以線性控制理論探討剪力構架之即時複合振動台試驗研究

Linear Control Strategy for Real-Time Hybrid Shake-Table Testing of a Shear-Frame

徐筱晴(Shiau-Ching Hsu)

指導教授 ： 蔡克銓

共同指導教授 ： 陳沛清(Pei-Ching Chen)

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202000748

摘要

本研究利用結構動力學與線性控制等學理，與簡化之油壓伺服致動器線性模型假設，欲針對即時複合振動台試驗提出合適控制方法，以改善過往加速度追蹤誤差、致動器出動力量延遲所造成之實驗不準確性，並期望同時能提升實驗之強韌性。
試體設計為三層樓之縮尺剪力鋼構架，兩層樓之下部結構為複合實驗之實際試體，其最上方之樓板可以外接一支外部致動器，模擬數值子結構欲回傳之層間剪力；除推導適用於本研究之時域運動方程式，延伸至可廣泛運用之頻率域狀態空間方程式；亦提出適用於即時複合實驗之加速度修正方法，以運動方程式之疊加法欲解決延遲之問題。
實驗在國家地震研究中心之小型結構實驗室進行，試體製造並安裝完成後，進行多項系統識別試驗，獲得之數值模型用以設計數值控制器。共使用三種控制器設計方法，分別為逆函數前饋控制器、相位領先補償器、強韌回饋控制器。
在進行純數值模擬複合試驗前，先進行全結構之三層樓標竿模型受地震輸入之傳統震動台實驗，各層加速度規量測值經濾波後之絕對加速度，視作為後續欲與純數值模擬複合試驗或實際複合試驗比較用之標準答案；利用純數值模擬複合試驗欲驗證模型假設與控制器設計方法之有效性，並應用提出之加速度修正方法，同時按不同之控制方法將設計完成之三項控制器安裝至數值模型中，比較各方法之優缺點。
本研究進行之實際實驗包含弦波試驗、擬地震複合試驗；前者依序進行內、外迴路之直接控制、逆函數前饋控制、相位領先補償控制方法，與強韌控制方法。分析弦波試驗之結果，下部致動器在小位移時仍能獲得良好之位移追蹤能力，雖外部致動器的位移與力量並沒有達到預期的振幅，其頻率內涵仍屬正確。分析擬地震複合試驗之結果，在期望位移比弦波試驗大數倍之情況下，下部與外部致動器皆獲得良好之位移控制結果，然外部致動器之力量仍與本研究的預期不符，除量級差距，線形亦與數值模擬完全不同，觀察發現其與致動器自身出動位移有關聯性；然在多次的擬地震複合實驗後，觀察發現實驗子結構已出現非線性行為，柱構件應當進入降伏，故實驗與至此告終。
總結如下，本研究將致動器、控制系統與試體本身皆設為線性模型，欲以線性控制理論來進行同時致動器的位移與力量追蹤控制，分析純數值模擬複合試驗之結果，不論是用何種控制器皆可獲得可接受之頻率域誤差；在擬地震複合實驗中，外部致動器力量雖不受控，除因試體可能已降伏並進入非線性行為，亦可能因本研究假定致動器為線性模型的假設過於簡化，且控制結構互制效應明顯影響試體與兩支致動器。建議未來若有學者想要研究類似本研究之議題，關於致動器與控制系統的模型假設，可以嘗試使用非線性之模型進行模擬，進而提升複合試驗之可行性。

關鍵字

線性控制 ； 前饋控制 ； 回饋控制 ； 位移控制 ； 力量控制 ； 即時複合振動台實驗 ； 控制結構互制效應

並列摘要

In order to improve the control performance of Real-Time Hybrid Shake-Table Testing(RTHSTT), deal with the delay effect from the servo hydraulic actuator and enhance the correctness of the acceleration tracking, this study adopts the theories of structural dynamics and linear control strategies. Appropriate controllers are designed for enhancing the robustness and feasibility of the RTHSTT.
The whole structure (Benchmark Model) is a small-scale three-story shear frame which is made by steel, and it can be divided into a two-story substructure and one-story superstructure. The below two-story specimen is the real experimental part of the hybrid testing, which is mounted on a shake-table, and its top floor can connect to an external actuator simulating the interlaminar shear force calculated from the numerical superstructure. Both the lower and external servo hydraulic actuator are assumed to be linear models. Besides, not only the equations of motion of this study but also a general linear state space model for hybrid testing are derived. In addition, an acceleration correction method is proposed to solve the delay problem of the numerical real-time hybrid simulation(RTHS) and RTHSTT.
The experiment of RTHSTT is conducted in the small structure laboratory of National Center for Research on Earthquake Engineering(NCREE). The identified numerical model of control framework is used to design the numerical controllers. There are three controllers including Pseudo Inverse Controller(PIC), Phase Lead Compensator(PLC), and Robust Feedback Controller(RFC).
Traditional shake-table testing for the benchmark model is conducted first before the numerical RTHS. The measured and filtered absolute accelerations of each floor are saved and used as a standard result to be compared. Then, through the numerical RTHS, the effectiveness of the model assumptions and controller design methods can be verified. At the same time, the proposed Acceleration Correction Method (ACM) is adopted to solve the delay problem. The results of the numerical RTHS are acceptable, and they show that the ACM and those three controllers are feasible.
This study conducts two-kind testing, including sinewave testing and simulated RTHSTT with known inputs. For the sinewave testing, inner-loop and outer-loop control, PIC, PLC, and RFC are tested to verify the stability of each control method. Except for the RFC, all the results of other control methods show that the lower actuator have good displacement-tracking ability. However, the displacement and the force of the external actuator do not confirm to the expectations, but the frequency content is acceptable.
For the simulated RTHSTT, the desired displacements are larger than the sine wave testing, and both the lower and the external actuator can get good displacement tracking results. Nevertheless, the force of the external actuator is still out of control. The achieved forces are much larger than the desired forces, and it shows some relationship between the force and the displacement of the external actuator. Even so, because the behaviors of the experimental specimen start to become nonlinear, and the columns might have yielded. Thus the experiment of this research is ended.
To sum up, the actuator, the control system and the experimental specimen are all assumed to be linear models, because the objective of this research is to use linear control theory to control and track the displacement and the force simultaneously. The analysis of the numerical RTHS shows the effectiveness of the proposed ACM and three control methods. Although the force of the external actuator in the simulated RTHSTT cannot satisfied with the desired values, this study reminds the future researchers that the assumptions of linear models need to be revised to enhance the feasibility of the RTHSTT.

並列關鍵字

linear control ； feedforward control ； feedback control ； displacement control ； force control ； real-time hybrid shake-table testing ； control-structure-interaction

參考文獻

Andreas H. Schellenberg, Tracy C. Becker and Stephen A. Mahin. (2016) “Hybrid shake table testing method: Theory, implementation and application to midlevel isolation,” Structural Control and Health Monitoring, 24(5), DOI:10.1002/stc.1915.

Brian M. Phillips, A.M.ASCE; and Billie F. Spencer Jr., P.E., F.ASCE. (2013) “Model-Based Multiactuator Control for Real-Time Hybrid Simulation,” Journal of Engineering Mechanics, Vol.139, No. 2, pp.219-228.

D.P. McCrum, and M.S. Willams. (2016) “An overview of seismic hybrid testing of engineering structures,” Engineering Structures, Vol.118, pp. 240-261.

Jin-Ting Wang, Yao Gui, Fei Zhu, Feng Jin and Meng-Xia Zhou. (2015) “Real-time hybrid simulation of multi-story structures installed with tuned liquid damper,” Structural Control and Health Monitoring, Vol.23, pp.1015-1031.

Matthew Stehman and Narutoshi Nakata. (2016) “IIR Compensation in Real-Time Hybrid Simulation using Shake Tables with Complex Control-Structure-Interaction,” Journal of Earthquake Engineering, Vol.20, No.4, pp.633-653.