검색 상세

부족구동 역학 시스템의 비선형 적응제어

Nonlinear Adaptive Control of a Class of Underactuated Mechanical Systems

초록/요약

This dissertation is devoted to a nonlinear adaptive stabilization and tracking control of a class of underactuated mechanical systems. Underactuated systems are mechanical control systems with fewer controls than the number of configuration variables. Control of underactuated systems has been one of the active research fields due to their broad range of applications in robotics, aerospace vehicles, and marine vehicle. For example, underactuated systems in real-life include flexible-link robots, mobile robots, walking robots, robots on mobile platforms, cars, locomotive systems, snake-type and swimming robots, acrobatic robots, aircraft, spacecraft, helicopters, satellites, surface vessels, and underwater vehicles. Recent survey shows that the control of general underactuated mechanical systems is still one of the major open problems. The objective of this dissertation is to develop several methods for the configuration stabilization and trajectory tracking of a class of underacuated mechanical systems. The configuration stabilization is addressed for non-minimum phase underactuated systems (e.g., inverted pendulum) having unstable zero dynamics. In this dissertation, the scope of configuration stabilization is focused on the global or semi-global stabilization as well as orbital stabilization (i.e., stabilization of limit cycle). On the other hand, the trajectory tracking is considered for both minimum and non-minimum phase underactuated systems. For minimum phase underactuated systems, decoupling control based on collocated partial feedback linearization is adopted, which includes additive variable structure control law (VSC) for the asymptotical stabilization of unactuated subsystems. On the other hand, a novel partial feedback linearization (so called ”Lagrangian preserving partial feedback linearization”) is developed and utilized for the decoupling control of non-minimum phase underacuated systems. In addition, an adaptive schem based on fuzzy systems is proposed, to cope with systems uncertainties including system parameter uncertainties, external disturbances, and actuator nonlinarities for more practical issues. The main results of this dissertation are summaried as follows. First, semi-global and orbital stabilizations are presented by using backstepping technique, sliding mode control (SMC), and a novel partial feedback linearization. In backstepping based approach, we define an error state that utilizes momentum conjugate to unactuated variables which make it easy to apply standard backstepping approach. In stability analysis for the whole systesm, a condition that ensures semi-global and almost global domain of attraction is provided. In SMC based approach, we firstly decompose an underacuated mechanical system into actuated and unactuated subsystems, followed by a design of individual control law for each subsystem. Semi-global stabilizations of equilibrium and relative equilibrium point, as well as orbital stabilization around equilibrium are demonstrated through an illustrative numerical example. In a novel partial feedback linearization based approach, we define a weakly (or marginally) minimum phase output of a non-minimum phase underactuated mechanical system. For this new output, partially feedback linearizing control is designed, which renders the integral of closed-loop zero dynamics be an energy-like function having Lagrangian form. This energy-like function has its maximum value at equilibrium point and differs from a Lyapunov function in the sense that it is not positive or negative definite. Then, two methods for the asymptotic stabilization of equilibrium are propsed; the first method utilizes a nonlinear dissipation control in such a way that the energy-like function converges to its maximum value (energy-maximizing control); second method considers a modified version of the energy-like function as a Lyapunov fucntion. Second, trajectory tracking of underactuated mechanical systems is based on the decoupling control and partial feedback linearization. For minimum pahse systems (e.g., overhead cranes), we adopt collocated partial feedback linearization and employ a nonlinear dissipation control law to guarantee the asymptotic stability of unactuated subsystem. To demonstrate the proposed method, we perform numerical simulations and experiments for an overhead crane without hoisting motion. For non-minimum phase systems (e.g., inverted pendulum), we utilize the Lagrangian preserving partial feedback linearization and design trajectory tracking control law for the redefined output. By introducing a nonlinear dissipation control, asymptotic and bounded trajectory trakcing is accomplished. Finally, fuzzy based adaptive scheme to deal with systems uncertainties is proposed, where fuzzy system is utilized to estimate two lumped uncertainties for each actuated and unactuated subsystem. In this scheme, we treat uncertainties as a lumped one which is coupled with each other. Thus, we can estimate both uncertainties for actuated subsystem and unactuated subsystem with one uncertainty observer for the unactuated subsystem.

more

목차

Contents

Acknowledgments ix
Abstract 1
Contents 5
List of Figures 11
List of Tables 14
Chapter 1 Introduction 15
1.1 Motivation 15
1.2 Background 16
1.3 Objectives 21
1.4 Outline of the dissertation 23
Chapter 2 Preliminaries 25
2.1 Comparison Functions 25
2.2 Lyapunov Stability 26
2.3 Barbalat’s Lemma 30
2.4 Input-to-State Stability (ISS) 30
2.5 Exponential Input-to-State Stability (Exp-ISS) 32
2.6 Small-Gain Theorem for ISS Systems 33
Chapter 3 Mechanical Control Systems 35
3.1 Introduction 35
3.2 Simple Lagrangian Systems 35
3.3 Symmetry in Mechanics 39
3.4 Stability of Hamiltonian Systems 40
3.5 Homoclinic Orbit 41
3.6 Fully-actuated Mechanical Systems 42
3.7 Underactuated Mechanical Systems 43
3.8 Feedback Linearization 45
3.8.1 Collocated Partial Feedback Linearization [Spong, 1996] 45
3.8.2 Noncollocated Partial Feedback Linearization [Olfati-Saber, 2000] 46
3.8.3 “Lagrangian Preserving” Partial Feedback Linearization 47
Chapter 4 Backstepping based Stabilization of a Class of Underacuated Mechanical Systems 49
4.1 Introduction 49
4.2 Problem Formulation 50
4.3 Stabilization of Relative Equilibrium 52
4.3.1 Dynamics of Inverted Pendulum 52
4.3.2 Definition of Error Variable 54
4.3.3 Control Design by Backstepping 54
4.4 Stabilization of Equilibrium 58
4.4.1 Definition of Error Variable 58
4.4.2 Control Design by Backstepping 59
4.5 Numerical Simulations 64
4.5.1 Stabilization of Relative Equilibrium 64
4.5.2 Stabilization of Equilibrium 69
4.5.3 Swing-up Control 74
4.6 Conclusion 76
Chapter 5 SMC based Stabilization of a Class of Underactuated Mechanical Systems 77
5.1 Introduction 77
5.2 System Description 79
5.3 Main Results 81
5.3.1 Dynamics of Inverted Pendulum 81
5.3.2 Individual Control Design 82
5.3.3 Coupling Control Design 84
5.3.4 Singularity-Free Coupling Control 87
5.3.5 FSMC based Coupling Control 89
5.4 Illustrative Numerical Simulations 93
5.4.1 Local Stabilization of Equilibrium 94
5.4.2 Semi-global Stabilization of Equilibrium 96
5.4.3 Semi-global Orbital Stabilization 98
5.4.4 Swing-up control 100
5.5 Conclusion 101
Chapter 6 Trajectory Tracking of 2-DOF Mimimum Phase Underactuated Mechanical Systems 103
6.1 Introduction 103
6.2 Overview and Problem Description 107
6.2.1 Fuzzy Logic System 107
6.2.2 Overhead Crane Dynamics 108
6.2.3 Adaptive Anti-Sway Trajectory Tracking Control Problem 112
6.3 Trajectory Tracking Control and Anti-Sway Control 114
6.3.1 Trajectory Tracking Control 114
6.3.2 FNC for Anti-Sway Control 115
6.4 Uncertainty Estimation and Adaptive Scheme 120
6.4.1 Coupled Uncertainty 120
6.4.2 FUO 121
6.4.3 AFNC 124
6.5 Simulations and Experiments 127
6.5.1 Numerical Simulations 127
6.5.2 Experiments with Miniature Overhead Crane 132
6.6 Conclusion 135
Chapter 7 Trajectory Tracking of 3-DOF Minimum Phase Underactuated Mechanical Systems 137
7.1 Introduction 137
7.2 Overview and Problem Description 139
7.2.1 Overhead Crane Dynamics 139
7.2.2 Adaptive Anti-Sway Trajectory Tracking Control Problem 142
7.3 Trajectory Tracking Control and Anti-Sway Control 143
7.3.1 Trajectory Tracking by Feedback Linearization 143
7.3.2 Stability of Trajectory Tracking Error Dynamics 144
7.3.3 FNC for Anti-Sway Control 146
7.4 Uncertainty Estimation and Adaptive Scheme 149
7.4.1 Coupled Uncertainty 149
7.4.2 FUO 150
7.4.3 AFNC 152
7.5 Numerical Simulations 156
Chapter 8 Stabilization and Trajectory Tracking of Nonminimum Phase Underactuated Mechnical Systems 161
8.1 Introduction 161
8.2 Orbital Stabilization by Lagrangian Preserving PFL 165
8.2.1 Lagrangian Preserving PFL 165
8.2.2 Orbital Stabilization 166
8.3 Asymptotic Stabilization of Equilibrium: Method 1 173
8.4 Asymptotic Stabilization of Equilibrium: Method 2 176
8.5 Trajectory Tracking: Method 1 180
8.6 Trajectory Tracking: Method 2 183
8.7 Adaptive Trajectory Tracking 186
8.7.1 Adaptive Trajectory Tracking: Method 1 186
8.7.2 Adaptive Trajectory Tracking: Method 2 189
8.8 Simulations 190
8.8.1 Oribital Stabilization 191
8.8.2 Asymptotical Stabilization by Method 1 194
8.8.3 Asymptotical Stabilization by Method 2 197
8.8.4 Swing-Up and Stabilization by Method 1 200
8.8.5 Swing-Up and Stabilization by Method 2 202
8.8.6 Trajecotry Tracking by Method 1 203
8.8.7 Trajecotry Tracking by Method 2 205
8.8.8 Adaptive Trajecotry Tracking 207
Chapter 9 Summary and Future Directions 213
9.1 Summary 213
9.2 Future Directions 216
Appendix A 223
Bibliography 225
Abstract in Korean 237

more
반출 Meta View 목록