多數真實系統普遍為非線性系統，然而在非線性系統下，一般的觀測器設計上較為複雜，因此本論文使用了順滑模態觀測器進行設計。有別於一般的觀測器，順滑模態觀測器在非線性系統下設計較為容易。順滑模態控制理論在順滑模態觀測器上充分地發揮了其優點。基於其許多優異的特性，順滑模態理論早在過去幾十年之間在強健控制領域上吸引了廣泛的關注，順滑模態理論所帶來的這些良好特性是建立在理想順滑模態上，其良好的特性包含:設計準則簡易、易於實現於非線性系統、對於匹配不確定性具有強健性，同時保障閉迴路系統的穩定性。然而，理想順滑模態是藉由一連串不連續的控制律所達成的，此種不連續控制訊號對於控制實現上具有一定難度；相反的，對於順滑模態觀測器來說，卻是得以順利實現的。除了系統模型架構外，為了進一步將數學問題與真實情況結合，本文也考慮了系統本身的不確定性，因此本論文是基於非線性系統存在非匹配不確定性下之順滑模態觀測器設計。對於高階非線性系統，藉由控制系統等效轉換技巧，可以更加容易掌握系統收斂特性。同時，為了提高增益矩陣設計的自由度與彈性，本文在觀測器設計過程中，引入了多目標線性矩陣不等式(Multi-Objective Linear Matrix Inequality, LMI)的數學方法，以達成減少非匹配不確定性對於系統的影響，並降低增益矩陣且維持系統的強健性。本論文最終目標為將所提出之觀測器設計方法應用至多層板金屬加熱系統的溫度估測，包含系統物理模型推導、系統參數鑑別以及觀測器設計，藉由所提出之方法，完成高強健性溫度狀態觀測器設計，並與真實系統的實驗數據進行交叉比對驗證，以確認達到系統即時監控溫度的目的。

This thesis is based on a sliding mode observer (SMO) design for nonlinear systems subjected to mismatched uncertainty. Most real systems are, in general, nonlinear systems but the general observer design is more complicated with the systems. Therefore, this thesis uses a SMO design. Being different from general observers, SMO are easily designed under nonlinear systems. Besides system model structure, for the integration of mathematical problems into real practices, this thesis also takes system uncertainty into consideration. In fact, under the nonlinear systems with uncertainties, the sliding mode control law fully exerts its advantages. With these advantageous characteristics, the sliding mode theory has been paid much attention in the field of robust control for decades.
The proposed excellent characteristics based on the sliding mode theory are due to its ideal mode which occurs out of a series of discontinuous control laws. The characteristics of this SMO includes its simple design criteria, an easy implementation in nonlinear systems, and the robustness to matched uncertainties, and it also guarantees the stability of closed loop systems. For high order nonlinear systems, it is easier to grasp the system convergence characteristics through control system equivalent conversion technique. In the observer design process, the mathematical method of multi-objective linear matrix inequality (LMI) is also used in this paper to reduce the impact of mismatched uncertainty on the system and the gain matrix, and maintain the robustness of the system.

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