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研究生： 王詩婷
Shi-Ting Wang
論文名稱： 利用投影法做系統的強健性分析與設計
The robustness analysis and design of uncertain system:utilizing projection method
指導教授： 莊堯棠
Yau-Tarng Juang
口試委員:
學位類別： 碩士
Master
系所名稱： 資訊電機學院 - 電機工程學系
Department of Electrical Engineering
畢業學年度： 90
語文別： 英文
論文頁數： 54
中文關鍵詞： 投影法 、強健穩定 、控制器設計
外文關鍵詞： projection method, robust stability, cotroller design
相關次數： 點閱：14  下載：0 
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    • 在本論文中，主要是針對具參數不確定的系統，做一個有系統的分析研究。由於在實際的環境中，不管儀器再精密或是情況再理想，一定有不可避免的干擾或是參數變動的問題。所以，這些不確定變數的強健穩定，是一個良好系統所不可或缺的。
    擾動的來源主要是由於下述幾種原因：系統的非線性關係，為了簡單起見而簡化原來較複雜的系統所帶來的誤差問題、系統參數的變動、周遭客觀環境的改變、不可避免的資料誤差等等都是可能的擾動原因。
    本文在擾動系統穩定度分析中，主要採用李亞普諾夫(Lyapunov) 的穩定定理為中心基礎，提出投影法來改善先前文獻用線性矩陣不等式去解擾動系統穩定性分析的保守度，並把問題做延伸去分析將不確定系統極點指定在某一特定區域內的強健穩定性，最後利用投影法提出一有系統的設計程序，對擾動系統做迴授控制器設計，使我們能更確認系統的穩定度。
    本論文的研究主要就是利用投影法對上述的狀況做一較完整的分析與設計。我們期望能夠得到一個較佳的穩定準則及較精確的條件，並設計控制器增加系統的穩定度。

    To keep a system working stability and sability including realistic conditions has become a very important topic in the control fields.
    In this thesis, first we analyze the robustness stability of linear uncertain system. Then the stability issues can be extended to assign all eigenvalues of uncertain system lie in a prescribed region. We propose a simple scheme, projection method, to analyze the robustness stability of uncertain systems and pole assignment. And further derive a systematic design method to find a state feedback controller such that the perturbed closed-loop system is stable.

    CONTENTS CHAPTER 1 Introduction …………………………………………………1 1.1 Motivation …………………………………………………1 1.2 Literature survey …………………………………………………2 1.3 Organization of this thesis …………………………………………………2 CHAPTER 2 The projection scheme introduction ………………………………4 2.1 Introduction …………………………………………………4 2.2 The arising issues form LMI method …………………………………………4 2.3 The concept of the projection scheme ……………………………………6 2.4 The related projection operators ………………………………………7 2.5 Conclusions ………………………………13 CHAPTER 3 Robust stability analysis and pole assignment for uncertain systems ………14 3.1 Introduction …………………………………………………14 3.2 Stability robustness analysis …………………………………………………14 3.3 Robust pole assignment of linear uncertain system …………………………15 3.4 Robustness analysis algorithm …………………………………………………17 3.5 Examples …………………………………………………18 3.6 Conclusions …………………………………………………22 CHAPTER 4 Design of feedback controller for uncertain system ……………23 4.1 Introduction …………………………………………………23 4.2 Problem formulation ………………………………………23 4.3 The design algorithm ………………………………………27 4.4 Examples ……………………………………………28 4.5 Conclusions …………………………………………………35 CHAPTER 5 Conclusions …………………………………………………36 List of Figures Fig. 2.1 The pole assign Region ………………………………………… 5 Fig. 2.2 The conservatism of LMI solver ………………………………………… 6 Fig. 3.1 Pole assignment in the plane …………………………………………16 Fig. 3.2 The pole assignment in the desire region …………………………… 20 Fig. 3.3 The pole assignment in the region ………………………………………… 22 Fig. 4.1 The pole assignment with decay rate ………………………………………… 25 Fig. 4.2 The poles of closed-loop are lied in the region …………………………29 Fig. 4.3 The poles of closed-loop are lied in left half plane …………………… 31 Fig. 4.4 The pole assignment with decay rate ……………………………………………33 Fig. 4.5 The pole assignment with decay rate ……………………………………………35

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