天鉤主動隔震系統應用於非剛體設備物之分析與實驗驗證

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姓名

吳柏諺(Po-Yen Wu) 查詢紙本館藏

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土木工程學系

論文名稱

天鉤主動隔震系統應用於非剛體設備物之分析與實驗驗證

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摘要(中)

本研究提出以天鉤(Skyhook)控制理論，應用於非剛體設備物，為二自由度Skyhook主動隔震系統，文中詳細說明運動方程式之推導及控制律設計，再進行數值模擬分析及實驗驗證。改良傳統Skyhook控制理論，原需以絕對速度回饋之控制力，調整為量測主動隔震平台相對地表速度及地表加速度，以相對地表速度及將地表加速度積分濾波獲取之地表速度訊號計算控制力，不僅能提升訊號量測的便利性，更能增加回饋訊號的穩定性。由於自行引入積分濾波器其參數可被充分掌握，可將Skyhook主動隔震系統擴展為包含積分濾波器之形式，使控制及最佳化設計皆能考量積分濾波器之影響。此外，Skyhook主動隔震系統具有兩個增益參數且並非全狀態回饋，因此利用離散時間系統直接輸出回饋，以非剛體設備物絕對加速度最小化為設計目標，配合參數迭代更新方法設計最佳化增益參數。於頻率反應函數分析中，對於一般地震的顯著頻率Skyhook主動隔震系統隔震成效優於被動隔震系統。於地震歷時分析中，Skyhook主動隔震系統對於近域及遠域地震皆有較被動隔震系統優異之隔震成效。於敏感度分析中與穩定性分析中，兩個控制力增益參數於一定範圍內之變化，系統雖對於增益參數變化敏感，但系統為穩定狀態。另外探討不同主動控制律對於主動隔震系統之隔震成效，比較全狀態回饋之LQR控制律，發現Skyhook主動控制可以量測較少之物理量達到與LQR相近之隔震成效。藉由伺服滑台上固定一小型隔絕微振之被動隔振器加上質量塊即為非剛體設備物，整體實驗配置模擬二自由度Skyhook主動隔震系統之動力行為，並以振動台實驗驗證其可行性。實驗結果表明，Skyhook主動隔震系統對於大多地震皆有一定之隔震效果。實驗結果與數值模擬之差距，經由功率頻譜密度分析，確認係伺服滑台對於高頻的控制命令有其延遲所致。

摘要(英)

In this study, the skyhook control theory is modified and applied to a non-rigid equipment, which becomes a two-degree-of-freedom skyhook active isolation system. The required signal of the traditional skyhook control is therefore adjusted from using the absolute velocity of the equipment to the relative velocity of active isolation platform relative to the ground and the ground absolute velocity. In addition, the ground absolute velocity signal is obtained by a designed integral filter from measuring the ground acceleration. These modifications can not only improve the convenience of signal measurement, but also increase the stability of the feedback signal. Since the parameters of the designed integral filter is well known, the dynamics of the integral filter can be fully considered in the augment system which includes the skyhook active isolation system and the integral filter. Therefore, the influence of the integral filter can be considered in the control and optimization design. The modified skyhook active isolation system has two gain parameters and is not full-state feedback, so that the two gain parameters are optimized by using the discrete-time direct output feedback with the parameter iterative update method to minimize the absolute acceleration of the non-rigid equipment. In the frequency response function analysis, the simulation results show that the skyhook active isolation system is more effective than the passive isolation system for the significant frequency range of ordinary earthquakes. In the seismic time history analysis, the skyhook active isolation system has better isolation performance than the passive isolation system for both near-fault and far-field earthquakes. In the sensitivity analysis and stability analysis, when the two control force gain parameters change within a certain range, the system is in a stable state although it is sensitive to the change of gain parameters. Furthermore, comparing with the LQR control law, it was found that the skyhook active control measures fewer signal to achieve a similar effectiveness to the LQR which using the full-state feedback. To investigate the performance and the dynamic behavior of the skyhook active control by shaking table experiment, a small passive vibration isolator with the proof mass is used to represent the non-rigid equipment. Then the non-rigid equipment is installed on a servo-controlled slider as the active skyhook isolation platform to verify the feasibility of the two-degree-of-freedom active isolation system. The experimental results show that the skyhook active isolation system has certain seismic isolation effect for most earthquakes. The difference between the experimental results and the numerical simulations was observed and confirmed by the power spectral density analysis, which was due to the delay of servo slider at high frequency command.

關鍵字(中)

★ 天鉤控制
★ 非剛體設備物
★ 二自由度主動隔震
★ 地表加速度積分回饋
★ 離散時間系統直接輸出回饋
★ 振動台實驗

關鍵字(英)

★ skyhook control
★ non-rigid equipment
★ two-degree-of-freedom active isolation
★ ground acceleration integral feedback
★ discrete-time direct output feedback
★ shaking table experiment

論文目次

摘要 i
ABSTRACT ii
目錄 iv
表目錄 vi
圖目錄 viii
符號說明 xv
第一章緒論 1
1-1 研究背景與動機 1
1-2 文獻回顧 2
1-3 研究內容 5
第二章天鉤隔震控制理論與方程式推導 6
2-1 天鉤隔震控制理論 6
2-2 二自由度主動隔震系統方程式推導 7
2-3 最佳化控制增益參數 11
2-3-1 最佳控制增益參數之系統設置 11
2-3-2 最佳控制增益參數設計運算 14
2-4 主動隔震控制流程 15
第三章二自由度天鉤主動隔震系統數值模擬分析 22
3-1 特徵分析 22
3-2 頻率反應函數 23
3-3 地震歷時數值模擬 26
3-3-1 輸入地震歷時 27
3-3-2 地震歷時下系統反應 28
3-4 敏感度分析 33
3-4-1 主動隔震平台勁度敏感度分析 34
3-4-2 主動隔震平台固有阻尼比敏感度分析 36
3-4-3 增益參數GD敏感度分析 38
3-4-4 增益參數GV敏感度分析 40
3-4-5 非剛體設備物勁度敏感度分析 42
3-4-6 非剛體設備物阻尼比敏感度分析 44
3-4-7 敏感度分析結果與討論 46
3-5 穩定性分析 47
第四章天鉤主動隔震與LQR主動隔震之比較 77
4-1 頻率反應函數 77
4-2 地震歷時數值模擬 80
第五章二自由度天鉤主動隔震系統振動台實驗 100
5-1 實驗設備與配置 100
5-2 非剛體設備物系統識別 101
5-3 控制介面與量測儀器 102
5-4 狀態預測系統之轉速控制 103
5-5 輸入之地震歷時 105
第六章實驗結果與討論 115
6-1 振動台加速度功率譜密度115
6-2 各項反應之實驗結果116
6-3 相同震波不同PGA之比較 117
6-4 不同震波之隔震效果比較 120
6-5 實驗與數值模擬之比較 121
第七章結論與建議 161
7-1 結論 161
7-2 未來研究與建議 165
參考文獻 166
附錄A 170

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指導教授

賴勇安(Yong-An Lai)

審核日期

2022-9-6

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