vii
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xiv
LIST OF FIGURES
xv
LIST OF SYMBOLS
xix
LIST OF ABBREVIATIONS
xx
LIST OF APPENDICES
xxi
INTRODUCTION
1
1.1
Unmanned Aerial Vehicle Helicopter System
1
1.2
Research on UAV Helicopter System: An Overview
2
1.3
Problem Statement
4
1.4
Research Objectives
5
1.5
Research Contributions
6
viii
1.6
2
Structure and Layout of the Thesis
UAV HELICOPTER SYSTEM
9
2.1
Introduction
9
2.2
Linearized Models of the UAV Helicopter System
with Hovering and 6m/s Forward Flight Conditions
2.3
2.4
3
6
10
The Uncertain Model with Bounded Uncertainties of
an UAV Helicopter System
13
Summary
19
AUTONOMOUS FLIGHT CONTROL SYSTEM FOR
AN UAV HELICOPTER SYSTEM
20
3.1
Introduction
20
3.2
The Hierarchical Structure of the Autonomous Flight
3.3
3.4
3.5
Control
20
The Flight Command Generator
22
3.3.1 The X position Channel Control
22
3.3.2 The Y position Channel Control
22
3.3.3 The Z position Channel Control
23
3.3.4 The yaw heading Channel Control
23
The Design of the Flight Command Generator
23
3.4.1 The X, Y and Z Position CNF Controller
24
3.4.2 The Yaw Heading Controller Design
26
Estimation of the Unmeasurable State Variables of
the UAV Helicopter System
26
3.5.1 Reduced Order Observer Design
27
3.5.2 Reduced Order Observer Gain Matrix
Calculation
29
ix
3.6
4
Summary
32
VARIABLE STRUCTURE CONTROL
33
4.1
Introduction
33
4.2
Switching Surface Design
35
4.2.1 The method of equivalent control
37
4.2.2 The Invariance Property of the Sliding Mode
Control to the Matched Uncertainties
38
4.2.3 Switching Surface Design based on Nominal
System for Uncertain System with Matched
Uncertainties
4.3
39
4.2.4 A Regular Form Approach
40
4.2.5 Quadratic Minimization technique
42
Control Law Design
45
4.3.1 Switching Scheme
46
4.3.1.1 Fixed-Order Switching Scheme
46
4.3.1.2 Free-Order Switching Scheme
47
4.3.1.3 Eventual Sliding Mode Switching
Scheme
4.3.1.4 Decentralized Switching Scheme
4.3.2 Reaching Condition
47
48
48
4.3.2.1 The Direct Switching Function
Approach
48
4.3.2.2 The Lyapunov Function Approach
49
4.3.2.3 The Reaching Law Approach
50
4.3.3 The Control Law Design Approach
51
4.3.3.1 Effect of the Sliding Mode
Switching Scheme
52
4.3.3.2 Effects of the Structure of the
Control Law
4.4
The Chattering Problem
53
55
x
4.5
5
Summary
56
UNIT VECTOR APPROACH MODEL FOLLOWING
SLIDING MODE CONTROL FOR UAV
HELICOPTER SYSTEM
57
5.1
Introduction
57
5.2
Unit Vector Approach Sliding Mode Control
58
5.2.1 The System Descriptions
59
5.2.2 The Switching Surface Design
59
5.2.3 The Proposed Unit Vector Control Law
61
5.2.4 Proof of Existence of an Ideal Sliding Mode
using the Regular Form Approach
5.2.5 The Dynamics of the Sliding Motion
5.3
62
65
The Design of Unit Vector Approach Model
Following Sliding Mode Control
66
5.3.1 The System Descriptions and Assumptions
66
5.3.2 The Sliding Surface Design of the Unit
Vector Approach MFSMC using the Regular
Form Approach
67
5.3.3 The Design of the Unit Vector Approach
MFSMC Control Law
5.4
69
The Design of the Unit Vector Approach MFSMC
for an UAV Helicopter System
71
5.4.1 The UAV Helicopter System
71
5.4.2 The Design of the Model by Direct
Eigenstructure Assignment
74
5.4.3 The Design of the Sliding Surface for the
Unit Vector Approach MFSMC for an UAV
Helicopter System using Regular Form
Approach
81
xi
5.4.4 The Design of the Control Law for the Unit
Vector Approach MFSMC for an UAV
Helicopter System
5.5
6
Summary
82
84
DETERMINISTIC CONTROL APPROACH
AUGMENTED MFVSC FOR UAV HELICOPTER
SYSTEM
85
6.1
Introduction
85
6.2
Deterministic Control Approach Augmented
MFVSC
87
6.2.1 System Descriptions and Assumptions
87
6.2.2 Dynamic Equation of the Augmented Model
Following Error System for New Control
Algorithm I
88
6.2.3 Design of the Switching Surface for the New
Control Algorithm I
92
6.2.4 Design of the Control Law for the New
6.3
Control Algorithm I in Regular Form
95
6.2.4.1 Proof of the Theorem 6.1
97
Design of the Controller for the UAV Helicopter
System using the New Control Algorithm I
99
6.3.1 The UAV Helicopter System
99
6.3.2 The Switching Surface Design for the New
Control Algorithm I
101
6.3.3 The Controller Design for the New Control
Algorithm I
6.4
Summary
103
105
xii
7
DETERMINISTIC CONTROL APPROACH
AUGMENTED MFVSC WITH NONLINEAR STATE
FEEDBACK FOR UAV HELICOPTER SYSTEM
106
7.1
Introduction
106
7.2
Deterministic Control Approach MFVSC with
Nonlinear State Feedback
107
7.2.1 System Descriptions and Assumptions for the
New Control Algorithm II
107
7.2.2 Dynamic Equation of the Augmented Model
Following Error System for the New Control
Algorithm II
109
7.2.3 Design of the Switching Surface for the New
Control Algorithm II
113
7.2.4 Design of the Control Law for the New
7.3
Control Algorithm II in Regular Form
116
7.2.4.1 Proof of Theorem 7.1
119
Design of the Controller for the UAV Helicopter
System using the New Control Algorithm II
124
7.3.1 The UAV Helicopter System
124
7.3.2 The Switching Surface Design for the New
Control Algorithm II
125
7.3.3 The Controller Design for the New Control
Algorithm I
7.4
8
Summary
125
126
SIMULATIONS
128
8.1
Introduction
128
8.2
Simulation Results
130
xiii
8.2.1 Simulation I: Simulation Results of Different
Controllers Performing Pirouetting Flight
with Flight Speed of 1.9635m/s
132
8.2.1.1 Summary
142
8.2.2 Simulation II: Simulation Results of
Different Controllers Performing Pirouetting
Flight with Flight Speed of 5.8905m/s
142
8.2.2.1 Summary
152
8.2.3 Simulation III: Results of New Control
Algorithm I Performing Pirouetting flight
with different Epsilon values
152
8.2.3.1 Summary
164
8.2.4 Simulation IV: Results of New Control
Algorithm I and II Performing Pirouetting
Flight with Epsilon value of 0.016
164
8.2.4.1 Summary
177
8.2.5 Simulation V: Results of Different Alpha and
Beta Settings for the Nonlinear Statefeedback Controller Performing the
8.3
9
Pirouetting Flight
178
8.2.5.1 Summary
190
Conclusion
191
CONCLUSION AND SUGGESTIONS
193
9.1
Conclusion
193
9.2
Suggestions for Future Work
194
REFERENCES
196
Appendices A-D
200-206
xiv
LIST OF TABLES
TABLE NO.
TITLE
PAGE
8.1
Simulation Configuration Settings
129
8.2
Selectable flight speeds and controller parameter settings
130
8.3
Parameter Settings of the Simulation I
132
8.4
Parameter Settings of the Simulation II
142
8.5
Parameter Settings of the Simulation III
153
8.6
Parameter Settings of the Simulation IV
165
8.7
Parameter Settings of the Simulation V
178
xv
LIST OF FIGURES
FIGURE
TITLE
PAGE
3.1
The hierarchical structure of the autonomous flight control
21
5.1
Eigenstructure assignment design flow chart
76
8.1
Yaw angle response of Simulation I
133
8.2
XY position response of Simulation I
134
8.3
Z position response of Simulation I
134
8.4
Error of the controlled output state Vx (Simulation I)
135
8.5
Error of the controlled output state Vy (Simulation I)
135
8.6
Error of the controlled output state Vz (Simulation I)
136
8.7
Error of the controlled output state Wz (Simulation I)
136
8.8
Switching function element Se1 (Simulation I)
137
8.9
Switching function element Se2 (Simulation I)
138
8.10
Switching function element Se3 (Simulation I)
138
8.11
Switching function element Se4 (Simulation I)
139
8.12
Control signal U1 (Simulation I)
140
8.13
Control signal U2 (Simulation I)
140
8.14
Control signal U3 (Simulation I)
141
8.15
Control signal U4 (Simulation I)
141
8.16
Yaw angle response (Simulation II)
143
8.17
XY position response (Simulation II)
144
8.18
Z position response (Simulation II)
144
8.19
Error of the controlled output state Vx (Simulation II)
145
8.20
Error of the controlled output state Vy (Simulation II)
145
8.21
Error of the controlled output state Vz (Simulation II)
146
8.22
Error of the controlled output state Wz (Simulation II)
146
xvi
8.23
Switching function element Se1 (Simulation II)
147
8.24
Switching function element Se2 (Simulation II)
148
8.25
Switching function element Se3 (Simulation II)
148
8.26
Switching function element Se4 (Simulation II)
149
8.27
Control signal U1 (Simulation II)
150
8.28
Control signal U2 (Simulation II)
150
8.29
Control signal U3 (Simulation II)
151
8.30
Control signal U4 (Simulation II)
151
8.31
Yaw angle response (Simulation III)
153
8.32
XY position response (Simulation III)
154
8.33
Z position response (Simulation III)
154
8.34
Error of the controlled output state Vx (Simulation III)
155
8.35
Error of the controlled output state Vy (Simulation III)
155
8.36
Error of the controlled output state Vz (Simulation III)
156
8.37(a)
Error of the controlled output state Wz (Simulation III)
156
8.37(b)
Zoom in of the Error of the controlled output state Wz
(Simulation III)
157
8.38
Switching function element Se1 (Simulation III)
158
8.39
Switching function element Se2 (Simulation III)
158
8.40(a)
Switching function element Se3 (Simulation III)
159
8.40(b)
Zoom in of the Switching function element Se3
(Simulation III)
159
8.41(a)
Switching function element Se4 (Simulation III)
160
8.41(b)
Zoom in of the Switching function element Se4
(Simulation III)
160
8.42
Control signal U1 (Simulation III)
161
8.43
Control signal U2 (Simulation III)
162
8.44
Control signal U3 (Simulation III)
162
8.45(a)
Control signal U4 (Simulation III)
163
8.45(b)
Zoom in of the Control signal U4 (Simulation III)
163
8.46
Yaw angle response (Simulation IV)
165
8.47
XY position response (Simulation IV)
166
8.48
Z position response (Simulation IV)
166
8.49
Error of the controlled output state Vx (Simulation IV)
167
xvii
8.50
Error of the controlled output state Vy (Simulation IV)
167
8.51(a)
Error of the controlled output state Vz (Simulation IV)
168
8.51(b)
Zoom in of the Error of the controlled output state Vz
(Simulation IV)
168
8.52(a)
Error of the controlled output state Wz (Simulation IV)
169
8.52(b)
Zoom in of the Error of the controlled output state Wz
(Simulation IV)
169
8.53(a)
Switching function element Se1 (Simulation IV)
170
8.53(b)
Zoom in of the Switching function element Se1
(Simulation IV)
171
8.54(a)
Switching function element Se2 (Simulation IV)
171
8.54(b)
Zoom in of the Switching function element Se2
(Simulation IV)
172
8.55(a)
Switching function element Se3 (Simulation IV)
172
8.55(b)
Zoom in of the Switching function element Se3
(Simulation IV)
173
8.56(a)
Switching function element Se4 (Simulation IV)
173
8.56(b)
Zoom in of the Switching function element Se4
(Simulation IV)
174
8.57
Control signal U1 (Simulation IV)
175
8.58
Control signal U2 (Simulation IV)
175
8.59
Control signal U3 (Simulation IV)
176
8.60(a)
Control signal U4 (Simulation IV)
176
8.60(b)
Zoom in of the Control signal U4 (Simulation IV)
177
8.61
Yaw angle response (Simulation V)
179
8.62
XY position response (Simulation V)
179
8.63
Z position response (Simulation V)
180
8.64
Error of the controlled output state Vx (Simulation V)
180
8.65
Error of the controlled output state Vy (Simulation V)
181
8.66(a)
Error of the controlled output state Vz (Simulation V)
181
8.66(b)
Zoom in of the Error of the controlled output state Vz
8.67(a)
(Simulation V)
182
Error of the controlled output state Wz (Simulation V)
182
xviii
8.67(b)
Zoom in of the Error of the controlled output state Wz
(Simulation V)
183
8.68
Switching function element Se1 (Simulation V)
184
8.69
Switching function element Se2 (Simulation V)
184
8.70(a)
Switching function element Se3 (Simulation V)
185
8.70(b)
Zoom in of the Switching function element Se3
(Simulation V)
185
8.71(a)
Switching function element Se4 (Simulation V)
186
8.71(b)
Zoom in of the Switching function element Se4
(Simulation V)
186
8.72(a)
Control signal U1 (Simulation V)
187
8.72(b)
Zoom in of the Control signal U1 (Simulation V)
187
8.73
Control signal U2 (Simulation V)
188
8.74(a)
Control signal U3 (Simulation V)
188
8.74(b)
Zoom in of the Control signal U3 (Simulation V)
189
8.75(a)
Control signal U4 (Simulation V)
189
8.75(b)
Zoom in of the Control signal U4 (Simulation V)
190
xix
LIST OF SYMBOLS

-
Ground velocity in x direction

-
Ground velocity in y direction
!
-
Roll angular rate
!
-
Pitch angular rate
"
-
Roll angle
#
-
Pitch angle
$
-
Ground velocity in z direction
!$
-
Yaw angular rate
!$%
-
Built-in filter gain in the yaw channel
&'
-
the first harmonics of longitudinal flapping angles of the main
blade tip-path plane
('
-
the first harmonics of lateral flapping angles of the main blade
tip-path plane
xx
LIST OF ABBREVIATIONS
AI
-
Artificial Intelligent
AMFC
-
Adaptive Model Following Control System
CNF
-
Composite Nonlinear Feedback
LMFC
-
Linear Model Following Control System
LQR
-
Linear Quadratic Regulator
MFSMC
-
Model Following Sliding Mode Control
MFVSC
-
Model Following Variable Structure Control
NDP
-
Neural Dynamic Programming
NED
-
North-East-Down
RC
-
Radio Control
SISO
-
Single Input Single Output
UAV
-
Unmanned Aerial Vehicle
UGV
-
Unmanned Ground Vehicle
VSC
-
Variable Structure Control
xxi
LIST OF APPENDICES
APPENDIX
A
TITLE
The Euclidean norm is preserved under orthogonal
transformation
B
PAGE
200
Controllability and observability of the matrix
pair (
)
C
Positive-definiteness in terms of quadratic forms
D
Definitions of existence and continuation of solutions
and tracks the reference signal to within neighborhood
201
203
205