地震工程即時複合試驗技術之研究

Abstract

即時複合試驗結合了數值模擬與結構試驗兩種方法，其中結構的慣性力與阻尼力常以數值模型模擬，試體的恢復力則由試體反應量測而得。基本原理與擬動態試驗相同，唯一不同的地方為此方法並不放慢實驗速度，試體在即時的狀態下運動，在數值模型取得試體反應後即運算出下一個步階位移，並驅動致動器施加目標位移於試體上，反覆進行至試驗結束。此方法可真實反應速度相依型構件在全結構下的真實受震行為。然而系統的時間延遲、致動器控制的精確度、試體與數值模型傳遞資料所需的時間，以及數值方法的運算速度與收斂性能等，皆為影響試驗結果的正確性，亦為相關研究人員極欲解決的問題。 為了能解決因延遲與控制誤差所導致即時複合試驗結果的正確性與穩定性問題，本研究使用系統控制理論，藉由加入外迴圈控制器的方法以改善系統的穩定性，並以兩個實例驗證外迴圈控制器的可行性。第一個為鋼板剪力牆反覆載重實驗，藉由設計的外迴圈PID控制器，成功地完成彎矩控制的實驗需求；另一個為一興建中的振動台位移控制，數值模擬結果顯示外迴圈控制器能有效降低因系統變異及量測噪音所造成控制精度的影響。 在近期的研究發現，在即時複合試驗誤差因素中，時間延遲造成的效應最為關鍵，甚至於影響一個複合試驗的收斂性。本研究使用擬延遲分析法，以Rekasius替代法轉換系統延遲微分方程至多項函式，並以魯茲穩定性法則分析系統的穩定性，可得到單自由度穩定之臨界延遲。此外由波德圖分析可知，在延遲系統中，致動器施加過大的位移將減少系統的臨界延遲。 為了精確控制油壓致動器，以得到正確的受震反應模擬，本研究發展二階相位補償器以補償系統延遲。考慮實驗過程中系統延遲並非保持不變，本研究使用了適性控制理論，使此二階補償器能在實驗過程中自動調整其延遲常數，達成有效且即時的延遲補償。此外，為了修正量測位移與目標位移造成的誤差所導致的系統不平衡等效外力，本研究提出了補償恢復力器將此外力於下一個積分步進行修正。此方法需求得試體的切線勁度，本研究以移動平均方法於實驗過程中求取切線勁度，即時地以運算出對應的補償力加入動力方程式中，以求得較精確的試驗結果。 為了驗證所提出補償方法的可行性，本研究進行了數個即時複合試驗。對於速度不相依型的試體，本研究使用一個單自由度的結構，此結構既有阻尼比設定為2%，是十分嚴峻且具挑戰性的實驗，其數值模型包含了質量與阻尼係數，而彈性恢復力則由真實試體進行試驗量測而得。實驗結果發現，本研究所提出的雙補償方法，皆能夠穩定並準確地執行一個低阻尼速度不相依型的即時複合試驗。 為了驗證所提出的補償方法適用於速度相依型試體，本研究使用一雙自由度的智慧型隔震結構，其提供隔震層阻尼力的磁流變阻尼器由實驗即時控制並量測所得。實驗結果證明，本研究所提出的二階相位補償器，能夠得到穩定且準確的即時複合試驗結果。 為了更進一步改善致動器控制的精確度，本研究將適性控制理論應用於前饋與回饋控制器方法上。此外，本研究導入了參數投影演算法，並配合魯茲穩定性法則，以確保此應用的穩定性與安全性。最後，以一個九層樓的抗彎構架進行即時複合試驗，其控制各樓層加速度反應的磁流變阻尼器由實驗即時控制並量測所得。實驗結果證明適性控制理論的應用，改善了既有的前饋與回饋控制器方法，並提升了即時複合試驗結果的正確性。 此研究所開發的即時複合試驗技術，除了可提供國內研究人員進行地震工程研究的一種新方法，更可節省試體製作的成本，對於節能減碳與永續發展，有莫大的助益。

Real-time hybrid testing is an innovative experimental technique for evaluating the dynamic responses of structural systems under seismic loading. It separates a structure into two substructures: numerical model and physical specimen that is difficult to simulate analytically. Servo-hydraulic actuators, however, have complex dynamics and induce inevitable time lag or delay and magnitude reduction between the command and the achieved displacements. This delay produces a negative damping effect and adds energy into a hybrid test which would result in inaccurate test results or even destabilize the overall structural system. In addition, the accumulative measurement error would result in inaccurate test results. Therefore, real-time hybrid testing requires high quality measurements, accurate control of actuators, and refined signal processing to perform versatile and reliable experiments. To improve the performance of an existing control system, an outer-loop control scheme has been investigated. Two experiments have been studied, including a cyclic loading test of a coupled steel plate shear wall, and a tracking control of a constructing shaking table. It has been shown that the additional outer-loop controller accomplishes the control target and the test requirements without changing the existing control system.

To realize the effects of actuator delay and control error on the real-time hybrid testing, the stability margin has been discussed by introducing a pseudo-delay technique. The critical time delay has been shown to depend on the test structural parameters. The structures with high damping or long period have a large critical time delay. In addition, a system with an undershoot amplitude error has a longer critical time delay than that with an overshoot amplitude error. The combined effects of time delay and amplitude error has been also investigated by Bode magnitude plots. To achieve good tracking performance of servo-hydraulic systems, a second order discrete adaptive phase lead compensator (PLC) has been proposed. It has been proved unconditionally stable as long as the selected weightings are located in the stable regions. In addition, an adaptive delay estimator based on the gradient adaptive law has been adopted to estimate the delay during the test. Numerical simulations have shown that the PLC compensates the system well regardless of that the servo-hydraulic system is modeled as a pure time delay system or a first-order transfer function. To reduce the effect of error propagation, a restoring force compensator has been proposed to correct the unbalanced force due to the displacement error. The compensation force is calculated by applying the proposed moving-averaged tangent stiffness method. Both the upper and lower bounds of the tangent stiffness have been specified to avoid unreasonable compensation. Furthermore, the sampling number used for computing the tangent stiffness of each step has been studied through the experimental validation. For rate-independent specimens, real-time hybrid testing on a portal frame has been conducted. The stiffness term is represented by a steel plate. Experimental results have indicated that the dual-compensation scheme can be applied on tests containing rate-independent components stably and accurately.

For rate-dependent specimens, real-time hybrid testing on a smart base-isolation system has been performed. The physical specimen is a magneto-rheological (MR) damper which is semi-actively controlled by different control methods. Experimental results have demonstrated that the adaptive second-order PLC can lead to fair test results for rate-dependent components. To further improve the tracking performance of servo-hydraulic systems, an adaptive model-based feedforward-feedback control strategy has been proposed. The accuracy and stability of this control scheme are validated through tracking performance testing and real-time hybrid testing of a nine-story shear building controlled by MR dampers. Experimental results have shown that the proposed adaptive model-based control achieves excellent displacement tracking for the real-time hybrid testing.