| 摘要: | 本研究於多自由度結構中加裝結構絕對加速度回饋之相位控制多元主動調諧質量阻尼器(Phase Control absolute Acceleration feedback-Multiple Active Tuned Mass Dampers, PCA-MATMDs)，推導出適用於多顆ATMD可分別配置於多自由度結構不同樓層之運動方程式，並分別以兩個案例探討兩種配置形式下之減振成效：第一種為兩顆MATMDs集中放置於五層樓結構之頂樓，並控制相同模態之相同樓層配置形式；第二種為兩顆MATMDs分別放置五層樓結構之頂樓與三樓，並分別控制不同模態之不同樓層配置形式。針對上述兩種配置，進行頻率反應函數、地震歷時分析與系統穩定性分析之數值模擬，並對第二種配置進行振動台實驗驗證。本研究所提之PCA-MATMDs利用量測各顆MATMDs相對速度與結構絕對加速度計算控制力，再將控制力施加於MATMDs與主結構之間，使各顆MATMDs與結構保持相位差-90度之Power Flow原理，此時達到最佳減振效益。由於結構加速度量測訊號會有雜訊干擾，進而影響控制效果，故設計濾波器來濾除雜訊。本研究將PCA-MATMDs之被動元件參數與主動控制力進行一同最佳化設計，計算方式採用分散式靜態輸出回饋 (Decentralized Static Output Feedback)搭配軟性更新(Soft update)迭代來求解，這種設計方法不需全狀態回饋，方便設計且具實務應用性。另外，對於相同樓層配置形式來說，MATMDs預期可以多顆小型ATMD取代傳統單一大型ATMD，如為對稱情況下，最佳化設計結果呈現兩顆MATMDs設計參數皆一致，故兩顆MATMDs控制力會相同並且比單顆ATMD控制力小，解決單顆ATMD之控制力需求過大之問題，同時避免某顆MATMDs負擔較大控制力之情形。而不同樓層配置之情形，頂樓之ATMD可控制第一模態，三樓之ATMD可控制第二模態，因此MATMDs可同時抑制第一模態與第二模態反應，達到多模態減震效果。根據兩種配置情形之數值模擬結果可知，不論是相同樓層配置還是不同樓層配置皆具良好減振效果。在增益參數穩定性分析中，此兩種配置情形皆維持穩定並且增益參數還有餘裕；另外，於時間延遲穩定性分析，只要兩種配置情形不超過最小延遲時間，系統就會維持穩定。最後對兩顆PCA-MATMDs加裝於五層樓構架中之不同樓層進行振動台實驗，結果進一步證實不同樓層配置MATMDs於多筆地震波下具備有效之減振效能，驗證其實用之可行性。;This study proposes Phase Control absolute Acceleration feedback-Multiple Active Tuned Mass Dampers (PCA-MATMDs) system applied to a multi-degree-of-freedom structure. A general form of the equations of motion is derived, applicable to configurations where MATMDs are individually installed on different floors of the MDOF structure. Two case studies are conducted to evaluate the vibration reduction performance under two configuration types: (1) Uniform floor and modal configuration: both MATMDs are installed on the top floor of the five-story structure to control the same mode; and (2) Diverse floor and modal configuration: MATMDs installed on the top and third floors to control different modes. For the above two configurations, numerical simulations including frequency response, seismic time history, and stability analyses were conducted for both configurations, while shaking table tests were performed for the diverse configuration. The control method is based on feedback of structural absolute acceleration and the relative velocity of each MATMD to calculate control forces. These forces are applied between the MATMDs and the structure to maintain a -90° phase difference according to the power flow principle, thereby achieving optimal vibration reduction. A filter is designed to eliminate measurement noise in the acceleration signal. The passive parameter and control gains of the MATMDs are jointly optimized using a Decentralized Static Output Feedback method combined with a soft update. This method avoids the need for full-state feedback, facilitating easier design and practical implementation. Additionally, for the uniform floor configuration, multiple small MATMDs are expected to replace a conventional single large ATMD. In the case of a symmetric system, the optimization results show that the two MATMDs have identical design parameters, reduces individual control force demands and ensures balanced. In the case of the diverse floor configuration, the ATMD on the top floor is designed to control the first mode, while the ATMD on the third floor targets the second mode. As a result, the MATMDs can simultaneously suppress both first- and second-mode responses, achieving multi-mode vibration reduction. Numerical simulation results show that both the uniform and diverse configurations provide effective vibration control performance. Stability analysis shows that both configurations maintain stability and possess adequate stability margins. Furthermore, the system remains stable for both configurations as long as the delay does not exceed the minimum allowable threshold. Shaking table experiments further confirmed that the PCA-MATMDs system achieves effective vibration reduction under the diverse configuration, demonstrating its practical feasibility. |
