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UNIVERSITI PUTRA MALAYSIA
A SENSORLESS POSITIONING SYSTEM FOR LINEAR DC MOTOR
EZRIL HISHAM B. MAT SAAT
FK 2008 17
A SENSORLESS POSITIONING SYSTEM FOR LINEAR DC MOTOR
By
EZRIL HISHAM B. MAT SAAT
Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia in Fulfilment of the Requirements for the Degree of Master of Science
JULY 2008
Dedication
TO MY FAMILY AND MY WIFE
ii
Abstract of thesis presented to the Senate of Universiti Putra Malaysia in fulfilment of the requirements for the degree of Master of Science
A SENSORLESS POSITIONING SYSTEM FOR
LINEAR DC MOTOR
By
EZRIL HISHAM B. MAT SAAT
JULY 2008 Chairman: Norhisam Misron, PhD Faculty: Engineering
In recent years, linear motor has gained popularity as linear motion drive in industry
and factory automation which provides an alternative to conventional rotary motor.
This development was encouraged by the advantages offered by linear motors such
as flexibility in size and design, clean and silent operation, ease of maintenance and
deliver high performance for applications requiring linear motion. However, the
main constraint for system designers to consider linear motors in their application is
the cost for every complete package of linear motor. Generally, linear motors are
expensive than their counterparts due to the number of permanent magnet used in the
motors and the sensory technologies used for positioning system.
Linear motors provide direct linear motion and normally are designed with specific
length which requires more permanent magnets than rotary motor. Therefore, the
costs of linear motors increase with the length of the motor itself. For a typical
linear motor driver, a positioning sensor, usually attached to the motor, provides
feedback positioning signal to the controller. This sensor is expensive and normally
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has the same length with the motor. The price for this type of sensor increases with
the size, which eventually increase the cost of linear motors.
For some applications, where positioning is not too critical such as robot end gripper,
the high precision and expensive positioning sensor is not necessary. Removing this
sensor from the system reduces the overall system cost, thus encouraging more
development and application of linear motors. This research and study proposes a
sensorless positioning system for linear DC motor (LDM). The ideas to control the
position of the LDM are by controlling the current supplied to the motor. The
technique used to control the current is by manipulating Pulse Width Modulation
(PWM) signal which is generated by a microcontroller circuit based on Atmel AVR
ATmega8535 processor.
A simple model of LDM was constructed for experimental purposes. A mechanical
spring was used in the motor design to absorb the force produced by the motor. The
displacement of the spring will then be used to determine the position of the motor.
Due to the harmonic oscillation produced in mass-spring system, the position of the
motor oscillates before reaching the final desired position. In order to eliminate the
harmonic oscillation effect, a few variants pattern of PWM signals are used to drive
the motor. These variant patterns are single stage, dual stage, triple stage and
quadruple stage. The variant patterns of PWM signals were created by combining
multiple values of duty cycle running in a single PWM signal.
A mathematical model for constructed LDM has been derived based on damped force
oscillation of mass spring system theory. The equation of motion for LDM is then
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simulated using Matlab software. The time response of the system based on
simulation results has been studied and proper adjustment to control parameters has
been made to improve the rise time, overshoot percentage and steady state error. The
adjusted driving parameters are then transferred to microcontroller unit for actual
laboratory experiment.
The objective of this research to develop a sensorless positioning system for LDM
which include a motor driver and control approach was successfully achieved.
Comparison between simulation results and laboratory experiment shows almost
identical results. Linear relation between motor position and timing parameters used
in control algorithms has been studied and linear equations have been derived. These
linear equations will be converted into microprocessor programming as feed-forward
control algorithms. Any desired motor position can be fed into the system and
microprocessor unit will generates a proper PWM driving signal to the motor. The
developed system can be used for any low cost applications which do not require
precise positioning.
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Abstrak thesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi keperluan untuk ijazah Master Sains
SISTEM PENETAPAN KEDUDUKAN TANPA PENDERIA BAGI MOTOR LINEAR DC
Oleh
EZRIL HISHAM B. MAT SAAT
FEBRUARY 2007
Pengerusi: DR. ENG. NORHISAM MISRON Fakulti: Kejuruteraan Kebelakangan ini, motor linear telah mula mendapat perhatian sebagai pemacu
gerakan linear di industri dan automasi perkilangan serta menawarkan alternatif
kepada motor putar yang sedia ada. Perkembangan ini dimangkinkan oleh
kelebihan-kelebihan yang ditawarkan oleh motor linear seperti saiz dan rekabentuk
yang fleksibel, operasi yang bersih dan senyap, penyelengaraan yang mudah serta
menawarkan prestasi tinggi untuk aplikasi-aplikasi gerakan linear. Bagaimana pun,
halangan utama kepada pereka bentuk sistem untuk menggunakan motor linear
dalam aplikasi mereka ialah kos bagi keseluruhan pakej motor linear. Umumnya,
motor linear lebih mahal berbanding saingannya disebabkan oleh bilangan magnet
kekal dan teknologi penderia yang digunakan bagi sistem penetapan kedudukan.
Motor linear menghasilkan gerakan linear secara terus dan biasanya direka bentuk
dengan kepanjangan tertentu yang memerlukan bilangan magnet kekal yang lebih
banyak berbanding motor putar. Oleh itu, kos bagi motor linear meningkat mengikut
kepanjangan motor itu sendiri. Bagi litar pemandu motor linear yang biasa, penderia
kedudukan biasanya digunakan bagi menyediakan isyarat suap balik kedudukan
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kepada litar pengawal. Penderia ini agak mahal dan biasanya mempunyai panjang
yang sama dengan motor. Harga bagi penderia jenis ini meningkat mengikut saiz,
seterusnya meningkatkan harga bagi setiap pakej motor linear.
Bagi sesetengah aplikasi yang tidak memerlukan ketepatan kedudukan seperti
pencengkam robot, penderia kedudukan yang mahal dan berketepatan tinggi adalah
tidak diperlukan. Tanpa penderia kedudukan ini di dalam sistem akan dapat
mengurangkan kos keseluruhan serta menggalakan lebih banyak pembangunan dan
aplikasi motor linear. Kajian ini mengkaji dan mencadangkan satu sistem penetapan
kedudukan tanpa penderia bagi motor linear DC (LDM). Idea yang digunakan untuk
mengawal kedudukan LDM adalah dengan mengawal jumlah arus yang di bekalkan
kepada motor. Teknik yang digunakan untuk mengawal arus adalah dengan
memanipulasikan isyarat denyut modulasi lebar (PWM). Isyarat PWM ini dihasilkan
oleh litar pengawal micro berasaskan pemproses Atmel AVR ATmega8535.
Sebuah model mudah LDM telah dibina bagi tujuan eksperimen. Satu pegas
digunakan di dalam reka bentuk motor bagi menyerap daya yang dihasilkan oleh
motor. Pemanjangan pegas ini akan digunakan bagi menentukan kedudukan motor.
Di sebabkan oleh ayunan harmonik yang berlaku di dalam sistem beban-pegas,
kedudukan motor akan berayun sebelum mencapai kedudukan terakhir yang
dikehendaki. Untuk membuang kesan ayunan ini, beberapa variasi isyarat PWM
akan digunakan untuk menggerakkan motor. Variasi isyarat PWM ini dinamakan
sebagai satu fasa, dua fasa, tiga fasa dan empat fasa. Variasi isyarat PWM ini
dihasilkan dengan menggabungkan beberapa nilai kitar kerja yang berbeza dan
digabungkan di dalam satu isyarat PWM.
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Satu model matematik bagi LDM yang dibina telah diterbitkan berasaskan kepada
teori ayunan paksa dengan redaman bagi sistem beban-pegas. Persamaan gerakan
bagi LDM ini kemudiannya disimulasikan menggunakan perisian Matlab.
Berdasarkan kepada hasil simulasi system respon masa, beberapa pengubahsuaian
akan dibuat terhadap parameter pemanduan bagi memperbaiki masa naik, peratusan
lajakan dan ralat keadaan mantap. Parameter pemanduan yang telah diubahsuai ini
kemudiannya akan dipindahkan kepada unit pengawal mikro bagi pelaksanaan
eksperimen makmal yang sebenar.
Objektif kajian ini untuk menghasilkan satu sistem penetapan kedudukan tanpa
penderia bagi LDM telah berjaya dicapai. Perbandingan yang dibuat ke atas hasil
simulasi dan eksperimen sebenar menunjukkan keputusan yang hampir sama. Satu
hubungan linear di antara kedudukan motor dan parameter pemasaan yang digunakan
di dalam algoritma pengawal telah dikenalpasti dan persamaan linear telah
diterbitkan. Persamaan linear ini kemudiannya diterjemahkan ke dalam bahasa
pengaturcaraan pengawal mikro sebagai algoritma pengawal suap hadapan.
Sebarang kedudukan motor yang dikehendaki boleh dimasukkan ke dalam sistem dan
pengawal mikro akan menghasilkan isyarat PWM yang bersesuaian kepada motor.
Sistem yang dibangunkan ini boleh digunakan untuk sebarang aplikasi kos rendah
yang tidak memerlukan ketepatan kedududukan yang tinggi.
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ACKNOWLEDGEMENTS All praise to supreme almighty Allah swt. the only creator, cherisher, sustainer and
efficient assembler of the world and galaxies whose blessings and kindness have
enabled the author to accomplish this project successfully.
The author gratefully acknowledges the guidance, advice, support and
encouragement he received from his supervisor, Dr. Norhisam Misron who keeps
advising and commenting throughout this project until it turns to real success.
Great appreciation is expressed to Dr. Senan Mahmood for his valuable remarks,
help advice and encouragement.
Appreciation also to the Faculty of Engineering for providing the facilities and the
components required for undertaking this project.
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I certify that an Examination Committee met on (February, 12 2008) to conduct the final examination of Ezril Hisham Mat Saat on his Master of Science thesis entitled “A Sensorless Positioning System for Linear DC Motor” in accordance with University Putra Malaysia (Higher Degree) Act 1980 and University Pertanian Malaysia (Higher Degree) Regulations 1981. The Committee recommends that the candidate be awarded the relevant degree. Members of the Examination Committee are as follows:
Norman Mariun, Ph.D. Professor Faculty of Engineering University Putra Malaysia (Chairman) Ishak Aris, Ph.D. Associate Professor Faculty of Engineering University Putra Malaysia (Internal Examiner) Hashim B. Hizam, Ph.D. Faculty of Engineering University Putra Malaysia (Internal Examiner)
___________________________________ Hasanah Mohd Ghazali, Ph.D. Professor/Deputy Dean School of Graduate Studies Universiti Putra Malaysia
Date:
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This thesis was submitted to the Senate of University Putra Malaysia and has been accepted as fulfilment of the requirement for the degree of Master of Science. The members of the Supervisory Committee were as follows:
Norhisam Misron, PhD Lecturer Faculty of Engineering University Putra Malaysia (Chairman) Senan Mahmood, PhD Professor Faculty of Engineering University Putra Malaysia (Member)
_____________________________
AINI IDERIS, PhD Professor and Dean School of Graduate Studies Universiti Putra Malaysia
Date: 10th July 2008
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DECLARATION
I hereby declare that the thesis is based on my original work except for quotations and citations which have been duly acknowledged. I also declare that it has not been previously or concurrently submitted for any other degree at UPM or other institutions.
_______________________________EZRIL HISHAM MAT SAAT
Date: 1st July 2008
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TABLE OF CONTENTS
Page
DEDICATION ii ABSTRACT iii ABSTRAK vi ACKNOWLEDGEMENTS ix APPROVAL x DECLARATION xii LIST OF TABLES xv LIST OF FIGURES xvi LIST OF ABBREVIATIONS xx
CHAPTER
I INTRODUCTION 1 1.1 Problem Statement 3 1.2 Scope of Study 4 1.3 Objectives 5 1.4 Thesis Layout 6
II LITERATURE REVIEW 7 2.1 Linear Motor 8 2.2 Linear DC Motor 10 2.3 Advantages of Linear Motor 11 2.4 Applications of Linear Motor 14 2.5 Basic Structure of Linear DC Motor 16 2.6 Basics of Motion Control 19 2.7 Cost Analysis 22 2.8 An Overview of Related Works 23 2.9 Summary 26
III METHODOLOGY 3.1 Basic Principle of Sensorless Positioning System 27 3.2 LDM Specification and Model Construction 30 3.3 LDM System Modeling 33 3.4 Matlab Simulation 46 3.5 Motor Driver 49 3.5.1 Microcontroller Unit 49 3.5.2 H-Bridge Circuit 52 3.5.3 PWM Signal 54 3.5.4 Forward and Reverse Motor Control 58 3.6 PWM Variant Pattern 59 3.7 Summary 61
xiii
IV RESULTS AND DISCUSSION 62 4.1 Preliminary Experiment 62 4.2 Effect of PWM Duty Cycle D to LDM Current 63 4.3 LDM Positioning using Single Stage Approach 65 4.4 LDM Positioning using Dual Stage Approach 70 4.5 LDM Positioning using Triple Stage Approach 76 4.6 LDM Positioning using Quadruple Stage Approach 82 4.7 Comparison and Discussion 87 4.8 Further Experiment for Quadruple Stage Approach. 89 4.9 Summary 92
V CONCLUSION AND SUGGESTION 93 5.1 Conclusion 93 5.2 Suggestions and Future Work Recommendation 95
REFERENCES 96 APPENDICE
A Motor Driver Schematic Drawing 99 B LDM Technical Drawing 100 C Matlab M-files 107 D Microcontroller Assembly Code 113
BIODATA OF STUDENT 116 LIST OF PUBLICATIONS 117
xiv
LIST OF TABLES
Table
Page
2.1 Table 2.1: Linear Motor Applications 15
3.1 Table 3.1: Equipment Specification and Configuration used in the Experiment
30
3.2 Table 3.2: LDM Specifications used in the Experiment. 31
3.3 Table 3.3: Truth Table for Motor Direction 52
4.1 Table 4.1: Performance Comparison of Four Approaches. 88
4.2 Table 4.2: Control Parameters Setting using Quadruple Stage Approach for Different Target Position.
90
xv
LIST OF FIGURES
Figure Page
2.1 Figure 2.1: Commercial Linear Induction Motor Manufactured by H2W Technologies Inc.
9
2.2 Figure 2.2: Commercial Linear Stepper Motor Manufactured by H2W Technologies Inc.
9
2.3 Figure 2.3: Basic Structure of Linear DC Motor. 16
2.4 Figure 2.4: Commercial Product Available in the Market. 22
3.1 Figure 3.1: Modification on the Basic Structure of the LDM. 28
3.2 Figure 3.2: Open Loop Sensorless Positioning System for LDM.
29
3.3 Figure 3.3: Research Methodology for Sensorless Positioning System for LDM.
29
3.4 Figure 3.4: Experiment Setup for Sensorless Positioning System for LDM.
31
3.5 Figure 3.5: Actual LDM Prototype used in the experiment. 32
3.6 Figure 3.6: Free Body Diagram of Mass Spring System. 34
3.7 Figure 3.7: Time Response for Different Cases of Damping Coefficientζ .
36
3.8 Figure 3.8: External Force in Single Stage Approach 39
3.9 Figure 3.9: External Forces in Dual Stage Approach 40
3.10 Figure 3.10: External Forces in Triple Stage Approach 42
3.11 Figure 3.11: External Forces in Quadruple Stage Approach 44
3.12 Figure 3.12: Matlab M-file Coding and Transient Response Plotting.
46
3.13 Figure 3.13: Flowchart for Matlab Simulation. 48
3.14 Figure 3.14: Motor Driver Prototype 49
3.15 Figure 3.15: Typical AtMega8535 Connections. 50
3.16 Figure 3.16: Connection Between Microcontroller and H-bridge Circuit.
51
3.17 Figure 3.17: H-Bridge Topology 53
3.18 Figure 3.18: PWM Signal for Different Duty Cycle running at same Frequency.
54
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3.19 Figure 3.19: Time Period for High and Low State for PWM Signal with 70% Duty Cycle running at 1 kHz Frequency
55
3.20 Figure 3.20: Flowchart for Generating PWM Signals. 57
3.21 Figure 3.21: Timing Diagram for Forward and Reverse Motor Control.
58
3.22 Figure 3.22: PWM Variant Pattern for Single Stage, Dual Stage, Triple Stage and Quadruple Stage.
60
4.1 Figure 4.1: LDM Motor Thrust Characteristics 63
4.2 Figure 4.2: Motor Current for Different Frequency and Duty Cycle of PWM Measured from Experiment.
65
4.3 Figure 4.3: PWM Driving Pattern for Single Stage Approach. 66
4.4 Figure 4.4: PWM Signal Observed from Actual Experiment in Single Stage Approach.
66
4.5 Figure 4.5: Flowchart for Matlab Simulation used in Single Stage Approach.
67
4.6 Figure 4.6: Motor Displacement Measured from Experiment for Different Values of Duty Cycle running at 9kHz.
68
4.7 Figure 4.7: Motor Displacement obtained from Matlab simulation for Different Values of Duty Cycle running at 9kHz.
69
4.8 Figure 4.8: Relation between PWM Duty Cycle and Motor Displacement using Single Stage Approach.
69
4.9 Figure 4.9: Time Response Performance of Single Stage Approach with 15% Duty Cycle.
70
4.10 Figure 4.10: PWM Driving Pattern for Dual Stage Approach 71
4.11 Figure 4.11: PWM Signal observed from Actual Experiment for Dual Stage Approach.
71
4.12 Figure 4.12: Flowchart for Microcontroller Coding in Dual Stage Approach.
72
4.13 Figure 4.13: Flowchart for Matlab Simulation in Dual Stage Approach.
73
4.14 Figure 4.14: Time Response Performance of Dual Stage Approach for Different Values of t1 Measured from experiment.
75
4.15 Figure 4.15: Time Response Performance of Dual Stage Approach for Different Values of t1 obtained from Matlab Simulation.
75
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4.16 Figure 4.16: PWM Driving Pattern for Triple Stage Approach. 77
4.17 Figure 4.17: PWM Signal Observed from Actual Experiment in Triple Stage Approach.
77
4.18 Figure 4.18: Flowchart for Microcontroller coding in Triple Stage Approach.
78
4.19 Figure 4.19: Flowchart for Matlab Simulation in Triple Stage Approach.
78
4.20 Figure 4.20: Time Response Performance of Triple Stage Approach for Different Values of t1. ( t2 =16 ms).
80
4.21 Figure 4.21: Time Response Performance of Triple Stage Approach for Different Values of t2 Measured from experiment. (t1= 20ms).
81
4.22 Figure 4.22: Time Response Performance of Triple Stage Approach for Different Values of t2 Obtained from Matlab Simulation.
81
4.23 Figure 4.23: PWM Driving Pattern for Quadruple Stage Approach
82
4.24 PWM Signal Observed from Actual Experiment in Quadruple Stage Approach.
83
4.25 Figure 4.25: Flowchart for Microcontroller coding in Quadruple Stage Approach.
84
4.26 Figure 4.26: Flowchart for Matlab Simulation in Quadruple Stage Approach.
85
4.27 Figure 4.27: Time Response Performance of Quadruple Stage Approach for Different Values of t3 Measured from Experiment.( t1=20ms, t2 = 8ms)
86
4.28 Figure 4.28: Time Response Performance of Quadruple Stage Approach for Different Values of t3 obtained from Matlab Simulation.
86
4.29 Figure 4.29: Time Response Performance of Quadruple Stage Approach with t mst 23ms201 = , t ms82 = and = .
87
4.30 Figure 4.30: Time Response Comparison for Single Stage Approach, Dual Stage Approach, Triple Stage Approach and Quadruple Stage Approach Measured from Experiment.
88
4.31 Figure 4.3: Time Response Comparison for Single Stage Approach, Dual Stage Approach, Triple Stage Approach and Quadruple Stage Approach Obtained from Matlab Simulation.
89
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4.32 Figure 4.32: Time Response Performance of Quadruple Stage Approach for Different Target Position.
91
4.33 Figure 4.33: Timing Parameters ( t , t , t ) used in Quadruple Stage Approach for Different Motor Target Position.
1 2 3 91
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xx
LIST OF ABBREVIATIONS
AC Alternating Current
DC Direct Current
FET Field Effect Transistor
LDM Linear DC Motor
LIM Linear Induction Motor
LSM Linear Stepper Motor
MOSFET Metal Oxide Semiconductor Field Effect Transistor
PWM Pulse Width Modulation
EMF Electromagnetic Field
CHAPTER 1
INTRODUCTION
In recent years, linear motors have been widely used in industry and commercial
products. Many machine tools and industrial equipments are now adopting linear
motor in the design due to the advantages offered by this device. Simple structure of
linear motor offers high flexibility to the machine in terms of size and space.
(Backman (2005)). Few components in motor structure and little lubrication make
installation and maintenance easy. Linear motors produce linear motion without
using any intermediate mechanical conversion devices. Unlike conventional rotary
motor, the absence of intermediate mechanical transmission devices such as gears,
belts and motor coupling eliminates backlash and compliance, reducing friction and
wears, thus increases motor efficiency (Lee et al. (2000)).
There are many types of linear motors currently available in the market. Commercial
linear motor comes in many shapes and sizes, operating principles and electric power
sources. The main constraint for system designers to consider linear motor in the
design is the cost. Linear motors are expensive, due to the large number of
permanent magnets used in the motor and the sensory technologies used in the
design. Linear motors provide direct linear motion, thus most of the design of linear
motors are in rectangular shape with specific length. Permanent magnets used in the
motor normally are mounted on both sides along the rails of the moving coil. The
number of permanent magnet increase with the length of the motor which increase
the cost for linear motor.
Any electrical motor including linear motor requires special electronic circuit for
proper power handling and motion control. These electronic circuits, also known as
motor driver or motor controller, are normally designed based on digital signal
processors (DSPs) or microcontroller unit (Panahi et al. (1997)). For motor
positioning purposes, these digital controllers require position sensors to detect the
position of the motor and send feedback signal to the controllers. Typical position
sensor for linear motor application includes linear encoders and incremental
encoders. Linear encoders measure the relative position of the moving and stationary
parts of the drive while incremental encoders measure the changes of position rather
than absolute position. These sensors are many times more expensive than typical
rotary motor sensor and the price increases with the size or length of the sensor.
The simplest method to control the speed of a DC motor is by controlling its driving
voltage. The higher the voltage is the higher speed the motor tries to reach. Speed
control of DC motor can be achieved by using variable supply voltage and the
direction can be changed by reversing the polarity of the power supply. On the other
hands, the torque produced by a DC motor is proportional to the amount of current
supply to the motor. The higher the current is the higher torque produced by the
motor. Positioning system for motor applications requires motor controller to
perform some sort of control algorithms. To obtain precise positioning, the
controller normally applies closed-loop control algorithms such as PID controller
(Yajima et al. (2001)), Adaptive controller (Zhao and Tan (2004)) and Sliding Mode
control (Li and Wikander (2004)). However, for simple and low cost applications
which do not require precise positioning, an open loop system can be an alternative.
2
1.1 PROBLEM STATEMENT
Nowadays, manufacturing industries are looking forward for high speed and high
accuracy drives to improve their machines to meet their production demands. Linear
motors practically can be used for any applications requiring linear motion and
provides solution for industries. However, not all application requires precise
positioning such as robot end gripper, electronic locking mechanism and sliding door
application. Linear motor used for robot end-gripper is only required to open the
end-gripper in horizontal or vertical axis. The tolerance for positioning is not tight,
thus high accuracy and expensive linear position sensor is not necessary in such
application.
The absence of feedback positioning sensor makes the system an open-loop system.
A characteristic of the open-loop system is that it does not use any feedback signal to
determine if its input has achieved the desired goal (Choudhury (2005)). Open-loop
control is useful for well-defined systems where the relationship between input and
the resultant state can be modeled by a mathematical formula. Therefore,
mathematical equations describing the system are essential for open-loop system and
necessary prior to implementation of the control system. These mathematical
equations will be used in early stage for simulation purposes and appropriate
adjustment to control algorithms parameters can be made to obtain optimum
performance of the system.
3
1.2 SCOPE OF STUDY
In this research, focus is given on the design and implementation of open-loop feed
forward control algorithms for LDM positioning system. The idea to control the
position of the motor is by controlling the forces produced by the motor. A basic
model of LDM based on design in (Norhisam et al. (2004)) will be constructed with
modification and improvement for experimental purposes. A modification is made
to the motor by connecting a mechanical spring to the moving coil. The purpose of
this mechanical spring is to absorb the forces produced by the motor. Once the
forces produced by the motor is equal to the forces absorbed by the spring, the
moving coil will stop at some distance. The displacement of the spring then will be
used to determine the position of the motor.
The technique used to control the forces produced by the motor is by controlling the
current supplied to the coil. In this research, the current control approach is done by
manipulating Pulse Width Modulation (PWM) signal through an H-Bridge circuit.
The duty cycle of the PWM signal will be used to determine the amount of current
flowing to the motor’s coil.
The equation of motion for the constructed motor will be derived based on damped
force vibration of Mass-Spring system (Malvino (1999)). This equation relates the
displacement of the spring and the forces produce by the motor. To observe and
study the characteristics of the system, Matlab software will be used to simulate the
derived equations. The output of the simulations will be analyzed and appropriate
adjustment to the control system parameters will be made to improve the time
response of the system.
4