在過去幾十年以來，液壓伺服致動器因頻率響應頻寬大、力量負載大以及加載速率高等優點，已被廣泛應用於結構的動態加載試驗。在需要快速以及出力大的動態加載試驗中，液壓致動器以閉迴路回饋控制達成穩定的位移控制，一般而言，液壓致動器系統採用比例-積分-微分(proportional-integral-derivative, PID)控制器來達成位移追蹤的控制目標，但由於回饋控制以及伺服閥與液壓缸體動態特性的因素，高頻率動態追蹤性能較不理想，無法滿足試驗的測試需求，因此改善致動器高頻動態位移追蹤性能對於結構動態加載試驗極為重要。
本研究提出了串級控制方法，改善致動器高頻動態追蹤性能。串級控制架構串聯了主控制器(力量控制)以及副控制器(位移控制)，主控制器(力量PID控制器)需要力量產生器產生目標力量，使用目標力量及量測力量之間的誤差作為力量PID之輸入訊號，透過力量PID控制器計算出補償位移，並將此位移加到目標位移訊號中，再經由副控制器(位移PID控制器)進行位移回饋控制。本研究首先建置十分講究的數值模型，以Simulink環境中Simscape物理模型模組組成的液壓伺服致動器系統，在Simulink的架構下進行串級控制器位移控制性能的數值模擬，數值模擬結果顯示，與常見的位移控制配合逆轉移函數前饋控制方法相比，串級控制在時間域與頻率域皆具有更佳的位移追蹤性能。
此外，在結構實驗室準備了一組簡單的鋼柱試體，以單支致動器進行動態加載試驗，並使用帶有參數校正的Bouc–Wen–Baber–Noori模型作為主迴路的力量產生器，實驗結果證實串級控制方法能夠有效的提升致動器高頻動態位移性能，與傳統的逆轉移函數前饋控制方法相比具有相近的位移控制性能。最後將提出的控制迴路應用於並聯致動器並聯的位移控制，除了前述的串級控制架構之外，通過逆勁度矩陣補償方法對致動器的力量進行校正，實驗結果顯示位移追蹤性能十分出色，且兩致動器經逆勁度矩陣補償後，其力量量值與相位十分相近，因此不會對試體造成額外的扭力。本研究所開發的實驗技術，未來可應用於大型結構動態試驗致動器之位移控制。

Servo-hydraulic actuators have been used for tests of structural specimens for decades mainly because of their wide frequency response bandwidth, large force capacity, and high loading rate. In most dynamic tests, hydraulic actuators are used with high velocity and large force requirements which necessitate a closed-loop feedback for tracking control and stabilization. Displacement control of actuators with a proportional-integral-differential (PID) controller is generally applied to dynamic tests of structures; however, PID control performance in high frequency range is normally not satisfactory due to various aspects such as the nature of feedback control, dynamics of electro-mechanical devices, etc. Consequently, improving displacement tracking performance of actuators in high frequency range is essential for dynamic tests of structural specimens.
In this study, cascade control which involves a primary control loop (force control) and a secondary control loop (displacement control) is proposed to improve displacement tracking performance of actuators in high frequency range. In the primary control loop, a force generator is required to generate force reference. Then a PID controller aims to reduce the difference between measured force and reference force, producing a displacement setpoint for the secondary control loop which employs a conventional PID controller for displacement tracking. The proposed cascade control framework is verified by conducting high-level numerical simulation which considers the mechanical components of a typical servo-hydraulic actuator by using Simscape within the Simulink environment. Numerical simulation results demonstrate that the proposed cascade control has superior displacement tracking performance compared to displacement control with inverse compensation.
Furthermore, the proposed cascade control is experimentally validated by controlling the displacement of a simple metallic specimen with single actuator in the structural laboratory. The Bouc–Wen–Baber–Noori model with calibrated parameters is adopted as the force generator for the primary control loop. Experimental results show that the cascade control effectively improves high-frequency dynamic displacement tracking performance of the actuator which is comparable to conventional displacement control with inverse compensation. Finally, the proposed control loop is extended to displacement control of the specimen with two parallel actuators. By applying inverse stiffness compensation for force correction, the two actuators are able to achieve extraordinary displacement tracking performance without introducing undesirable torsion to the specimen.

[1] 姚亭君，邱建國，界面滑移對於震損RC填充牆耐震容量之影響，碩士論文，國立台灣科技大學營建工程系，2021.
[2] Abagnale, C.； Aggogeri, F.； Borboni, A.； Strano, S.； Terzo, M. Dead-zone effect on the performance of state estimators for hydraulic actuators. Meccanica 2016, 52, 2189–2199.
[3] Strano, S.； Terzo, M. Riccati Equation Based Nonlinear Filter： A Case Study for Hydraulic Actuators in the Presence of Dead-Zone.In Advances in Italian Mechanism Science； Springer： Cham, Switzerland, 2017； pp. 145–152.
[4] Lampinen, S.； Koivumäki, J.； Mattila, J.； Niemi, J. Model-Based Control of a Pressure-Compensated Directional Valve with Significant Dead-Zone. In Fluid Power Systems Technology； American Society of Mechanical Engineers： New York, NY, USA, 2019.
[5] Dasgupta, K., & Murrenhoff, H. (2011). Modelling and dynamics of a servo-valve controlled hydraulic motor by bondgraph. Mechanism and Machine Theory, 46(7), 1016–1035. doi：10.1016/j.mechmachtheory.2010
[6] Sung, H.-J.； Lee, J.-H.； Min, H.-K.； Park, M.-K. Robust hydraulic position control based on uncertainty and disturbance estimation.In Proceedings of the 2017 17th International Conference on Control, Automation and Systems (ICCAS), Ramada Plaza, Korea,18–21 October 2017； pp. 1132–1136.
[7] Jin, L.；Wang, Q. Accurate model identification of the inertial mass dynamic of hydraulic cylinder with model uncertainty. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 2018, 233, 501–510.
[8] Zhao, J.； Wang, Z.； Zhang, C.； Yang, C.； Bai, W.； Zhao, Z. Modal space three-state feedback control for electro-hydraulic servo plane redundant driving mechanism with eccentric load decoupling. ISA Transactions, 2018. 77： p. 201-221.
[9] Ayalew, B., & Jablokow, K. W. (2006). Cascaded Robust Nonlinear Position Tracking Control of an Electrohydraulic Actuator： Sliding Mode and Feed Forward. Fluid Power Systems and Technology. doi：10.1115/imece2006-13943
[10] Wos, P. and R. Dindorf (2013). "Adaptive Control of the Electro-Hydraulic Servo-System with External Disturbances." Asian Journal of Control, 2013. 15.
[11] Elbayomy, K.M., J. Zongxia, and Z. Huaqing, PID Controller Optimization by GA and Its Performances on the Electro-hydraulic Servo Control System. Chinese Journal of Aeronautics, 2008. 21(4)： p. 378-384.
[12] Ye, Y., et al., Position control of nonlinear hydraulic system using an improved PSO based PID controller. Mechanical Systems and Signal Processing, 2017. 83： p. 241-259
[13] Fan, Y., J. Shao, and G. Sun, Optimized PID Controller Based on Beetle Antennae Search Algorithm for Electro-Hydraulic Position Servo Control System. Sensors (Basel, Switzerland), 2019. 19(12)： p. 2727.
[14] Fister, D., et al., Parameter tuning of PID controller with reactive nature-inspired algorithms. Robotics and Autonomous Systems, 2016. 84： p. 64-75.
[15] Bouc, R. (1967), “Forced vibration of mechanical systems with hysteresis,” Proceedings of the Fourth Conference on Non-linear oscillation, Prague, Czechoslovakia.
[16] Wen, Y.K. (1976), “Method for Random Vibration of Hysteretic Systems,” ASCE J. Engng. Mech. Div.102(EM2), pp. 249-263.
[17] Baber, T.T. and M.N. Noori, Modeling General Hysteresis Behavior and Random Vibration Application. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1986. 108(4)： p. 411-420.
[18] Foliente, G.C., M.P. Singh, and M.N. Noori, Equivalent linearization of generally pinching hysteretic, degrading systems. Earthquake Engineering & Structural Dynamics, 1996. 25(6)： p. 611-629.
[19] Sengupta, P. and B. Li, Modified Bouc–Wen model for hysteresis behavior of RC beam–column joints with limited transverse reinforcement. Engineering Structures, 2013. 46： p. 392-406.
[20] Jiang, K., Wen, J., Han, Q., & Du, X. (2020). Identification of nonlinear hysteretic systems using sequence model‐based optimization. Structural Control and Health Monitoring, 27(4).doi：10.1002/stc.2500
[21] Chen, P.C., Ting, G.C., and Li, C.H. (2020). A versatile small-scale structural laboratory for novel experimental earthquake engineering. Earthquakes and Structures, 18(3)： p. 337-348.
[22] Ma F, Zhang H, Bockstedte A, Foliente GC, Paevere P. Parameter analysis of the differential model of hysteresis. ASME J Appl Mech.2004；71(3)：342-349.
[23] Chen, Pei‐Ching, and Keh‐Chyuan Tsai. "Dual compensation strategy for real‐time hybrid testing." Earthquake engineering & structural dynamics 42.1 (2013)： 1-23