using individual set of rules for each Kp, Ki and Kd. Each of the

rules will be used thus the controller will able to adapt to any changes in parameter.

The main purpose of this thesis to show dynamic respond of speed by using adaptive

fuzzy PID controller to control speed of motor and keep motor speed constant when

varied in load. The simulation will compare the Adaptive fuzzy PID with both Fuzzy

PID controller and conventional PID controller. The final result based on the thesis

8

stated that for the same operation condition the BLDC motor speed control using

Adaptive Fuzzy PID controller technique had better performance compared with

conventional PID controller.

2.1.2 Simulation of a Variable Speed Brushless DC Motor Using Neural

Network Controller

According to the previous study by Adiimah (2011) was identified and concluded

that the mathematical model of BLDC motor and artificial neural network algorithm

is derived and controller was developed to track the variations of speed reference and

stabilize the output speed during under load variations. The nonlinearity of the

BLDC motor cause it is difficult to handle by using conventional method

proportional integral differential (PID) controller. To overcome the nonlinearity a

neural network with online learning method based back propagation algorithm is

developed. MATLAB Simulation program was used for design platform to verify the

effectiveness of the proposed controller. The design has the ability to learn

instantaneously and adapt its on controller parameter based on external disturbance

and internal variation of the converter with minimum steady state error, overshoot

and rise time of the output voltage. Based on the MATLAB simulation, the proposed

Neural Network Controller is designed to feed by variable speed of input to control

Brushless DC motor. The final result showed the NNC produce better performance

than PID controller.

2.1.3 Fuzzy Controller in Induction Motor Speed Control with Constant Flux

Another study that been done by Hassan (2005) for three phase induction motor drive

by using Fuzzy Logic Controller. Constant flux technique (V/F) was used to control

speed of induction motor. By using Fuzzy Logic Controller, speed error is calculated

with comparison between reference speed command and speed signal feedback.

Speed error and delta error changed are Fuzzy controller input. In full load, driver

response has almost similar trajectory with classical PI and Fuzzy controller.

9

Furthermore, in no load Induction motor with fuzzy controller has response faster

than classical PID controller. In another test, sudden changing has exerted in motor

speed, speed command was set for two running condition: no load and full load with

increasing and decreasing speed command. In this test speed regulation is almost

suitable with implementation of Fuzzy logic for Induction motor. The MATLAB

simulation verifies that with Fuzzy Logic Controller steady state error in speed

control is acceptable and laboratory test show that design and implementation are

suitable.

2.1.4 Real Time Implementation of DSP based Fuzzy Logic Controller for

Speed Control of BLDC Motor

The objective of the paper is to design and develop an intelligent speed control

algorithm for BLDC motor in Vissim software which is an environment for model

based development of embedded controller for Texas instruments DSOs. In this

paper, TMS320F2812 DSP is used as the controller; signal conditioning components

are used for high processing speed and to obtained precision in the overall control

system. Based on the design the speed was controlled in a closed loop by measured

the actual speed of the motor. TMSC320F2812 Is a low-cost 32-bit fixed-point DSP,

this device best feature of digital signal processing, reduced instruction set

computing (RISC), and microcontroller architectures, firmware and tool sets. The

modified Harvard architecture of CPU enables instruction and data fetches to be

performed in parallel. The speed of motor is measured by means of Hall sensor

encoder and given as input to ADC (AD7266). The set speed is assigned to motor by

toggle switch, once done the ADC data read the requirement and fed for Fuzzy Logic

Controller to calculate output value and the output controller in term changes the

duty cycles of PWM to increase or decrease the speed. The energy that switching

power converters deliver to BLDC motor is controlled by Pulse Width Modulation

(PWM). Once the current speed equal the set speed, the motor will run at the set

speed. Based on this paper the implementation system has a fast respond with small

overshoot and zero steady state error compared to conventional PI controller.

10

2.2 Operation of BLDC motor

Permanent magnet brushless motor is categorized into two types by observing from

the back EMF waveform which are; Brushless AC (BLAC) and Brushless DC

(BLDC). BLDC motor becomes more popular in many industrial applications such

as in High Voltage industry, instrumentation, robotic, military defense, aviation,

actuation and machine tools [2], [4], [5]. Table 2.1 is stated comparison for the

advantages and disadvantages between all types of motor that used in the industry

nowadays.

Table 2.1: Motor types comparison [24]

In a BLDC motor, the electromagnet does not make any movement. Instead

the permanent magnet rotates and armature remains stationary to substitute the

function of commutators. BLDC motor needs a device to detect rotor position and

transfer current to move armature. In order to do this, the commutator assembly is

replaced by an intelligent electronic controller, which is performed the same power

distribution as a brushed DC motor [11].

11

2.2.1 BLDC Motor Construction and Operating Principles

According to the research that had done by Ramesh et al. (2011), BLDC motor has

two main types which are trapezoidal and sinusoidal type. In the trapezoidal motor,

back EMF induced in the stator windings will has a trapezoidal shape and the phase

must be supplied with quasi-square current for ripple free torque operation.

Sinusoidal type has a sinusoidal shaped back EMF and required sinusoidal phase

current for ripple free torque operation. The sinusoidal motor needs a high resolution

position sensor because the rotor position needs to be checked at the time interval for

optimal operation. Other than that, the sinusoidal motor also required more complex

hardware and software. The BLDC motor works by switching the DC power supply

to the stator phase windings of the motor by using power devices while the rotor

position is used to determine the switching sequence.

Refer from the Figure 2.1, it shown the transverse section for BLDC motor.

The position detection usually placed using three Hall-effect sensors. The purpose is

to detect the presence of small magnets that attached to the motor shaft. Usually three

Hall-effect sensors are used for every 60 degree electrical. BLDC motor contains

strong permanent magnet rotor and fixed stator windings. The stationary stator

windings are normally three phases, which means three separate voltages are

supplied to the three different sets of windings [11], [13].

Figure 2.1: BLDC motor transverse section [11]

12

To replace the function of commutators and brushes, the BLDC motor

requires an inverter and a position sensor that detects rotor position for proper

commutation of current. The rotation of the BLDC motor is based on the feedback of

rotor position which is obtained from the hall sensors. BLDC motor usually uses

three hall sensors for determining the commutation sequence. In BLDC motor the

power losses are in the stator where heat can be easily transferred through the frame

or cooling systems are used in large machines. BLDC motors have many advantages

over DC motors and induction motors. Some of the advantages are better speed

versus torque characteristics, high dynamic response, high efficiency, long operating

life, noiseless operation and has higher speed ranges [13], [18], [19].

From the previous study and literature that been reviewed, there is two

magnetic fields interact each other which result in movement. In brushless DC

motor, the permanent magnet stator set up the first magnetic field hence the rotor

winding produce the second field. When these two magnetic fields interact each

other will result in rotation. The two fields try to align each other however the

commutator continuously switches power from winding to winding which will

maintain the two magnetic fields at a 90 degree relationship. When a BLDC motor

rotates, each winding generates a voltage known as back electromotive force or back

EMF, which opposes the main voltage supplied to the windings according to Lenz’s

Law. Back EMF depends on the three factors; the angular velocity of the rotor,

magnetic field that is generated by rotor magnets and number of turns in the stator

windings [22].

The commutation phase sequence is like AB-AC-BC-BA-CA-CB, where A,

B, C are stand for three phases. Each conducting stage is called as one step.

Therefore, only two phases conduct current at any time, leaving the third phase

floating. In order to produce the maximum torque, the inverter should be

commutated every 60 degree, so current is in phase with the back EMF. The BLDC

motor can be controlled either by sensor or sensorless mode. The sensorless mode

commonly used due to the sensing part and sensorless control are higher requirement

for control algorithm and more complicated to design the electronic parts [22], [26],

[27].

CHAPTER 3

METHODOLOGY

3.1 Introduction

This chapter is discussed the planning of the research methodology that will be

adopted in achieving the objectives of the study. The purpose of this study is to

develop the dynamic model of BLDC motor and apply two types of controller

namely Proportional-Integral (PI) and Fuzzy Logic Controller (FLC) to control the

output response. The performance of the designed fuzzy and classical PI speed

controllers for BLDC motor is compared and investigated. The researches have been

designed and implemented after gathering all information from internet and journals.

13

2.2.2 Mathematical Equations of BLDC Motor

Figure 2.2 shows a DC motor equivalent model where Va= armature voltage (V), Ra=

armature resistance (Ω), La= armature inductance (H), Tm= motor torque (N-m), θ= angular

position of rotor shaft (rad), Jm= motor inertia (Kg-m2), Bm= viscous friction coeeficient

(Nm-s/ rad), KM= torque constant (N-m/ A) and Kb= back EMF constant (Vs/ rad). Based on

the DC motor model shown in Figure 2.2, the equations of the BLDC motor can be derived

as:

Figure 2.2: DC motor model [14]

By using the Kirchoff’s Voltage Law (KVL);

0)()( =+∂

∂++− tEbt

IaLRtVa (2.1)

By taking the Laplace Transform, equation (2.2) can be expressed in term of s as;

0)()()()( =+++− sEbssLIasRIasVa (2.2)

The motor torque, TM is related to the armature current, Ia by a constant coefficient of KM;

)()( sKmIasTm = (2.3)

The back electromotive force (back EMF) is relative to angular velocity, mω by;

tKKEb m

Bmb ∂∂

==θω (2.4)

14

Substitute equation (2.4) into equation (2.2), so;

0)()()( =∂

∂+++−

tKssLIasRIasVa m

B

θ (2.5)

0)()()()( =+++− sSKssLIasRIasVa mB θ (2.6)

By using Newton’s Second Law;

tBm

tJmTm mm

∂∂

+∂

∂=

θθ2

(2.7)

Then, again substitute equation (2.3) into equation (2.7) to obtain;

tBm

tJmsKmIa mm

∂∂

+∂

∂=

θθ2

)( (2.8)

Again, by taking the Laplace Transform, equation (2.8) can be expressed in term of s as;

)()()( 2 sBmSsJmSsKmIa mm θθ += (2.9)

From equation (2.9), )(sIa can be expressed as;

[ ]Km

BmJmssSsIa m +

=)(

)(θ

(2.10)

Substitute equation (2.10) into equation (2.6) to obtain;

[ ][ ]Km

KmKbRasLaBmJmssSsVa m +++

=)(

)(θ

(2.11)

Finally, the transfer functions of the BLDC motor can be obtained where the actual output can be identified by the position of θm(s) while the voltage of Va(s) can be as desired input. The overall transfer function of the BLDC motor is;

[ ][ ] KmKbRasLaBmJmss

Km

sVa

sm

+++=

)(

)(θ (2.12)

The constant values of input voltage (Va), torque constant factor (Km), motor inertia

(Jm), damping ratio (Bm), resistance (Ra) and the inductance (La) for the BLDC motor must

be known before simulating the BLDC motor model in MATLAB. An electrical and

mechanical time constants of the motor plays an important role whenever the load is rapidly

accelerated and decelerated frequently. The mechanical time constant in these motors are

reduced by reducing the inertia of the rotor.

15

Figure 2.3: BLDC motor block diagram [4]

From Figure 2.3, it shows the block diagram for BLDC motor which contains two

loops. The first loop is current control loop that accomplishes torque of BLDC motor while

the second loop is the speed control loop which acts to adjust the speed of the BLDC motor

[4], [14], [18].

Figure 2.4: Configuration of BLDC motor and VSI system [4]

16

Based to the research done by Tan et al. (2011), due to the mathematical modeling for

BLDC motor, the design of the BLDC motor involves in complex process such as modeling,

device of control scheme, simulation and parameter tuning. The trapezoidal back EMF is

modeled as a function of rotor position so that the rotor position can be calculated according

to the operation speed. The back electromotive forces are expressed as a function of rotor

position (Ɵ). The equation can be derived as below:

( )( )( )

( )Rb

c

b

a

c

b

a

KE

f

f

f

E

e

e

e

ωθθθ

=

=

, (2.13)

Where bK is referred as back EMF constant,( )θaf , ( )θbf and ( )θcf are function of rotor

position while be and ce are trapezoidal of back EMF.

( )( )

( )

+

−−

−+

=

c

b

a

c

b

a

c

b

a

c

b

a

e

e

e

i

i

i

dt

d

ML

ML

ML

i

i

i

R

R

R

V

V

V

00

00

00

00

00

00

(2.14)

The motion equation is:

( )RLEm BTT

J

p

dt

Dω

ω −−

=2

(2.15)

The trapezoidal shape function with limit values between +1 and -1

( )

( ) ( )

( )

( )

≤<≤<≤<

≤<

−−

+−

≤<

=

πθππθπ

πθππθπ

θπ

θπ

πθθπ

θ

26/11

6/116/7

6/76/5

6/56/

12/6

1

6/6

16/0/6

af (2.16)

17

The expression of electromagnetic torque:-

Te = ke ( fa (θ) ia + fa (θ) ib + fc (θ) ic ) (2.17)

Speed and torque characteristics of BLDC motor:

[ ]∫ −++= dtTTTTJ

PLcbam )(

2ω (2.18)

The error and change in error:

e1 [n] = wref [n]– wr [n] (2.19)

e2 [n] = e1 [n] – e1 [n-1] (2.20)

18

2.3 Fuzzy Logic Controller System

Fuzzy Controller (FC) is also known as Fuzzy Logic Controller (FLC). The fuzzy theory had

been proposed in 1965. Lotfi A. Zadeh from America California University had been the

number one to propose this fuzzy control theory via his book of ‘Fuzzy Set Theory’. In recent

years, fuzzy logic controller is widely implemented in numerous industrial applications and

to the process which has a difficult model but straight forward control rules. Besides, this

type of controller does not require an explicit knowledge of motor and the load criterion [13].

Generally, PID controller is widely used in BLDC motor control. However it does not

give satisfactory result when the control parameters are non linear and loading condition

changes rapidly. By using fuzzy logic controller, it will guarantee for stable operation for any

changes in motor parameters or load disturbance [14].

Theoretically, an expected set of output are calculated from the set of inputs. The

mathematical calculation is represented with a set of formula which represents the system

behavior. However, the given mathematical formula is complex to apply in certain condition

if compared with fuzzy logic controller. This controller is able to provide a useful method to

create practical solution for controlling complex system. Moreover it can be noted that the

controller design does not requires explicit knowledge of the motor and load characteristics.

Fuzzy logic controller is allowed to use word and sentences instead of number and equations.

This is accomplished by forming IF-THEN rules which describe the characteristic of the

system. Besides, this controller can make a decision making with incomplete information [7],

[8], [15].

19

Figure 2.5: Fuzzy logic controller block diagram [12]

Figure 2.6: Membership function of fuzzy controller [2]

From Figure 2.5, it shows fuzzy logic controller in a closed loop system. The FLC

block diagram has two input values (e1, e2) and one defuzzify output (u) as illustrated in

Figure 2.6. Both input variables are quantized into 3, 5 and 7 membership functions which

are Negative (N), Negative Small (NS), Negative Medium (NM), Negative Big (NB), Zero

(Z), Positive (P), Positive Small (PS), Positive Medium (PM) and Positive Big (PB). There

are four main stages in this controller which are fuzzification, rule base, inference engine and

20

defuzzification block. In the fuzzification process, the set of input data are compiled and

converted into fuzzy set by using fuzzy linguistic variables and membership functions. After

fuzzification process, it will goes to the next step named as fuzzy inference or inference

engine. In this step, output value of the fuzzy logic controller is determined by using a rule

base of [2], [11], [25] ;

IF (first condition) AND (second condition) THEN (conclusion)

For example;

If e1 is NB and e2 is NB Then u is PB,

If e1 is NB and e2 is NM Then u is PB,

If e1 is NB and e2 is NS Then u is PM,

If e1 is NB and e2 is Z Then u is PM,

………………………………………..

and continuously for all inputs.

By the research had done by Cunkas and Aydogdu (2010), the function of FLC might

be consisted of 9 rules, 25 rules or 49 rules. The inference method which has been chosen is

the Max-Min method that was proposed by Mamdani. The Max-Min rule of inference and the

center of gravity method have been used in defuzzifier process. Defuzzification is achieved

by using the centre of gravity, which also known as the centroid. The output obtained by

using the centroid given as:

Where Dj is the membership function, µ (Dj) the value of membership function while n is the

number of activated rules.

21

Table 2.2: Rule base of FLC [2]

According to the research from Jantzen (2007), a few conditions must be satisfied in

order FLC to become a linear controller. The conditions are:

1) Set of input linguistic variables must be large enough so that input values stay in

limits.

2) Linguistic values must consist of symmetric triangular fuzzy sets that intercept with

neighbouring sets at a membership value of so that for any time instant, membership

values add to 1 condition.

3) Rule base must consist of combinations of all fuzzy sets.

4) Output linguistic variables must consist of singleton fuzzy sets positioned at the sum

of the peak positions of input fuzzy sets.

5) Should be multiplication and defuzzification.

22

2.4 PID Controller Systems

PID controller is a simple three term controller. The letter of P stands for Proportional, I is

stands for Integral and D is referred as Derivative. This controller has been used for several

decades in industries for process control application. The reason for PID wide popularity lies

in the simplicity of design especially to control linear system and has a good performance

including low percentage overshoot and small settling time for slow process plants. A PID

controller will correct the error between the actual output and the desired input by calculating

and give an output of correction that will adjust the process accordingly [1], [20], [23].

Figure 2.7: Schematic model of PID controller [20]

Figure 2.7 is referred as the schematic model of PID controller. In the above figure,

control signal u (t) is a linear combination of error e (t), its integral and derivative where TI is

referred as an integral time while the derivative time is notes as TD. The control u from the

controller to the plant is equal to the Proportional gain (KP) times with the magnitude of the

error plus the Integral gain (KI) times the integral of the error plus the Derivative gain (KD)

times the derivative of the error that shown in equation (2.21) and (2.22) below, where KP =

Proportional gain, KI = Integral gain and KD = Derivative gain.

23

dt

tdeKdtteKteKtu DIP

)()()()( ∫ ++= (2.21)

++= ∫ dt

tdeTdtte

TteKtu D

IP

)()(

1)()( (2.22)

2.4.1 Tuning PID paramaters

PID controllers are tuned by using hand tuning or Ziegler-Nichols methods.

Normally, hand-tuning method is conducted by the experience control engineers according to

the rules which are stated in Table 2.3. However, these rules are not always valid. Besides, it

takes a long time to find the optimal values [20], [21].

Table 2.3: Rules for hand-tuning in PID controller [20]

Operation Rise Time, tr Peak Overshoot, Mp Stability

KP Faster Increases Decreases

TD Slower Decreases Increases

1/TI Faster Increases Decreases

Procedure for the hand-tuning method:

1) The derivative and integral actions are removed by setting TD and 1/TI equal to zero.

2) KP is tuned so that it will give the desired response except the final offset value from

the set point.

3) KP is slightly increased TD is adjusted to dampen the overshoot.

4) 1/TI is tuned such that final offset is removed.

5) The steps from no.3 are repeated until the value KP is reached as large as possible.

24

The second method to tune PID parameters is Ziegler-Nichols frequency response

method. This method will give poor results especially for the systems with a time lag much

greater than the dominating time constant. The damping is generally poor [21]. Table 2.4

shows the rules for the Zeigler-Nichols. This tuning method is used to find the controller

parameters of classical PID.

Table 2.4: Rules for Zeigler-Nichols [21]

Controller Proportional gain,

KP

Integral time,

TI

Derivative time,

TD

P 0.5 KU - -

PI 0.45 KU TU / 1.2 -

PID 0.6 KU TU / 2 TU / 8

Procedure for Zeigler-Nichols method:

1) KP is increased until the system response oscillates with constant amplitude and the

gain values of ultimate gain, KU value is recorded.

2) The oscillation period is calculated and records it as TU.

3) The parameters are tuned by using Table 2.4.

68

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72

VITA

The author was born in June 15, 1984 in Kemaman, Terengganu, Malaysia.

She went to Sekolah Rendah Sultan Ismail (SRSI) in Kemaman, Terengganu before

she continues her study in a secondary school at Sekolah Menengah Sains Sultan

Mahmud (SESMA) in Kuala Terengganu. Then, early 2002, she continues her study

in Matriculation Program at Pusat Asasi Sains Universiti Malaya (PASUM) in Kuala

Lumpur. One year later, she pursued her degree at Universiti Tenaga Nasional

(UNITEN) which is located between Putrajaya and Bangi. She is graduated with the

B.Eng (Hons) in Electrical and Electronic Engineering in August, 2008. In January

2009, she becomes a lecturer for Diploma Program at Kolej Poly-Tech MARA

(KPTM) in Kuantan branch. She was admitted to Master Program in Electrical

Engineering in early January 2011.

73

APPENDIX A

BLDC Motor system without controller

74

APPENDIX B

BLDC motor system with PI controller

75

APPENDIX C

BLDC motor with Fuzzy logic controller in MATLAB/Simulink