vii
TABLE OF CONTENTS
CHAPTER
TITLE
PAGE
ii
DECLARATION
1
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF ABBREVIATIONS
xiv
LIST OF SYMBOLS
xvi
INTRODUCTION
1
1.1 Background
1
1.2 Statement of the Problem
3
1.3 Objectives of the Study
4
1.4 Scope of the Study
4
1.5 Research Methodology
5
1.6 Thesis Outline
6
viii
2
3
LITERATURE REVIEW
8
2.1 Introduction
8
2.2 Previous Designs of Ball and Beam Balancer System
8
2.3 Synchronization
13
2.4 Cooperative Control
14
MODELING & SIMULATION
15
3.1 Introduction
15
3.2 Theoretical Analysis of DMBB Model
15
3.2.1 Assumptions
16
3.2.2 Model of DC Motor
18
3.2.3 Model of the Ball Moving on the Beam
22
3.2.4 Model of the Transmission Part
24
3.2.5 DMBB Model for Simulation
26
3.3 Simulation
3.3.1 Model Parameters
27
3.3.2 Controller Design of DMBB Model
29
3.3.2.1 Controller for DC Motors
30
3.3.2.2 Controller for Ball Position
34
3.3.3 Simulation by MATLAB / Simulink
4
27
38
PROTOTYPE DESIGN
41
4.1 Introduction
41
4.2 Components to Construct the Prototype
42
4.2.1 Actuator (DC Motor)
42
4.2.2 Motor Driver
44
ix
4.2.3 Sensors to Form the Feedback
4.2.3.1 Position Sensor
50
4.2.3.2 Rotary Displacement Sensor
51
4.2.4 Mechanical Parts
5
50
55
EXPERIMENT
57
5.1 Introduction
57
5.2 PCI-1711 DAQ Board
57
5.2.1 Introduction of PCI-1711 DAQ
57
5.2.2 Installation of the DAQ Board
59
5.2.3 Connections of the Prototype with PC through
60
PCI-1711
5.3 LabVIEW Application
6
REFERENCES
62
5.3.1 Introduction of LabVIEW
62
5.3.2 Program by LabVIEW
63
CONCLUSIONS AND RECOMMENDATIONS
67
6.1 Conclusion
67
6.2 Recommendation
68
69
x
LIST OF TABLES
TABLE NO
TITLE
PAGE
3.1
Parameters of the Ball & Beam Model
28
3.3
The Effect of Increasing Each of the PID Controller
30
Parameters
4.1
Parameters of Selected DC Motors
44
4.2
Logic Truth Table for LMD18200
47
4.3
Selected ICs to Make the Driver Circuit
49
5.1
Signals of the Prototype
60
xi
LIST OF FIGURES
FIGURE NO
TITLE
PAGE
1.1
Designed DMBB Prototype
2
1.2
Flow Chart of Research Methodology
6
2.1
‘Ball on balancing beam’ built by Berkeley Robotics
9
Laboratory (Arroyo 2005)
2.2
‘Ball and Beam Balancer’ built by The University of
10
Lakehead (Ambalavanar , Moinuddin & Malyshev
2006)
2.3
Ball and Beam module presented by ‘Quanser’ (Quanser
11
2006)
2.4
Ball and Beam System; a) Single Motor System, b) Dual
11
Motor System
2.5
Configuration of Dual Motor System
12
2.6
Dual-motor Ball and Beam System (Manavaalan
12
Gunasekaran and Ramprasad Potluri 2008)
3.1
Sketch Diagram of DMBB Initial State
17
3.2
Sketch Diagram of DMBB Dynamic
17
3.3
Sketch Diagram of DC Motor
18
3.4
Block Diagram of DC Motor Model
21
3.5
Sketch Diagram of Ball on Beam
22
3.6
Sketch Diagram of Force Analyze for Ball on Beam
22
3.7
Diagram of System Geometric Relationship of DMBB
25
xii
3.8
Geometric Relationship of Ball & Beam part and Motor
25
part
3.9
Derived DMBB Model
27
3.10
Block Diagram of the DMBB
29
3.11
Open-Loop Step Response of Motor Angle Output
32
3.12
Performance of PD Controller for DC Motor with Step
33
Input
3.13
Performance of PD Controller for DC Motor with Sine
33
Input
3.14
Block Diagram of Uncompensated Inner Loop System
35
3.15
Step Response of Uncompensated Inner Loop System
36
3.16
Bode Plot of Uncompensated Inner Loop System
36
3.17
Bode Plot of Open Loop System with Designed
37
Compensator
3.18
Simulation Block Diagram for the System
38
3.19
Simulation Result for the Ball Position
39
3.20
Simulation Result with Sine Wave Input
40
3.21
Simulation Result with Square Wave Input
40
4.1
Dimension of the Selected DC-Motor (from datasheet)
43
4.2
Illustration of Planetary-Gear System
43
4.3
Schematic of H Bridge
45
4.4
Operation of H-bridge; a) Left to Right Current Flow, b)
45
Right to Left Current Flow
4.5
Functional Block Diagram of LMD18200
46
4.6
Schematic of PWM Waveform; a) PWM with Duty
47
Cycle of 75%, b) PWM with Duty Cycle of 50%, c)
PWM with Duty Cycle of 75%
4.7
Circuit Diagram of Motor Driver
48
4.8
PCB of Motor Driver
49
xiii
4.9
Sketch Diagram of Position Sensor
51
4.10
Encoder Circuit Diagram
52
4.11
Quadrature Encoding of the Incremental Optical
53
Encoder; a) Forward (Clockwise) Encoding, b) Reverse
(Counter clockwise) Encoding
4.12
Encoder Feedback Signals Monitored by Oscilloscope
54
4.13
Mechanical Parts Details of DMBB Prototype
56
4.14
Overview of the Designed Prototype
56
5.1
PCI-1711 DAS Set
58
5.2
Installation Flow Chart of DAQ Card
59
5.3
Connections of the Prototype
61
5.4
LabVIEW 8.6 Program
62
5.5
Elements for LabVIEW from Advantech
64
5.6
Block Diagram of Main Program
65
5.7
Block Diagram of Sub Program for Motor1
65
xiv
LIST OF ABBREVIATIONS
SMBB
-
Single Motor Ball & Beam Balancer System
DMBB
-
Dual Motor Ball & Beam Balancer System
DC
-
Direct Current
PC
-
Personal Computer
SISO
-
Single Input, Single Output
MIMO
-
Multiple Input, Multiple Output
P
-
Proportional
PD
-
Proportional-Derivative
PID
-
Proportional-Integral-Derivative
LQR
-
Linear Quadratic Regulator
MATLAB
-
Matrix Laboratory
LabVIEW
-
Laboratory Virtual Instrumentation Engineering Workbench
KVL
-
Kirchhoff’s Voltage Law
EMF
-
Electromotive Force
PM
-
Phase Margin
GM
-
Gain Margin
DIY
-
Do It Yourself
IC
-
Integrated Circuit
CMOS
-
Complementary Metal Oxide Semiconductor
DMOS
-
Double Diffused MOSFET
PWM
-
Pulse Width Modulation
Ch
-
Channel
xv
Ref
-
Reference
CCP
-
Capture/Compare/PWM
ECCP
-
Enhanced CCP
A/D
-
Analog to Digital
DAQ
-
Data Acquisition
AO
-
Analog Output
AI
-
Analog Input
DO
-
Digital Output
DI
-
Digital Input
DAS
-
Data Acquisition System
PCI
-
Peripheral Component Interconnect
SCSI
-
Small Computer System Interface
CD
-
Compact Disc
DLL
-
Dynamic Link Library
VI
-
Virtual Instrument
MOT
-
Motor
xvi
LIST OF SYMBOLS
-
Input voltage to DC motor
-
Armature resistance of DC motor
-
Armature inductance of DC motor
-
Armature voltage of DC motor
-
Armature current of DC motor
-
Torque constant of DC motor
-
Back EMF constant of DC motor
-
Torque at the motor shaft
-
Torque from load
-
Gear ratio of reduction gearbox
-
Effective moment of inertia
-
Viscous friction coefficient
-
Motor shaft angle speed output
-
Motor shaft angle acceleration
-
Gain constant of DC motor model
-
Time constant of DC motor model
-
Force on ball
m
-
Mass of the ball
r
-
Distance of the ball on the beam
g
-
Acceleration of gravity
-
Beam’s tilt angle from the horizontal position
-
Friction force
xvii
-
Rotational angle of the ball
-
Radius of the ball
-
Rotational radius of the ball
-
Torque on the ball
-
Inertia of the ball
-
Angular acceleration of the ball
-
Rotary angle of motor1
-
Rotary angle of motor2
-
Rotary angle of motor1 gear shaft
-
Rotary angle of motor2 gear shaft
-
Sum of the rotary angle of motor1 and motor2
L
-
length of the beam
l
-
Length of the arm
-
Gain constant of ball beam model refer to the tilt angle of
beam
-
Transfer function of DC motor integrated with gearbox
-
Transfer function of the ball position refer to gear shaft
output
-
New gain constant of DC motor after reduction.
-
New Gain constant of ball beam model refer to the gearbox
shaft angle
-
DC motor speed transfer function
u
-
Output of PID controller
e
-
Error signal
-
Proportional gain
-
Integral gain
-
Derivative gain
-
Transfer function of PID controller
-
Integral time constant
-
Derivative time constant
-
Transfer function of motor controller
R
xviii
-
Open loop transfer function for DC motor
-
Transfer function of lead compensator
K
-
Gain constant of lead compensator
z
-
Zero of lead compensator
p
-
Pole of lead compensator
α
-
The specific value of p and z
-
Necessary additional phase is required to give the desired
phase margin
-
The inner loop transfer function
-
Desired phase margin
-
Makeup value of the phase margin
-
Overshoot
-
Settling time
-
Peak value
-
Final value
-
Output voltage from position sensor
-
Voltage applied to position sensor
-
Frequency of the PWM feedback signal from encoder
-
Rotary speed of the code disk
-
Resolution of encoder
OS%
n