強健控制器設計是控制理論中一個重要的研究領域，主要討論系統中具有不確定的參數(或動態模式誤差)或外部環境干擾的情況下，如何設計控制器使此擾動系統保持穩定，而且有良好的強健性能。μ合成理論是解決這方面問題的利器。然而，其會導致高階數的控制器，增添硬體實現之困難。而且當雜訊來自指定頻段，有時效果不佳。因此，本論文將聚焦於閉回路系統特定頻段的強健H∞性能，提出固定階數的控制器設計方法。
    本論文研究連續時間、線性、非時變、含不確定參數的擾動系統的強健性能控制問題，其中性能意指特定頻段的H∞性能。本論文結合Iwasaki等人提出的廣義KYP (Generalized Kalman- Yakubovich-Popov, GKYP) 引理與μ理論，提出兩種類型的強健控制器設計方法，使得閉迴路系統具有適度的穩定邊界，並且儘量最小化擾動系統在指定頻段的 範數。我們發現所謂的尺度因子扮演著如同權重函數之角色，可用來居中協調穩定邊界與指定頻段的強健H∞性能。不同於現存μ合成方法，在我們所研擬的新型μ合成方法中，控制器與廣義乘數運算子的階數在求解過程皆可維持固定。而且，相關條件之求解等同求解線性矩陣不等式(Linear Matrix Inequalities，LMIs)，其可由現存軟體有效解得。

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 and possess a robust performance in the presence of real parametric uncertainty (or un-modeled dynamics). μ synthesis is a powerful tool to solve this problem. However, the method would lead to high-order controllers, which increases the implementation complexity in hardware. In addition, the resulting performance may not be satisfactory, for example when the method is applied to a disturbance attenuation problem in which the disturbances were known coming from a particular finite frequency range. Therefore, this thesis aims at providing a fixed-order controller design that improves the robust finite frequency H∞  performance of the perturbed system. 
Specifically, this thesis investigates the robust performance control problem for continuous-time linear time-invariant systems with uncertain real parameters. We combine the GKYP Lemma and μ theory to derive two methods, each of which renders the closed-loop system a desired stable margin and in addition, minimizes the robust H∞  norm in a finite frequency range. We found that the so-called scaling factor acts like a weighting function. It tradeoffs between stability margin and robust finite frequency H∞  performance. In contrast with the existing μ synthesis methods, the new method has the feature that the order of the controllers and that of the generalized multipliers were kept fixed during the process of design. On the other hand, the relevant solvability conditions are all in terms of linear matrix inequalities (LMIs) which can be efficiently solved by computer software.

中文摘要 I
英文摘要 II
目錄 III
圖目錄 V
表目錄 VI
第一章	緒論 1
1.1	文獻回顧與研究動機 1
1.2	論文架構 3
第二章	背景知識與問題敘述 4
2.1	問題敘述 7 
2.2     重要引理 12
第三章	基於多目標控制方法之μ合成定階控制器設計 15
3.1	前言 15
3.2	控制器與廣義乘數運算子設計條件 16
3.3	指定頻段μ合成定階控制器設計:方法一 18
3.4	指定頻段μ合成定階控制器設計:方法二 34
第四章	基於尤拉參數式之μ合成降階控制器設計 35
4.1	前言 35
4.2	指定頻段μ合成降階控制器設計:方法三 36
4.3	指定頻段μ合成降階控制器設計:方法四 43
第五章	數值模擬 44
第六章	結論與未來研究方向 62
參考文獻 63
附錄
附錄一	定理3.1之證明 65
附錄二	定理3.2之證明 66
附錄三	定理3.3之證明 71
附錄四	定理4.1之證明 81
圖目錄
圖2.1	Δ-P-K 系統架構 7
圖2.2	架構轉換 8
圖2.3	Δ-Pαγ-K 架構 9
圖3.1	條件轉換架構(一) 20
圖3.2	條件轉換架構(二) 24
圖3.3	整體設計流程圖 29
圖4.1	條件(4.1)之轉換 36
圖4.2	條件(4.2)與(4.3)之轉換 36
圖5.1	參數式擾動之控制系統架構圖 44
圖5.2	Δ-P-K架構 45
圖5.3	閉迴路響應圖(一) 50
圖5.3	閉迴路響應圖(二) 51
圖5.4	低頻高斯雜訊產生方式 52
圖5.5	方法一與方法二對低頻高斯干擾訊號抑制效果 53
圖5.6	方法三與方法四對低頻高斯干擾訊號抑制效果 54
表目錄
表2.1	引理2.3中的變數 14
表5.1	交替求解之功效(一) 46 
表5.2	不同穩定邊界要求下之性能(一) 46 
表5.3	交替求解之功效(二) 47
表5.4	不同穩定邊界要求下之性能(二) 47 
表5.5	交替求解之功效(三) 48
表5.6	不同穩定邊界要求下之性能(三) 48
表5.7	交替求解之功效(四) 49
表5.8	不同穩定邊界要求下之性能(四) 49

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