摘 要

本論文之目的，主要針對不同類型之具有時變時間延遲因素的受擾系統，進行其穩定控制與參考模式追蹤控制問題的研究與設計。文中將以李阿普諾夫穩定性理論為基礎，結合著順滑模式控制技術與適應控制法則，設計出一種簡易但具有強韌特性的可變結構控制器，以促使受擾系統得以達成穩定控制的目的。其中所採用的適應控制法則將用來估測受控系統所受有的未知之擾動量的大小，以摒除在使用傳統可變結構控制器時必須預知擾動量大小的限制，並利用可變結構控制器與適應控制法則的效能，以促使整個受控系統具有更強韌的穩定特性。在受控系統被導引進入順滑平面之後，該系統將具有預先所設計好的響應特性，且該響應與時間延遲項無關。此外，控制設計者一般所要求的較高的控制精準度也可經由調整控制器的控制參數來達成。最後對於文中每一類型系統所設計的控制器，將分別以一個電腦模擬的數值範例，來說明其應用上的可行性。

Abstract

In this dissertation, four variable structure controllers are proposed for four different class of systems subjected to uncertainties and time varying delays respectively. In most cases, the variable structure control is incorporated with an adaptive law to drive the tracking error between the desired model and the controlled plant to zero. By using the Lyapunov stability theorem, the adaptive law is utilized for adapting the unknown upper bounds of the lumped perturbations so that the objective of asymptotical stability is achieved, and the variable structure control scheme is used for enhancing the robustness of stability of the controlled systems. Once the system enters the sliding region, the dynamics of controlled systems are insensitive to matching perturbations. It also shows that the proposed methodologies ensure the property of the globally uniformly ultimate boundness for the overall controlled system. Finally, four numerical examples are given for demonstrating the feasibility of the proposed control schemes.

Contents

摘要 i

Abstract ii

List of Figures v

List of Notations viii

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief sketch of the contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Controller Design for Perturbed Time-Varying Delay Systems
6
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 System descriptions and problem formulations . . . . . . . . . . . . . . . . 7
2.3 Analysis of the nominal system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Switching hyperplane design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.5 Adaptive variable structure control design . . . . . . . . . . . . . . . . . . 11
2.6 Simulation example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Controller Design for Time-Delay Systems with Input Nonlinearities 22
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 System descriptions and problem formulations . . . . . . . . . . . . . . . 23
3.3 Switching hyperplane design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4 Adaptive variable structure control design . . . . . . . . . . . . . . . . . . 27
3.5 Simulation example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4 Controller Design for Large-Scale Systems 46
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 System descriptions and problem formulations . . . . . . . . . . . . . . . 46
4.3 Design of decentralized switching hyperplane . . . . . . . . . . . . . . . 48
4.4 Decentralized variable structure control design . . . . . . . . . . . . . . 49
4.5 Analysis of robust stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 A modified control strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.7 An illustrate example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5 Adaptive Controller Design for Large-Scale Systems 59
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 System descriptions and problem formulations . . . . . . . . . . . . . . . 59
5.3 Decentralized switching hyperplane design . . . . . . . . . . . . . . . . . 62
5.4 Adaptive variable structure control design . . . . . . . . . . . . . . . . . . 63
5.5 Simulation example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6 Summary 79
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

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