即時複合實驗(real-time hybrid testing, RTHT)技術為近年國內外地震工程研究領域逐漸採用之動力實驗研究方法。由於RTHT係將待測試之結構系統拆解為數值子結構與物理子結構二個部份，其中僅後者需進行實體測試，前者之反應則以電腦加以模擬，因此相較於傳統全模型振動台實驗，可有效降低實驗之成本；而若與全模型數值模擬比較，則RTHT之實驗結果則更接近真實之地震反應。然而RTHT於鋼筋混凝土(RC)結構之應用較為少見，主要係因為RC結構力學特性較複雜，且具有勁度及強度衰減之行為與較高之初始勁度，使得油壓伺服致動器難以精確控制。有鑑於此，本文旨在以簡化之剪力屋結構模型建立RC結構RTHT之實驗平台，並以一棟七層樓RC結構之振動台實驗加以驗證。所建立之實驗平台將引入虛擬柱之概念，以克服當RTHT實驗中數值子結構為不穩定結構時易產生之動力不穩定現象，且可改善油壓致動器控制誤差所導致之實驗誤差。同時該平台之硬體設備係採用光纖記憶體共享之數位控制器及Simulink軟體所構成。
　　為便於了解中高樓RC結構於地震力下之耐震反應，國家地震工程研究中心曾於其台南實驗室進行1/2縮尺之七層樓RC結構振動台實驗。因此本文期能以所發展之虛擬柱RTHT實驗平台及簡化之剪力屋RC構架數學模型，重現該7層樓RC結構之振動台實驗結果。為達此目的，本文首先以實驗方法探討各類時間延遲補償器(time-delay compensator)對油壓控制系統之補償功效，研究發現以離散時域逆轉換補償器(inverse compensation method，ICM)於單自由度雙跨RC構架之RTHT前導實驗最為穩定且有效。惟ICM補償器在七層樓RC結構之RTHT中則仍會發生不穩定之發散現象。因此，本文提出含線性或非線性虛擬柱之RTHT實驗構想，並推導其理論公式及以實驗加以驗證。在小地震力作用下，實驗與理論結果皆顯示，含線性虛擬柱之RTHT實驗的確可消除系統不穩定的問題，且可有效改善硬體設備控致誤差所產生的實驗誤差，若與理論模擬結果比較，含線性虛擬柱之RTHT各樓值反應峰值誤差約僅1%左右；而與振動台實驗結果比較則顯示各樓層之加速度反應十分接近，其峰值與頻率差異亦不大。惟於大地震力作用下，則因受限於油壓致動器性能不足無法進行RC試體進入非線性行為，故改以數值模擬方式進行含非線性虛擬柱之RTHT實驗研究(含致動器之時間延遲效應)，其模擬實驗結果顯示，非線性虛擬柱仍可有效大幅改善實驗穩定性問題，但卻無法完全消除硬體設備之控制誤差，使得RTHT實驗結果與理論分析結果產生較大的誤差，而加入ICM補償器對於實驗結果之改進則十分有限。

Real-time hybrid testing (RTHT) technology is a kind of experimental method which widely utilized in earthquake engineering for studying in recent years. However, the application of RTHT for reinforced concrete (RC) structures is very rare due to the complex mechanical properties of the RC structures. The RC structures have a very high initial stiffness and stiffness and strength decay with large deformation, which may make the actuators in RTHT are difficult to be controlled as desire. To solve the problem, this paper is to provide a RTHT testing technique for a RC structure with a simple numerical model. To verify the accuracy of the RTHT for a 1/2-scaled seven-story RC structure, the RTHT results are compared with the shaking table test (STT) results. Moreover, the computed control command of the RTHT will diverge, due to the unstable numerical substructure (NS) model. Therefore, this paper proposes a compensation method which adds a linear or nonlinear virtual columns into the unstable NS model, the theoretical formula will be introduced, and be verified by using the RTHT.
　　The comparison of the RTHT results and the theoretical results shows that under the small-scale earthquake excitation, the problem of system instability in the RTHT can be eliminated by using the linear virtual column and the control error caused by of hardware equipment also can effectively be reduced. Moreover, the peak error of each floor in the RTHT results with a linear virtual column is only about 1% which are compared with the theoretical results. The comparison of the RTHT results and the STT results shows that acceleration responses of each floor in the RTHT is very close with those of the shaking table test, and the differences of the peak values and the frequency responses between the RTHT results and the STT results are quite small. However, the nonlinear RTHT test of the RC specimen under the large-scale earthquake excitation is not able to be carried out due to the limitation of the performance of the actuator used in the RTHT. But, the numerical analysis of the RTHT with a nonlinear virtual column (considering the control delay time of the actuator) will be introduced in this paper The simulation results show that the stability of the RTHT test with the nonlinear virtual column also can be effectively improved, but the control error of the hardware equipment is not able to be eliminated, which will cause large error between the RTHT results and the theoretical results.

1. Aktan HM. (1986) “Pseudo‐dynamic testing of structures.” Journal of Engineering Mechanics. 112(2):183-197.
2. Balendra T, Lam KY, Liaw CY, Lee SL. (1987) “Behavior of eccentrically braced frame by pseudo‐dynamic test.” Journal of Structural Engineering. 113(4):673-688.
3. Buchholz JJ, von Grünhagen W. (2008) “Inversion impossible.” GRIN Verlag. 1st Edition.
4. Carrion JE and Spencer BF. (2006) “Real-time hybrid testing using model-based delay compensation.” The 4th International Conference on Earthquake Engineering. Taipei, Taiwan. October 12-13.
5. Chae Y, Kazemibidokhti K, Ricles JM. (2013) “Adaptive time series compensator for delay compensation of servo-hydraulic actuator systems for real-time hybrid simulation.” Earthquake Engineering and Structural Dynamics. 42(11):1697-1715.
6. Chae Y, Lee J, Park M, Kim CY. (2018) “Real‐time hybrid simulation for an RC bridge pier subjected to both horizontal and vertical ground motions.” Earthquake Engineering and Structural Dynamics. 47(7):1673-1679.
7. Chen C and Ricles JM. (2009) “Analysis of actuator delay compensation methods for real-time testing.” Engineering Structures. 31(11):2643-2655.
8. Chen PC, Chang CM, Spencer BF, Tsai KC. (2014) “Model-based tracking control framework for real-time hybrid simulation.” The 12th International Conference on Motion and Vibration Control. Hokkaido, Japan. August 3-7.
9. Chen PC, Dong MW, Chen PC, Nakata N. (2020) “Stability analysis and verification of real-time hybrid simulation using a shake table for building mass damper systems.” Frontiers in Built Environment. 2020(6):109.
10. Chu SY, Lu LY, Yeh SY. (2018) “Real-time hybrid testing of a structure with a piezoelectric friction controllable mass damper by using a shake table.” Structural Control and Health Monitoring. 25(3):e2124.
11. Darby AP, Williams MS, Blakeborough A. (2002) “Stability and delay compensation for real-time substructure testing.” Journal of Engineering Mechanics. 128(12):1276-1284.
12. Guo W, Zeng C, Gou H, Gu Q, Wang T, Zhou H, Zhang B, Wu J. (2021) “Real-time hybrid simulation of high-speed train-track-bridge interactions using the moving load convolution integral method.” Engineering Structures. 2021(228):111537.
13. Guo W, Yang Z, Feng Q, Dai C, Yang J, Lei X. (2022) “A new method for band gap analysis of periodic structures using virtual spring model and energy functional variational principle.” Mechanical Systems and Signal Processing. 2022(168):108634.
14. Hakuno M, Shidawara M and Hara T. (1969) “Dynamic destructive test of a cantilever beam controlled by an analog-computer.” Transactions Japan Society of Engineers. 1969(171):1-9.
15. Hashemi MJ, Al-Ogaidi Y, Al-Mahaidi R, Kalfat R, Tsang H-H, Wilson JL. (2017) “Application of hybrid simulation for collapse assessment of post-earthquake CFRP-repaired RC columns.” Journal of Structural Engineering. 143(1):04016149.
16. He WH, Xiao Y, Guo YR, Fan YL. (2013) “Pseudo-dynamic testing of hybrid frame with steel beams bolted to CFT columns.” Journal of Constructional Steel Research. 2013(88):123-133.
17. Hong Y, Tang Z, Liu H, Li Z, Du X. (2021) “Gain-margin based discrete-continuous method for the stability analysis of real-time hybrid simulation systems.” Soil Dynamics and Earthquake Engineering. 2021(148):106776.
18. Horiuchi T, Inoue M, Konno T, Namita Y. (1999) “Real-time hybrid experimental system with actuator delay compensation and its application to a piping system with energy absorber.” Earthquake Engineering and Structural Dynamics. 28(10):1121-1141.
19. Huang L, Chen C, Guo T, Chen M. (2019) “Stability analysis of real-time hybrid simulation for time-varying actuator delay using the Lyapunov-Krasovskii functional approach.” Journal of Engineering Mechanics. 145(1):04018124.
20. Kim JG, Nam KU, Kang YJ. (2020) “Method to estimate rotational stiffness: Trial masses, virtual masses, and virtual springs.” Journal of Sound and Vibration. 2020(477):115321.
21. Li H, Maghareh A, Montoya H, Condori Uribe JW, Dyke SJ, Xu Z. (2021) “Sliding mode control design for the benchmark problem in real-time hybrid simulation.” Mechanical Systems and Signal Processing. 2021(151):107364.
22. Li T, Ma L, Sui Y, Su M, Qiang Y. (2020) “Soft real-time hybrid simulation based on a space steel frame.” Bulletin of Earthquake Engineering. 2020(18):2699-2722.
23. Li T, Su M, Sui Y, Ma L. (2021) “Real-time hybrid simulation on high strength steel frame with Y-shaped eccentric braces.” Engineering Structures. 226(11):111369.
24. Meijering E. (2002) “A Chronology of Interpolation : from ancient astronomy to modern signal and image processing.” Processing of the IEEE. 90(3):319-342.
25. Nakashima M, Kato H, Takaoka E. (1992) “Development of real-time pseudo dynamic testing.” Earthquake Engineering and Structural Dynamics. 21(1):79-92.
26. Nakashima M and Masaoka N. (1999) “Real-time on-line test for MDOF systems.” Earthquake Engineering and Structural Dynamics. 28(4):393-420.
27. Ning X, Wang Z, Wu B. (2020) “Kalman filter-based adaptive delay compensation.” Applied Sciences. 10(20):7101.
28. Paquette J and Bruneau M. (2003) “Pseudo-dynamic testing of unreinforced masonry building with flexible diaphragm.” Journal of Structural Engineering. 129(6):708-716.
29. Park J, Strepelias E, Stathas N, Kwon O-S, Bousias S. (2021) “Application of hybrid simulation method for seismic performance evaluation of RC coupling beams subjected to realistic boundary condition.” Earthquake Engineering and Structural Dynamics. 50(6):375-393.
30. Reinhorn AM, Sivaselvan MV, Liang Z, Shao X. (2004) “Real-time dynamic hybrid testing of structural systems.” The 13th World Conference on Earthquake Engineering. Vancouver, Canada. August 1-6.
31. Sadraddin HL, Cinar M, Shao X, Ahmed M. (2020) “Testing platform and delay compensation methods for distributed real-time hybrid simulation.” Experimental Techniques. 44(6):787-805.
32. Saouma V, Haussmann G, Kang DH, Ghannoum W. (2014) “Real-time hybrid simulation of a nonductile reinforced concrete frame.” Journal of Structural Engineering. 140(2):04013059.
33. Schellenberg AH, Becker TC, Mahin SA. (2017) “Hybrid shake table testing method: Theory implementation and application to midlevel isolation.” Structural Control and Health Monitoring. 24(5):e1915.
34. Shao X, Mueller A, Mohammed BA. (2016) “Real-time hybrid simulation with online model updating methodology and implementation.” Journal of Engineering Mechanics. 142(2):04015074.
35. Speedgoat “Target Machine Setup Guide”.
36. Strano S and Terzo M. (2016) “Actuator dynamics compensation for real-time hybrid simulation an adaptive approach by means of a nonlinear.” Nonlinear Dynamics. 2016(85):2353-2368.
37. Sun YB, Cao TJ, Xiao Y. (2019) “Full-scale steel column tests under simulated horizontal and vertical earthquake loadings.” Journal of Constructional Steel Research. 2019(163):105767.
38. Suzuki T, Puranam AY, Elwood KJ, Lee HJ, Tsai RJ, Hsiao FP, Hwang SJ. (2019) “Seismic response of half-scale seven-story reinforced concrete structure with torsional and damage irregularities.” International Conference in Commemoration of 20th Anniversary of the 1999 Chi-Chi Earthquake. Taipei, Taiwan. September 15-19.
39. Tang D, Chen L, Tian ZF, Hu E. (2020) “Developing a virtual stiffness-damping system for airfoil aeroelasticity testing.” Journal of Sound and Vibration. 2020(468):115061.
40. Tommasino P, Melendez-Calderon A, Burdet E, Campolo D. (2014) “Motor adaptation with passive machines: A first study on the effect of real and virtual stiffness.” Computer Methods and Programs in Biomedicine. 2014(116):145-155.
41. Waldbjoern JP, Maghareh A, Ou G, Dyke SJ, Stang H. (2021) “Multi-rate Real Time Hybrid Simulation operated on a flexible LabVIEW real-time platform.” Engineering Structures. 2021(239):112308.
42. Wang Z, Ning X, Xu G, Zhou H, Wu B. (2019) “High performance compensation using an adaptive strategy for real-time hybrid simulation.” Mechanical Systems and Signal Processing. 2019(133):106262.
43. Wang Z, Yan X, Ning X, Wu B. (2020) “Test verification of two-stage adaptive delay compensation method for real-time hybrid simulation.” Shock and Vibration. 2020:7848421.
44. Witteveen W, Koller L, Penninger D. (2022) “Non-simultaneous real-time hybrid simulation of a numerical and experimental mechanical system with moderate nonlinearities via iterative coupling based on Frequency Response Functions.” Mechanical Systems and Signal Processing. 2022(163):108055.
45. Woods JE, Lau DT, Erochko J. (2020) “Evaluation by hybrid simulation of earthquake-damaged RC walls repaired for in-plane bending with single-sided CFRP sheets.” Journal of Composites for Construction. 24(6):04020073.
46. Wu B, Wang Z, Bursi OS. (2012) “Nearly-perfect compensation for time delay in real-time hybrid simulation.” The 15th World Conference on Earthquake Engineering. Lisbon, Portugal. September 24-28.
47. Wu B, Wang F, Han W. (2022) “Virtual element method for a frictional contact problem with normal compliance.” Communications in Nonlinear Science and Numerical Simulation. 2022(107):106125.
48. Yu Z, Peng P, Runhua G, Tao W, Weichen X. (2017) “Substructure hybrid testing of reinforced concrete shear wall structure using a domain overlapping technique.” Earthquake Engineering and Engineering Vibration. 16(4):761-772.
49. Zhou C, Fang C, Kandic M, Wang P, Kent K, Menzies D. (2021) “Large-scale hybrid real time simulation modeling and benchmark for nelson river multi-infeed HVdc system.” Electric Power Systems Research. (2021)197:107294.
50. 呂仲岳 (2017) “應用即時複合實驗進行配置PFCMD多自由度系統控制參數之最佳化探討”，國立成功大學土木工程研究所，碩士論文。指導教授：朱世禹。
51. 林煒松 (2019) “採用不同振動台進行即時複合實驗之效能探討”，國立成功大學土木工程研究所，碩士論文。指導教授：朱世禹。
52. 林錦洋 (2021) “足尺變曲率滑動隔震結構之即時複合實驗”，國立成功大學土木工程研究所，碩士論文，九月。指導教授：盧煉元。
53. 徐安 (2019) “即時複合實驗於互制式減震系統效能驗證之應用”，國立成功大學土木工程研究所，碩士論文，九月。指導教授：盧煉元。
54. 陳沛清，蔡克銓 (2013) “地震工程即時複合試驗技術之研究”，國家地震工程研究中心，NCREE-13-001。
55. 國家地震工程研究中心 (2018) “國震中心台南實驗室啟動實驗規劃書”。
56. 黃炫文 (2021) “OpenFresco於鋼筋混凝土構架複合實驗之應用及驗證”，國立成功大學土木工程研究所，碩士論文，九月。指導教授：盧煉元。
57. 黃語彤 (2018) “高樓配置半主動模糊控制LSCMD之即時複合實驗驗證”，國立成功大學土木工程研究所，碩士論文。指導教授：朱世禹。
58. 葉士瑋 (2017) “具摩擦特性振動控制系統即時複合實驗之振動台實驗驗證”，國立成功大學土木工程研究所，博士論文，七月。指導教授：朱世禹、盧煉元。
59. 葉士瑋，張汎博，盧煉元，蕭輔沛 (2021) “PRTTM記憶體共享即時控制器標準作業程序書”，國家地震工程研究中心，NCREE-21-010。
60. 雷凱婷 (2020) “TMD於離岸風機結構之減震效能振動台實驗與即時複合實驗研究”，國立成功大學土木工程研究所，碩士論文，九月。指導教授：盧煉元。
61. 蕭予欣 (2019) “考慮進斷層脈衝效應之隔震設計法及其機率式性能評估”，國立成功大學土木工程研究所，碩士論文，七月。指導教授：盧煉元、蕭輔沛。