臺灣博碩士論文加值系統

本文探討主動控制系統中，LQR與 兩控制律在相同的控制條件下降低結構動態反應效用之比較。研究結果顯示，不論是控制理論推演，控制後動態特性方程式、解析式，或是數值模擬分析結果，均可證明LQR控制律為 控制律當控制參數 趨近於無窮大時之特例。所以， 控制律不但包含LQR控制律，更能藉由調整兩控制參數 與 增加結構主要模態阻尼比，使得具有更佳的減振效果。同時，對於控制力施加時間延遲效應，本研究發現，採用 控制方法，若選擇控制參數 愈小，容許的時間延遲愈長，可見 控制律更具強健性，為一較佳控制法則。

In this study, we want to discuss the control effectiveness of reducing structural response by applying two different control algorithm, H∞ and LQR control algorithm, which are under the same control conditions. The research shows that, no matter the control theory, equations for getting the feedback gains, or analytic frequency and damping ratio equations, we all can prove that LQR control algorithm could be the special case of H∞ control algorithm when parameter γ closes to infinity. Besides, H∞ control algorithm could be more effective for reducing structural response, cause rising damping ratio higher and keeping frequency closing to the original structural frequency by lowing down parameter γ. And another class in control force execution time delay, we find that adopting smaller parameter γ could extend the maximum allowable delay time under the same control conditions. Therefore, we put it into a conclusion that H∞ control algorithm not only include LQR control algorithm, but also can be more robust, is a better active control algorithm.

誌 謝 i
摘 要 ii
Abstract iii
目 錄 iv
表 目 錄 vi
圖 目 錄 viii
第一章 緒論 1
1.1研究動機與目的 1
1.2文獻回顧 2
1.3本文內容 4
第二章 連續時間LQR與H∞控制理論 6
2.1 LQR之控制理論、解析解 7
2.1.1狀態回饋控制理論 7
2.1.2直接輸出回饋控制理論 8
2.2 H∞之控制理論、解析解 10
2.2.1狀態回饋控制理論 11
2.2.2直接輸出回饋控制理論 12
第三章 LQR與H∞之關係比較 16
3.1控制理論之比較 16
3.2求解方程式之比較 17
3.2.1狀態回饋 17
3.2.2直接輸出回饋 17
3.2.3直接輸出回饋與狀態回饋之關係 18
3.3樓房結構受地震擾動不同控制律之參數選擇 20
3.3.1 LQR控制律之參數選擇 21
3.3.2 H∞控制律之參數選擇 22
第四章 控制效用之比較 23
4.1單自由度結構控制系統 23
4.1.1狀態回饋控制之比較 24
4.1.2直接輸出回饋之比較 31
4.1.3變化頻率單自由度結構之比較 35
4.2多自由度結構控制系統 35
4.2.1控制權重參數之選擇 36
4.2.2控制效用之比較 37
第五章 時間延遲系統穩定分析比較 40
5.1時間延遲與系統模態特性之比較 40
5.1.1單自由度系統 40
5.1.2多自由度系統 44
5.2時間延遲對轉換函數及動態歷時影響之比較 45
5.2.1單自由度系統 45
5.2.2多自由度系統 46
第六章 結論與建議 48
參考文獻 50
表…………………………………………………………………….53
圖………………………………………………………………….69

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