本文基於李亞普諾夫之穩定理論，針對具有多輸入多輸出的數位系統，來設計一個強韌數位參考模型的可變結構狀態追蹤控制器。此可變結構控制器將包含三部份。第一部份為回授控制器，目的在計算李亞普諾夫方程式微分時消除可量測之回授信號。第二部份是切換控制器，用來決定李亞普諾夫方程式遞減的速度。第三部份是適應控制器，用於克服干擾。這三部份所合成的強韌可變結構控制器能夠使系統追蹤誤差軌跡逼近一有效區間內。由於提出的控制器中使用適應機制，因此不需事先知道干擾上界，就能保證整個控制系統的穩定度。又此干擾上界並非常數而是與狀態變數相關。最後，用一數值的例子以及一實際的例子來證明本文結果的可行性。

Based on the Lyapunov stability theorem, a methodology of designing robust discrete-time model reference variable structure state tracking controller is proposed in this thesis for a class of multi-input multi-output (MIMO) discrete-time systems. This variable structure controller is composed of three types of controllers. The first one is the feedback control law, which can eliminate the nominal term in the derivative of a Lyapunov function. The second one is the switching control law, which can determine the decreasing rate of the Lyapunov function. The third one is the adaptive control law, which is used to overcome the perturbations. The resultant robust variable structure controllers are capable of driving all the trajectories of tracking errors toward a small bounded region. The information of upper bound of the perturbation, which is not a constant and is dependent on the norm of state variable, is not required beforehand due to some adaptive mechanisms are embedded in the proposed control scheme, and the stability of the overall controlled system is guaranteed. A numerical example and a practical example are given to demonstrate the feasibility of the proposed control scheme.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . iv
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . 3
Chapter 2 Design of Robust Discrete-Time Tracking Controllers 4
2.1 System Descriptions and Assumptions . . . . . . . . . . . . . . 4
2.2 Design of Switching Surface . . . . . . . . . . . . . . . . . . . 6
2.3 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Analysis of System’s Stability . . . . . . . . . . . . . . . . . . 9
2.5 Estimation of Perturbation . . . . . . . . . . . . . . . . . . . . 23
Chapter 3 Example and Simulation Results 25
3.1 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Practical Example . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 43
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 44

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