以系統控制方法重現高樓層樓版受震反應歷時之研究

Abstract

地震工程研究中，常使用地震模擬振動台之實驗方法，以觀察安裝於振動台上待測試體之受震反應。地震模擬振動台藉由致動器推動剛性測試平台以重現地震歷時，然而因為振動台之衝程限制，常無法重現部分高樓層樓版反應或長週期地震歷時。本研究在不改變既有振動台配置之前提下，以一組被動轉移裝置，配合線性及非線性控制器之分析與設計，得以在轉移裝置上獲得較原振動台更大之總衝程，重現高樓層之樓版反應歷時。 線性控制器包括傳統的比例-積分-微分控制器、開迴路前饋控制器以及閉迴路線性二次高斯控制器，此外由於使用摩擦單擺系統做為被動轉移裝置，其阻尼比隨系統狀態之不同而變化，造成線性控制器之性能表現不佳，因此須考慮阻尼比對控制器穩定性及系統表現之影響。本研究利用力平衡及庫倫摩擦理論進行運動方程式的推導，得到非線性模型，再以該模型進行非線性控制器的設計，包含適應性前饋控制、增益補償法及ξ-scheduling方法。 本研究以一高雄市34層樓的鋼構造建築為例，使用發展之實驗技術重現該建築頂樓樓板之受震反應歷時，並使用正弦週期掃頻評估安裝控制器之效果，實驗結果可應用於不同尺度之地震模擬振動台，做為重現高樓層樓版反應或長週期地震歷時方法之重要參考。

Shaking table, known as earthquake simulators, is used to reproduce record of earthquakes. An original shaking table system is made up of an actuator, a servo valve, a controller, and rigid platform. By exciting an actuator, the response of specimens, which is mounted on the rigid platform, can be investigated in real time. However, causing to the stroke limit of the actuator, it’s difficult to reproduce floor responses of high-rise buildings which are subjected to earthquakes or long-period time histories. In order not to change the configuration of the shaking table, a passive transfer system with linear and nonlinear control strategy is used to enlarge the stroke limit of the shaking table, then the floor responses mentioned before could be reproduced. The linear controllers including feedforward control, PID control and LQG control are used to verify the feasibility and controllability of the passive transfer system. However, the transfer system which is made up of friction pendulum system contains a nonlinear factor related to damping ratio, causing to the poor reproduction of time histories. To improve the performance of passive transfer system, the nonlinear controllers based on the motion equation of friction pendulum system are introduced, including adaptive feedforward control, magnitude matching method and ξ-scheduling method. These methods mentioned above are verified by reproducing both floor responses of high-rise buildings which are subjected to earthquakes and sweep sine history, and the analysis of experimental result could be referenced for designing passive transfer system for different scale of shaking table systems.