本研究針對多自由度結構，提出結合結構加速度回饋之相位控制複頻疊加主動調諧質量阻尼器(Phase Control Acceleration feedback-Multiple Frequency Superposition Active Tuned Mass Damper， PCA-MFSATMD)，以提升建築物於地震作用下之安全性。在 ATMD 之相位控制方面，其概念係藉由維持 ATMD 與結構間−90°相位差之方式計算所需控制力，以達成減震控制；研究發現，當多自由度構架配置PCA-ATMD並放大控制力以強化第一模態之控制效果時，控制增益增大至一定程度後，結構第一模態反應降低，但此時結構高模態反應增加，致使增益無法持續提升，若欲進一步提升整體控制效果，必須同步抑制高模態反應，方能繼續增加控制增益。有鑒於此，本研究基於疊加原理，將多顆 ATMDs 之系統等效轉化為單顆MFSATMD系統，以實現多調諧頻率之多模態減震控制。該MFSATMD系統具備三項關鍵性質：其一，單顆 MFSATMD 之質量(與慣質)等於多顆 ATMDs 質量(與慣質)之總和；其二，透過質量分配比(Mass Allocation Ratio)之關係，MFSATMD 之衝程反應可表示為各 ATMDs 衝程與其對應質量分配比乘積之線性組合；其三，MFSATMD 之總出力等同於各 ATMDs 阻尼力、回復力與相位控制力之總和。此外，PCA-MFSATMD之最佳設計參數可採分散式靜態輸出回饋(Decentralized Static Output Feedback)方法求解。為驗證系統可行性，本研究以單顆MFSATMD置於五層樓結構頂樓並調諧至結構前四個模態為對象，進行頻率反應函數分析、地震歷時分析與振動台實驗；數值模擬與實驗結果均顯示，該系統能有效控制多個目標模態頻率，進而得以放大第一模態控制增益，顯著降低結構之地震反應。實驗中運用 ERA 特徵系統實現演算法(Eigensystem Realization Algorithm)由量測資料推求實際結構參數，經與振動台空架構試驗結果擬合後確認其符合實際構架反應，可供後續數值模擬之用；同時藉由衝程修正方式，使 PCA-MFSATMD 質量塊之衝程能確實回歸原點位置。;This study proposes a Phase Control Acceleration feedback-Multiple Frequency Superposition Active Tuned Mass Damper (PCA-MFSATMD) incorporating structural acceleration feedback for multi-degree-of-freedom (MDOF) structures， with the aim of enhancing the seismic safety of buildings. Regarding the phase control of the ATMD， the required control force is computed by maintaining a −90° phase difference between the ATMD and the structure， thereby achieving vibration mitigation.The results show that， when a PCA-ATMD is applied to a MDOF structure and the control force is amplified to enhance first-mode suppression， increasing the control gain initially reduces the first-mode response. However， beyond a certain gain level， the higher-mode responses increase， thereby limiting further gain enhancement. Therefore， further improvement in the overall control performance requires simultaneous suppression of the higher-mode responses. Based on the superposition principle， the system of MATMDs is equivalently transformed into a single MFSATMD system to achieve multimodal vibration control with multiple tuning frequencies. The proposed MFSATMD system possesses three key properties. First， the mass (and inerter) of a single MFSATMD is equal to the total mass (and inerter) of the MATMDs; second， the stroke response of the MFSATMD is derived based on the mass allocation ratio. It can be expressed as a linear combination of the strokes of the individual ATMDs weighted by their corresponding mass allocation ratios; and third， the total output force of the MFSATMD equals the sum of the damping forces， restoring forces， and phase control forces of the individual ATMDs. Moreover， the optimal design parameters of the PCA-MFSATMD can be obtained using a decentralized static output feedback approach. To verify the feasibility of the proposed system， a single MFSATMD was installed on the top floor of a five-story structure and tuned to the first four structural modes. Frequency response function analysis， seismic time-history analysis， and shaking table tests were conducted. Both the numerical simulations and the experimental results demonstrate that the proposed system can effectively control multiple target modal frequencies， thereby enabling amplification of the first-mode control gain and significantly reducing the seismic response of the structure. In the experiments， the Eigensystem Realization Algorithm (ERA) is employed to identify the actual structural parameters from the measured data; after being fitted against the bare-frame shaking table test results， the identified parameters are confirmed to match the actual frame response and can be applied in subsequent numerical simulations. In addition， a stroke correction scheme is adopted to ensure that the stroke of the PCA-MFSATMD mass block reliably returns to its origin position.
