After being developed and investigated in the last decades, research on RTST has gained important achievements and the research is currently facing challenges on both numerical and experimental problems. Achievements on RTST can be seen in the development of algorithms and experimentations for testing and the collaboration between structural laboratories in the world.
Various integration schemes are currently used for RTST such as the CDM, OS and α- OS methods (Nakashima et al. 1990, Combescure and Pegon 1997, Tada et al. 2007), predictor-corrector method (Ghaboussi et al. 2006), Newmark-β implicit with sub-step control (Roik and Dorka 1989, Dorka et al. 1998). The simplest and most popular method is CDM; however, it is not suitable for testing structural systems with high range of frequencies because of its conditional stability. Implicit methods such α-OS, predictor-corrector method, etc., are more accurate because these methods use highly accurate integration schemes to obtain the implicit solution of the numerical part at the next step. Different techniques are used in implicit integration schemes to deal with the interaction between substructures. The OS and α-OS methods apply their prediction displacements as explicit terms on the experiment, correct the restoring force by using stiffness and solve for the implicit response of the numerical substructure at the end of the next step. An analog feedback (Thewalt and Mahin 1987) or digital feedback with sub-step control (Dorka et al. 1998) can be used to deal with such interaction between the numerical and the experimental substructure within a time step.
Although several algorithms have been developed, substructure research is still facing with some problems on accuracy and stability. Implicit integrations as Newmark-β implicit schemes with low numerical damping effect (or no numerical damping) are usually preferred because of their high accuracies. However, numerical errors in the integration processes and errors due to time lag in control system may cause instability in tests of low damping structures. In contrast, other algorithms with certain numerical damping can assure stability, however they usually induce high numerical damping in high frequency range. This may cause poor accuracy in the substructure simulation at high frequencies.
Experimentally, there are some problems on real-time control of hydraulic systems for RTSTs. The first problem is that the response of hydraulic system is relatively good in low frequencies but poor in the high frequency range. The considered range of frequencies in dynamic response of structures in civil engineering is about from 0.1 Hz to 20 Hz. On the other hand, both, the hydraulic system and the experimental structures, are usually run as nonlinear systems. Thus, a traditional Proportional - Integral - Differential (PID) control cannot provide highly accurate response in the required range of frequencies. Some advanced control methods such as adaptive inverse control (Wildrow et al. 1995), Minimal Synthesis Control (MCS) (Stoten et al.
1990, 1994, 1998, 2001, Hodgson et al. 1999, Bonnet et al. 2007) and high gain adaptive control (Bobrow et al. 1995) can be used to improve response of hydraulic system in higher range of frequencies.
The second issue is time lag phenomenon in hydraulic system. As presented by Horiuchi et al. (2001), time lag introduces negative damping into the substructure test system. The effect of negative damping results in an increasing response of the tested structure and may cause instability in RTST if the negative damping is larger than the structural damping. There are some phase lag compensations such as time delay prediction (Horiuchi et al. 2001), Darby's time delay compensation (Darby et al. 2001) and model based method (Spencer at al. 2007). These methods still have some disadvantages (see section 4.2). Therefore, phase lag compensation is still a critical issue in RTST.
Currently, topics relating to substructure simulation are discussed and investigated in earthquake engineering laboratories as well as in collaborations among Japan, United States, European countries, China and Taiwan. An interesting topic is geographically distributed testing among laboratories in the world. The major advantage of distributed testing is to enhance testing capabilities and to exchange and share experiences among laboratories. In order to do this, a software framework is needed for distributing the several numerical and experimental activities of a test into different simulation systems and experimental sites and connecting them together via Intranet or Internet (Pearlman et al. 2004, Pan et al. 2005, 2006, Mosqueda et al. 2005, Kwon et al. 2005, Yang et al. 2007, Wang et al. 2007). The research programs with intensive investigation on RTST and network collaboration are hybrid simulation at NEES (the Network for Earthquake Engineering Simulation in USA (http://www.nees.org/), E- Defense in Japan (Ohtani et al. 2003), E-FAST and SRIES projects in Europe. Some
distributed tests have just been performed in Japan (Pan et al. 2006), in Taiwan (Yang et al. 2007) and in France (Dorka et al. 2007).
For a short summary on the state of the art, RTST has been actively developed in the last decades and attained a number of achievements on the testing method as well as test facilities. However, the research on RTST is still in need of further development.
2 CONTROL OF SUBSTRUCTURE TEST
The main purpose of this chapter is to review the background of numerical methods and control algorithms for substructure testing. From discussion on the methods, an advanced substructure control algorithm will be selected for further investigation and development in this thesis.