強健穩定控制器設計是控制領域的重要問題之一，該問題主要討論在有模式誤差(例如:元件之參數擾動或未建模之動態成分)或外界干擾的情形下，如何設計控制器使系統保持穩定。

    過去參數擾動情形的研究，大都是利用(D,G)-K疊代交替的計算方法來設計控制器。在這架構中，控制器與乘數運算子之求解是固定其中一個求解另一個，然後交替進行。為了提高系統對擾動的容忍範圍，常需增加它們的階數，因此所得到的控制器階數經常高，增加了硬體實現的困難度，這是(D,G)-K疊代交替設計的一大缺點。近年來，有其他的學者嘗試以雙線性矩陣不等式(bilinear matrix inequality，BMI)的方式來設計控制器，但仍未脫離控制器與乘數運算各自求解的窠臼。

    有別於以往的(D,G)-K疊代交替設計方法，本論文提出一套新型BMI架構的設計方法，不僅能同時求解控制器與乘數運算子，而且在交替式求解的過程中控制器與乘數運算子的階數都不會增加。從模擬結果中得知我們所提出的μ合成方法的確比過去的方法有更好的效果。

The design of robustly stabilizing controllers is an important issue in the control area, which focuses on synthesizing a controller to keep the closed-loop system stable in the face of possibly various types of modeling errors (such as mismatched system parameters or un-modeled dynamics) and external disturbances.

    For the real parametric uncertainty cases, the so called (D,G)-K iteration controller synthesis method or named real μ synthesis, had been developed. This method proceeds by designing an optimal   controller K with the (D,G)-scalings fixed and computing the (D,G)-scalings with K fixed, and then continues iteratively. In order to enlarge the stability margin of the system, the orders of the controller and the scalings/multipliers are often increased, which makes the hardware implementation of the controller difficult. This is a serious drawback of this method which has its origin at the separate design framework. Recently, some researchers proposed a BMI approach to the robust controller design problem. Nevertheless, the separate design framework of the controller and the multiplier remains. In this thesis, we present a novel robust controller design method in BMI formulation. Quite different from the conventional (D,G)-K iteration method, the proposed method can perform simultaneous search for the controller and the multiplier. In addition, the orders of the controllers and the multipliers are kept fixed during the whole design procedure. Simulation results demonstrate that our method indeed performs better than many other methods.

中文摘要 I
英文摘要 II
頁目錄 IV
圖目錄 VI
表目錄 VIII

頁目錄 :
第一章 緒論 1
   1.1 文獻回顧與研究動機 1
   1.2 論文架構 4
第二章 背景知識與問題敘述 5
   2.1 前言 5
   2.2 重要定理 7
   2.3 問題敘述與轉換 12
     2.3.1 問題敘述 12
     2.3.2 問題轉換 13
     2.3.3 強健穩定條件 17
第三章 現有參數式μ合成方法 19
   3.1 前言 19
   3.2 D-K疊代交替法及其延伸 22
   3.3 BMI交替計算方法 33
第四章 新型參數式μ合成方法 37
   4.1 前言 37
   4.2 強健穩定條件 38
   4.3 雙線性矩陣不等式條件 44
   4.4 新型參數式μ合成演算法 47
第五章 數值模擬 51
   5.1 前言 51
   5.2 數值例子 52
第六章 結論與未來研究方向 71
參考文獻 73

圖目錄 :
圖2.1 M-delta 迴路 7
圖2.2 系統 L_t 8
圖2.3 乘數運算子伴隨系統 9
圖2.4 delta-P-K 架構 12
圖2.5 M-delta 迴路 13
圖2.6 架構轉換(一) 14
圖2.7 架構轉換(二) 14
圖2.8 架構轉換(三) 15
圖2.9 架構轉換(四) 15
圖2.10 架構轉換(五) 16
圖2.11 被動架構 16
圖2.12 乘數運算子伴隨系統 18
圖3.1 delta-P-K 架構 20
圖3.2 D-K疊代交替(一) 22
圖3.3 D-K疊代交替(二) 23
圖3.4 delta_t-Mr_t 系統 26
圖3.5 Pw_t 示意圖 29
圖4.1 (a) delta-P-K 架構 ; (b) 被動架構 37
圖4.2 被動架構偕同乘數運算子 38
圖4.3 條件(iii)示意圖 39
圖4.4 修正模型(一) 40
圖4.5 訊號流程圖 40
圖4.6 修正模型(二) 41
圖4.7 修正模型(三) 42
圖4.8 整體設計流程 47
圖5.1 參數式擾動之控制系統架構圖 51
圖5.2 例一：具參數式擾動之控制系統架構圖 52
圖5.3 delta-P-K 架構 53
圖5.4 例二：參數式擾動之控制系統架構圖 62
圖5.5 delta-P-K 架構 62

表目錄 :
表5.1 穩定邊界比較 60
表5.2 模擬結果比較表 60
表5.3 穩定邊界比較 69 
表5.4 模擬結果比較表 69

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