在工程領域的應用上，動態系統中的干擾會對系統的輸出造成影響。而其中一個降低干擾對系統輸出影響的方法是建構一個估測器來估測干擾訊號，再使控制命令基於估測值去消除干擾訊號所造成的影響，一般的估測器是利用系統的逆系統來達成目的，然而此方法並不適用於線性非時變非極小相位系統。此類問題的主要難處在於非極小相位零點的存在，吾人是無法直接利用系統的逆轉來設計估測器的，因為這將會造成一個不穩定估測器。

此篇論文吾人針對線性非時變非極小相位系統提出一個新穎的方法來估測系統的未知輸入，吾人所提出之方法的核心概念為「求解一不穩定微分方程的有界解」。文中，吾人提出一個數學演算法來求得此解，並適用於連續時間系統模型以及離散時間系統模型。

In real-world applications, the output performance of a dynamical system is often affected by external disturbances. One way to reduce, or even eliminate, the influence of the disturbance is to construct a observer to estimate the disturbance signal, so that a control action based on the disturbance estimate can be taken to against its effect. In general, an input disturbance observer can be constructed based on the inverse of the plant dynamics, but this method is not applicable when the plant has non-minimum phase zeros. In this case, inverting the non-minimum phase zeros would result in unstable dynamics, and hence an unstable observer, which is unacceptable.

In this thesis we propose a novel approach for designing input disturbance observers for LTI non-minimum phase systems. The core concept of the method that we proposed lies in finding a bounded solution of an unstable differential equation. Based on this concept,
a mathematical algorithm is developed to "inverse" the effect of non-minimum phase zeros without incurring unbounded signals. The technique is then applied in building input disturbance observers for continuous-time and discrete-time LTI non-minimum phase systems. The effect of our approach is verified by several numerical examples and compared with the existing methodologies in the literature.

誌謝i
中文摘要ii
英文摘要iii
目錄 iv
圖目錄vi
表目錄viii
第一章 緒論1
1.1 簡介與文獻回顧1
1.2 研究動機、目的與貢獻4
1.3 論文架構5
第二章 求解不穩定常微分方程之有界解6
2.1 問題描述6
2.2 求解不穩定微分方程7
2.3 解的存在與唯一性11
第三章 基於UZ逆轉之未知輸入估測器架構 18
3.1 連續時間估測器架構18
3.2 改良之連續時間估測器架構21
3.3 即時估測演算法之細節31
3.3.1 結合頻率估測器之即時演算法31
3.3.2 UZ 逆轉之改善33
第四章 離散時間版本36
4.1 求解不穩定差分方程36
4.2 離散時間估測器架構40
4.3 改良之離散時間估測器架構43
第五章 數值模擬結果46
5.1 連續時間未知輸入估測器模擬46
5.2 連續時間改良之未知輸入估測器模擬56
5.3 離散時間未知輸入估測器模擬58
5.4 離散時間改良之未知輸入估測器模擬63
第六章 結論與未來展望 65
參考文獻 66

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