本論文針對具有匹配擾動之多輸入多輸出非線性系統設計一個離散型適應性順滑模態控制器以解決追蹤之問題。大致上，控制器設計過程主要分成兩個部分。第一部分為設計離散型順滑面函數，使得受控軌跡能到達至順滑面附近。第二部分則引入適應機制來設計控制器。其中，系統中擾動的上界是未知的，且與時間與狀態有關，該假設代表控制器能夠容忍更多擾動之形式。由於擾動估測器的建構，使得擾動估測誤差的上界資訊不需事先預知。結果也顯示出順滑變數之軌跡將收斂至一小區間內，且可藉由調整控制器參數來調整追蹤精準度。最後，分別提供一個數值範例與一個實例範例以驗證所提出控制器設計的可行性。
關鍵詞: 順滑模態控制，離散系統，擾動估測器，適應控制，匹配擾動。

In this thesis a design methodology of adaptive discrete-time sliding mode controllers for a class of MIMO nonlinear systems with matched perturbations is proposed to solve tracking problems. Basically, the designing process of controllers contains two parts. The first part is to design the discrete sliding surface function, so that the controlled trajectory can reach a band of sliding surface. The second part is designing the controllers and adaptive mechanisms embedded. The unknown upper bounds of perturbations encountered in the systems depend on both states and time, this assumption allows the proposed control scheme tolerating more kinds of perturbations. Perturbation estimators are also constructed so that there is no need to know the upper bound of perturbation estimation error beforehand. It is shown that the trajectories of sliding variables will converge to a small bounded region, and the tracking accuracy can be adjusted through the design parameters. A numerical example and a practical example are given to demonstrate the feasibility of the proposed control scheme.
Keywords: sliding mode control, discrete-time system, perturbation estimation, adaptive control, matched perturbations

論文審定書 ……………………………………………………………………… i
誌謝 ………………………………………………………………………… ii
中文摘要 ………………………………………………………………………… iii
Abstract ………………………………………………………………………… iv
List of Figures ………………………………………………………… vii
Chapter 1 Introduction 1
1.1 Motivation …………………………………………………………………… 1
1.2 Brief Sketch of the Contents ……………………………………………… 3
Chapter 2 System Structure and Controller Design 4
2.1 System Descriptions and Problem Formulations…………………………….. 4
2.2 Design of the Sliding Surface………………………………………………… 6
2.3 Design of the Discrete-time Controller and Stability Analysis ...……………. 9
2.4 Estimation of Perturbation………………………………………………… 20
Chapter 3 Simulations and Examples 22
3.1 Numerical Example ......…………………………………………………….. 22
3.2 Practical Example ….…………………………………………………………27
Chapter 4 Conclusions 54
Bibliography 55

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