由於一般控制系統中皆具有不確定量的存在，因此，只針對常態系統做考慮所設計的控制器，將無法確保在有不確定量的影響下，能否使系統同時滿足強韌穩定和強韌H∞性能。在本論文中，將以結構奇異值靈敏度的概念做為控制器參數調整的依據，藉此調整初始控制器中的某些參數，使得新的控制系統在不確定量的影響，同時滿足強韌穩定和強韌H∞性能。但這個方法在計算上會有費時和因不連續性而導致誤判的問題，因此，本論文中提出斜式結構奇異值靈敏度的概念，將可改善前述使用結構奇異值靈敏度在數值計算上的缺失。最後，舉兩個數值上的例子，由模擬結果來驗證利用斜式結構奇異值靈敏度做控制器參數調整之依據的可行性。

Since uncertainty exists inevitably in control systems, it is questionable whether the controller, designed to compensate a nominal plant well, still guarantees the criteria of robust stability and robust H∞ performance for the perturbed plant. In this thesis, controller parameters tuning based on the sensitivity concept of structured singular value, called μ-sensitivity, will be adopted to do the parameter adjustment so that, when the influence of uncertainty is considered, the robust stability and robust performance properties of the nominal closed-loop system will be preserved. In view of the time consuming effect of numerical computation and the misjudgment due to discontinuity problem involved in the μ-sensitivity analysis, this thesis proposes the sensitivity concept of skewed structured singular value, called ν-sensitivity, to remedy these drawbacks. Finally, the feasibility of the ν-sensitivity based controller parameters tuning technique is verified by the simulation results of two examples.

摘要 i
圖表 iii
第一章 緒論 1
1-1 節 文獻回顧與研究動機 1
1-2 節 論文綱要 3
第二章 結構奇異值和斜式結構奇異值 4
2-1 節 線性分式轉換 4
2-2 節 混合型結構奇異值 6
2-3 節 結構奇異值分析 9
2-4 節 斜式結構奇異值 12
第三章 應用斜式結構奇異值靈敏度做控制器參數調整 15
3-1 節 問題描述 15
3-2 節 結構奇異值靈敏度和斜式結構奇異值靈敏度 17
3-3 節 參數調整之設計步驟與流程圖 21
第四章 數值模擬 29
4-1 節 PID 控制器的參數調整 29
4-2 節 輸出迴授控制器之參數調整 35
第五章 結論 47
參考文獻 48

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