本論文主要是將奇異擾動(singular perturbation)理論應用到控制器的設計。首先，將奇異擾動應用到機械系統的輸出回授(output feedback)類似比例微分(proportional-derivative, PD)控制器的設計，只需測量位移量即可進行速度控制，控制器演算法為低階動態輸出回授控制的法則，簡單而且容易實現。另外，為因應含有不確定項及未知干擾的系統，提出以Lyapunov定理分析經由代數Riccati與矩陣不等式求解的回授系統穩定性控制法則。本論文最後針對非匹配式未定參數(mismatched parameter uncertainties)及匹配式非線性擾動(matched nonlinear perturbations)的線性MIMO系統提出干擾估測器(disturbance observer)為主的控制演算法，並應用高增益積分估測器做輸出回授的控制器，使輸入干擾快速收歛。最後以數值範例來驗證可行性。

The thesis is mainly to design the controller by applying the theory of singular perturbation. First of all, using the singular perturbation technique to design the output feedback controller of mechanic systems, it is similar to the design of a proportional-derivative control law. We can precede the speed control by only measuring the displacement. The controller algorithm is the rule of low-order dynamic output feedback control. It is simple and easily accomplished. Besides, when the mechanical system contains uncertain items, this thesis presents robust stability of the closed-loop system. It also offers the analysis of Lyapunov theory by solving a Riccati algebra equation and a linear matrix inequality. Furthermore, for the mismatched parameter uncertainties and matched nonlinear perturbations in a linear MIMO system, the thesis proposes a disturbance-observer based controller in which the input disturbance can be effectively estimated by using a high-gain integration observer. Finally, it is verified the practicability by numerical examples.

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