Dual compensation strategy for real-time hybrid testing Pei-Ching Chen 1,2 and Keh-Chyuan Tsai 2, * ,† 1 National Center for Research on Earthquake Engineering, National Taiwan University, Taipei, Taiwan 2 Civil Engineering Department., National Taiwan University, Taipei, Taiwan SUMMARY Real-time hybrid testing is an experimental technique for evaluating the dynamic responses of structural systems under seismic loading. Servo-hydraulic actuators, by nature, induce inevitable time delay between the command and the achieved displacements. This delay would lead to incorrect test results and even cause instability of the system; therefore, delay compensation is critical for stability and accuracy of hybrid simula- tions of structural dynamic response. In this paper, a dual delay compensation strategy is proposed by a combination of a phase lead compensator and a restoring force compensator. An outer-loop feed-forward phase lead compensator is derived by introducing the inverse model in the z domain. The adaptive law based on the gradient algorithm is used to estimate the system delay in the format of parametric model during the test. It is shown mathematically that the parameter in the delay estimator is guaranteed to converge. The restoring force compensator is adopted to improve the accuracy of experimental results especially when the structure is subjected to high frequency excitations. Finally, analytical simulations of an inelastic SDOF structure are conducted to investigate the feasibility of the proposed strategy. The accuracy of the dual compensation strategy is demonstrated through several shaking table tests. Copyright © 2012 John Wiley & Sons, Ltd. Received 9 September 2011; Revised 1 March 2012; Accepted 1 March 2012 KEY WORDS: real-time hybrid testing; delay compensation; adaptive law 1. INTRODUCTION Experimental testing has been widely used to examine the seismic responses of structures in earthquake engineering. Various test methods have been adopted in the past decades, such as quasi- static testing, shake table testing, and pseudo-dynamic testing [1–5]. Recently, many rate-dependent seismic devices have been developed to improve the seismic performance of structural systems under the strikes of earthquakes. These devices, for example, viscous dampers, are sensitive to loading rate. Conventional experimental test methods involving an expanded time scale are therefore no longer applicable for these devices. As a result, real-time hybrid testing or simulation, as presented by its name, has attracted the interests of researchers in recent years. Real-time hybrid testing, combining numerical simulation with experimental testing, provides an efficient method to evaluate the dynamic responses of rate-dependent structural systems subjected to earthquake excitation. During a real-time hybrid test, the equations of motion are solved using a step-by-step integration scheme, where the inertia and damping forces are analytically modeled and the restoring force is measured from the test structure. The measured restoring force is then fed back to the integration algorithm to calculate the command displacement for the next time step. Unlike the conventional testing methods, the command displacements in a real-time hybrid test are imposed by servo-hydraulic actuators in a real-time manner. Inevitably, there is a small but significant enough time delay between the command and the achieved displacements because of the dynamics *Correspondence to: Keh-Chyuan Tsai, Civil Engineering Department, National Taiwan University, Taipei, Taiwan. † E-mail: kctsai@ntu.edu.tw Copyright © 2012 John Wiley & Sons, Ltd. EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. (2012) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.2189