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研究生： 陳爾君
Erh-Chung Chen
論文名稱： 強健模糊觀測狀態回饋控制-Circle與Popov定理
Robust Fuzzy Observer-based control-Circle and Popov Theorem
指導教授： 羅吉昌
Ji-Chang Lo
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
畢業學年度： 92
語文別： 中文
論文頁數： 90
中文關鍵詞： 強健控制 、Popov定理 、Circle定理 、平行分散補償控制器 、雙線性矩陣不等式 、T-S模糊系統架構 、觀測狀態回饋控制器 、動態輸出回饋控制器 、線性矩陣不等式
外文關鍵詞： Robust control, Lure-type Lyapunov function, Parallel distributed compensator(PDC), Popov theorem, Circle theorem, Bilinear matrix inequality(BMI), Linear matrix inequality(LMI), T-S Fuzzy Model, Observer-based controller, Dynamic output feedback controller
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    • 本篇論文主要分成三大部份來討論:第一部份為廣義控制器的定義及系統數學架構的推導;第二部份引用Circle和Popov兩大定理推導出系統穩定的充份條件;第三部份則是利用推導出的定理來做電腦模擬,設計適合的控制器。在控制器方面,主要定位在觀測狀態回饋控制器的設計,動態輸出回饋控制器的推導方式也有介紹。
    在第一部份中,定義出一個廣義控制器,利用廣義控制器推導而得到的廣義穩定條件,可以退化為觀測狀態回饋控制閉路系統穩定條件以及動態輸出回饋控制閉路系統穩定條件。這樣的廣義控制器方便我們設計觀測狀態回饋控制器以及動態輸出回饋控制器,在本論文中則是提出觀測狀態回饋控制器的設計方法與電腦模擬。
    第二部份裡,引用非線性系統控制領域中的Circle和Popov定理,配合第一部份中的系統架構,以及使用Lyapunov定理,推導出連續和離散系統的穩定條件。因為觀測狀態回饋控制器本身架構的關係,所推導出的穩定條件會形成非線性矩陣不等式型式,產生不能直接用LMIs求解的問題。但本論文引用兩階段求解的方法來解決這問題,間接使用LMIs來求解,完成觀測狀態回饋控制器的設計。
    第三部份裡,用了三個例子來做電腦模擬,分別是非線性系統的控制、倒單擺的平衡、倒車入庫控制,探討本文理論分析對於非線性系統的控制情形。

    No

    第一章 緒論 1 {1.1}文獻回顧 1 {1.2}研究動機 2 {1.3}論文架構 3 {1.4}符號標記 4 第二章 控制系統數學模型 5 {2.1}系統的數學模型 5 {2.2}控制器的數學模型 6 {2.2.1}廣義控制器 7 {2.2.2}用廣義控制器表達觀測狀態回饋控制器 8 {2.2.3}用廣義控制器表達動態輸出回饋控制器 8 {2.3}閉迴路系統 9 {2.3.1}廣義閉迴路系統 9 {2.3.2}觀測狀態回饋閉迴路系統 10 {2.3.3}動態輸出回饋閉迴路系統 11 第三章 預備定理與非線性函數之限制 13 {3.1}預備定理 13 {3.1.1}預備定理1(蕭氏轉換) 13 {3.1.2}預備定理2(全等轉換) 14 {3.2}非線性函數的限制與特定型式 14 第四章 連續系統Circle定理之應用 16 {4.1}系統定理推導 16 {4.2}穩定檢測條件 18 {4.3}電腦模擬 24 {4.3.1}系統架構 24 {4.3.2}求解 27 第五章 連續系統Popov定理之應用 35 {5.1}系統定理推導 35 {5.2}穩定檢測條件 36 {5.3}電腦模擬 41 {5.3.1}系統架構 42 {5.3.2}求解 43 第六章 離散系統Circle定理之應用 50 {6.1}系統定理推導 50 {6.2}穩定檢測條件 51 {6.3}電腦模擬 55 {6.3.1}系統架構 55 {6.3.2}求解 56 第七章 離散系統Popov定理之應用 66 {7.1}系統定理推導 66 {7.2}穩定檢測條件 69 {7.3}電腦模擬 74 {7.3.1}系統架構 74 {7.3.2}求解 75 第八章 結論與未來方向 84 {8.1}總結 84 {8.2}未來研究方向 85 參考文獻 86

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