本文針對具有匹配及非匹配擾動之多輸入非線性系統，提出一種適應性超扭曲控制架構，用以解決系統狀態校準之問題。首先設計順滑平面，接著再設計相對應的超扭曲控制器。藉由引入適應機制及擾動估測器的架構，進而不需要事先預知擾動及擾動估測誤差的上界，同時能避免施加過多的控制增益。在此控制架構下確實能使狀態在有限時間內到達順滑平面並停留在平衡點上。最後，本論文提供一個數值及一個實際範例來驗證所提出的控制策略其可行性。

關鍵詞: 超扭曲演算法，順滑模態控制，非匹配擾動，有限時間收斂，適應控制。

In this thesis a design methodology of adaptive super twisting control is proposed for a class of multi-input nonlinear systems with matched and mismatched perturbations to solve state regulation problems. The sliding surface is firstly designed, and then the super twisting controller is designed accordingly. An adaptive and perturbation estimation mechanisms are also embedded in the proposed control scheme, so that there is no need to know the upper bounds of perturbations as well as perturbation estimation error in advance. Applying excessive control input energy to systems is also avoided due to utilization of perturbation estimator. The proposed control strategy can indeed drive the states into the sliding surface first, then into the equilibrium point and stay thereafter within a finite time. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control strategy.

Keywords: super twisting algorithm, sliding mode control, mismatched perturbation, finite time convergence, adaptive control.

論文審定書 ……………………………………………………………………… i
誌謝 …………………………………………………………………………....... ii
中文摘要 ………………………………………………………………………… iii
Abstract …………………………………………………………………………. iv
List of Figures …………………………………………………………............ vii
List of Notations ………………………………………………………….......... ix
Chapter 1 Introduction 1
1.1 Motivation …………………………………………………………………… 1
1.2 Brief Sketch of the Contents ……………………………………………… 3
Chapter 2 Introduction of Super-Twisting Algorithm 4
2.1 Introduction ………………………………………………………………….. 4
2.2 Super-Twisting Algorithm …………………………………………………... 5
2.3 Analysis of Super-Twisting Algorithm Based on Lyapunov Function …. 9
Chapter 3 Design of Super-Twisting Controllers 16
3.1 System Descriptions and Problem Formulations …………………… 16
3.2 Design of Sliding Surface …………………………………………………. 17
3.3 Design of Controllers ……………………………………………………… 21
3.4 Stability Analysis ……………………………………………………......... 23
Chapter 4 Computer Simulation and Practical Application 29
4.1 Numerical Example ……………………………………………………….. 29
4.2 Practical Application …………………………………………………….... 31
Chapter 5 Conclusions 41
Bibliography 42
Appendix 49
Appendix A 49
Appendix B 50
Appendix C 50

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