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Loading...Motion Control of Underactuated Mechanical Systems
Intelligent Systems, Control and Automation: Science and Engineering
Javier Moreno-Valenzuela , Carlos Aguilar-Avelar
Contents
1 Introduction . 1
1.1 Background 1
1.1.1 Underactuated Systems . 1
1.1.2 Nonlinear Dynamics and Control . 3
1.1.3 Parameter Identification . 6
1.1.4 Motion Control of Underactuated Systems 7
1.2 Motivations and Objectives . 9
1.3 Outline 9
2 Preliminaries 13
2.1 Fundamentals of Nonlinear Systems 13
2.2 Fundamental Properties 15
2.3 Concepts of Stability . 15
2.4 Barbalat’s Lemma 18
2.5 Boundedness and Ultimate Boundedness 18
2.6 Feedback Linearization 19
2.7 Artificial Neural Networks . 22
2.7.1 Universal Function Approximation Property . 24
3 Identification of Underactuated Mechanical Systems 27
3.1 Introduction 27
3.2 Identification of the Furuta Pendulum . 28
3.2.1 Dynamic Model . 28
3.2.2 Filtered Regression Model . 30
3.2.3 Discretization of the Filtered Regression Model 32
3.2.4 Experimental Platform 33
3.2.5 Motion Control Experiment 34
3.2.6 Joint Velocity Calculation . 35
3.2.7 Least Squares Algorithm 36
3.2.8 Results of the Identification Procedure . 37
vii3.3 Identification of the Inertia Wheel Pendulum . 40
3.3.1 Dynamic Model . 40
3.3.2 Filtered Regression Model . 42
3.3.3 Discretization of the Filtered Regression Model 43
3.3.4 Experimental Platform 44
3.3.5 Motion Control Experiment 45
3.3.6 Joint Velocity Calculation . 45
3.3.7 Least Squares Algorithm 46
3.3.8 Results of the Identification Procedure . 47
3.4 Concluding Remarks 49
4 Composite Control of the Furuta Pendulum . 51
4.1 Introduction 51
4.2 Dynamic Model . 52
4.3 Control Problem Formulation . 53
4.4 Design of the Proposed Scheme . 54
4.4.1 Feedback Linearization Part 54
4.4.2 Energy-Based Compensation . 55
4.4.3 Summary of the Composite Controller . 59
4.5 Analysis of the Closed-Loop Trajectories 60
4.6 Controller for the Performance Comparison 61
4.6.1 Output Tracking Controller 61
4.7 Experimental Evaluation . 62
4.7.1 Experimental Results . 62
4.7.2 Performance Comparison 65
4.8 Concluding Remarks 68
5 Feedback Linearization Control of the Furuta Pendulum 69
5.1 Introduction 69
5.2 Dynamic Model and Error Dynamics . 70
5.3 Control Problem Formulation . 72
5.4 Design of the Proposed Scheme . 72
5.5 Analysis of the Closed-Loop Trajectories 73
5.5.1 Ultimate Bound . 78
5.5.2 Boundedness of the Error Trajectories 79
5.6 Controllers for the Performance Comparison . 80
5.6.1 PID Controller 80
5.6.2 Output Tracking Controller 81
5.7 Experimental Evaluation . 82
5.7.1 Experimental Results . 82
5.7.2 Performance Comparison 85
5.8 Concluding Remarks 91
viii Contents6 Adaptive Neural Network Control of the Furuta Pendulum 93
6.1 Dynamic Model and Error Dynamics . 94
6.2 Control Problem Formulation . 96
6.3 Design of the Proposed Scheme . 96
6.4 Analysis of the Closed-Loop Trajectories 99
6.5 Controllers for the Performance Comparison . 108
6.5.1 PID Controller 108
6.5.2 Jung and Kim Controller 109
6.5.3 Chaoui and Sicard Controller 109
6.6 Experimental Evaluation . 110
6.6.1 Experimental Results and Performance Comparison . 110
6.7 Concluding Remarks 118
7 Composite Control of the IWP 119
7.1 Introduction 119
7.2 Dynamic Model . 121
7.3 Control Problem Formulation . 122
7.4 Design of the Proposed Scheme . 122
7.4.1 Feedback Linearization Controller . 122
7.4.2 Energy-Based Compensation . 124
7.4.3 Summary of the Composite Controller . 128
7.5 Analysis of the Closed-Loop Trajectories 128
7.6 Integral Extension 130
7.7 Controller for the Performance Comparison 131
7.7.1 LQR Motion Controller . 131
7.8 Experimental Evaluation . 131
7.8.1 Swing-up Control ? Motion Control . 132
7.8.2 Experimental Results . 133
7.8.3 Performance Comparison 135
7.9 Concluding Remarks 140
8 Feedback Linearization Control of the IWP . 141
8.1 Dynamic Model and Error Dynamics . 143
8.2 Control Problem Formulation . 145
8.3 Design of the Proposed Scheme . 145
8.4 Analysis of the Closed-Loop Trajectories 146
8.5 Controllers for the Performance Comparison . 150
8.5.1 State Feedback Controller . 150
8.5.2 Particular Feedback Linearization Controller . 151
8.6 Experimental Evaluation . 154
8.6.1 Experimental Results . 155
8.6.2 Performance Comparison 157
8.7 Concluding Remarks 158
Contents ix9 Adaptive Control of the IWP . 159
9.1 Introduction 159
9.2 Dynamic Model and Error Dynamics . 160
9.3 Control Problem Formulation . 163
9.4 Design of the Proposed Schemes 163
9.4.1 Model-Based Controller . 163
9.4.2 Neural Network-Based Controller . 165
9.4.3 Regressor-Based Adaptive Controller 167
9.5 Analysis of the Closed-Loop Trajectories 168
9.5.1 Analysis for the Neural Network-Based Adaptive
Controller . 168
9.5.2 Analysis for the Regressor-Based
Adaptive Controller 170
9.6 Controller for the Performance Comparison 171
9.7 Experimental Evaluation . 171
9.7.1 Experimental Results . 171
9.7.2 Performance Comparison 173
9.8 Concluding Remarks 175
10 Discussion on Generalizations and Further Research 177
10.1 Introduction 177
10.2 Generalization for Linear Systems . 178
10.3 Motion Control for 2-DOF Underactuated Mechanical
Systems . 181
10.4 Motion Control of Higher DOF Underactuated Mechanical
System: FJR as Case Study 182
10.4.1 Model 182
10.4.2 Control Problem 183
10.4.3 Open-Loop System 183
10.4.4 Output Design and Feedback Linearization Control . 184
10.5 Concluding Remarks 187
Appendix A: MATLAB Codes for Parameter Identification
of the Underactuated Mechanical Systems in Chap. 3 189
Appendix B: Conditions to Ensure that Matrix A in Chaps. 5 and 6
is Hurwitz . 201
Appendix C: Convergence Proof of the Swing-up Controller
for the IWP in Chaps. 7 and 8 205
Bibliography 209
Index 221
x ContentsAcronyms
AGN Additive Gaussian noise
AMC Advanced motion controls
DAQ Data acquisition board
DC Direct current
DOF Degrees of freedom
FJR Flexible joint robot
IAE Integral of absolute error
IDA-PBC Interconnection and damping assignment-passivity based control
ISE Integral of squared error
IWP Inertial wheel pendulum
LQR Linear quadratic regulator
LS Least squares
MAV Mean absolute value
MIMO Multi-input–multi-output
NMPC Nonlinear model predictive control
PC Personal computer
PCI Peripheral component interconnect
PD Proportional derivative
PI Proportional integral
PID Proportional-integral-derivative
PWM Pulse-width modulation
RMS Root mean square
SISO Single-input–single-output
TORA Translational oscillator with rotational actuator
UAV Unmanned aerial vehicle
UUB Uniformly ultimately bounded
VTOL Vertical take-off and landing
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