臺灣博碩士論文加值系統

經由許多的理論推導、數值模擬及試驗驗證證實主動控制確實能降低結構動態反應，在主動結構控制實際應用時，量測訊號與施力等整體控制系統的離散特性將會使控制力施行遭遇困難，因此本文將應用考慮外力擾動且具強健性之 控制法則，發展離散時間系統之控制理論，應用於建築結構受地震力作用之減振。此外，在 控制理論中，能藉由調整兩控制參數 與 以增加結構系統主要模態阻尼，在控制設計上具有較大彈性及較佳的減振效果，選擇 值愈小或 值愈大，控制效果愈佳，但對任一結構系統而言， 值必須滿足一下限值且 也必須滿足一上限值，否則將造成整體控制系統不穩定。另一方面，本研究將理論推演求得同時考慮控制力施加時間延遲及取樣時間之離散時間系統回饋增益值，探討取樣時間對控制效果之影響。當實際應用時，只需將經由線外計算常數時間延遲回饋增益值乘以輸出量測，即可得知所施加的控制力大小，如此可確保控制系統穩定，達到預期減振目標，增進結構主動控制之實際應用的可行性。

In recent years, with numerous theoretical development and experimental verifications, both active and semi-active structural control systems have been accepted and implemented to control wind- or earthquake-induced vibration of buildings around the world. In addition, due to flexibility, reliability, and high speed, digital computers have been used for on-line signal processing and calculation of control forces in real-time control. Therefore, it is more logical and more realistic to formulate the control systems in discrete-time fashion prior to their implementation. In this study, an optimal discrete-time control algorithm is developed to reduce the structural seismic responses. Both sampling period and control force execution time delay are considered to derive the optimal state feedback gains. Discrete-time control forces are then calculated from the multiplication of output measurements by the pre-calculated time-invariant delayed gain matrix. Parametric studies of a single-degree-of-freedom (SDOF) system demonstrate the relationships of the delayed gains and the modal properties corresponding to the sampling period used and the intentionally added delay time. To achieve optimal control performance, the strategy to select both control parameters and was investigated extensively. Numerical verification results show that decrease in or increase in yields better control performance with an acceptable magnitude of control force. The selective ranges of and making a controlled system become overdamped or unstable were found. To assure system stability and better performance than LQR control, the upper and lower bounds of and are derived and illustrated graphically. An optimal design flowchart is also proposed.

謝 誌 i
中文摘要 ii
Abstract iii
目 錄 iv
表 目 錄 vii
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 3
1.3 本文內容 6
第二章 離散時間系統之 控制理論 8
2.1 離散時間系統之狀態方程式 10
2.1.1連續時間狀態方程式之離散化 10
2.1.2 無時間延遲之離散時間系統 11
2.1.3 具時間延遲之離散時間系統 11
2.2 離散時間系統之 控制理論 13
2.2.1 連續時間系統之 控制理論 13
2.2.2 離散時間系統之 控制理論 17
2.3 建築結構地震反應之 控制 20
2.3.1位移控制輸出 21
2.3.2能量控制輸出 22
2.4 離散時間系統之動態特性 23
2.4.1 控制後系統自然頻率及阻尼比 23
2.4.2 位移及加速度轉換函數 26
第三章 無時間延遲離散時間系統 控制之數值模擬 28
3.1 單自由度結構控制系統之數值驗證 28
3.1.1 最佳回饋增益矩陣 29
3.1.2 控制後系統參數 30
3.2 取樣週期對回饋增益及系統模態特性之影響 30
3.3 控制參數選擇之策略 31
3.3.1 控制參數對控制效用之影響 31
3.3.2 控制參數選擇之極限值 33
3.3.3 最佳控制參數選擇流程 35
3.4 連續時間與離散時間系統之控制效用比較 35
3.4.1 頻率域之控制效用比較 36
3.4.2 真實地震力作用下之振動控制效用比較 36
第四章 具時間延遲離散時間系統 控制之數值模擬 38
4.1時間延遲對系統參數與動態特性之影響 39
4.1.1具時間延遲之單自由度結構控制系統模態特性 39
4.1.2 取樣週期與時間延遲之關係 41
4.1.3 控制參數與時間延遲之關係 42
4.2 時間延遲對轉換函數及動態歷時反應之影響 43
4.3 具時間延遲連續時間與離散時間系統之控制效用 44
第五章 多自由度結構控制系統之 減振效用分析 45
5.1 頻率域之控制效用 45
5.2 真實地震力作用下之振動控制效用 46
5.3 具時間延遲下控制系統之穩定分析 46
第六章 結論與建議 48
參考文獻 51

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