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Real-time hybrid simulation (RTHS) is a widely applied test method in structural engineering, which is developed from pseudo-dynamic test. Much of the past work has been centered on one-dimensional RTHS using a single hydraulic actuator. When the complexity of the problem demands to increase the number of degrees of freedom to be enforced on the boundary conditions, more than one hydraulic actuator must be used. Multiple-actuator or multi-axial RTHS (maRTHS) requires that more than one hydraulic actuator exerts the required motion on experimental substructures demanding the implementation of multiple-input multiple-output (MIMO) control strategies. A new maRTHS benchmark control problem has been developed, focusing on a frame subjected to seismic load at the base, substantially transforming and intensifying the complexity of the problem. The time delay generated by the dynamic characteristics of the loading system and the transmission process as well as the high coupling between the hydraulic actuators and the nonlinear kinematics escalates the complexity of the actuator control tracking. A sliding mode adaptive delay compensation method suitable for maRTHS is proposed, which utilizes a MIMO sliding mode method to reduce the coupling effects of actuators and the adaptive compensation method to compensate the residual delay. The effectiveness of the method is verified by numerical simulating different working conditions in the Benchmark Problem Platform.

Shaking table substructure testing (STST) takes the substructure with complex behavior physically tested, with the behavior of the rest structural system being numerically simulated. This substructure testing allows the payload of a shaking table being fully utilized in testing of the most concerned part, thus significantly increases its loading capacity. The key to achieve a successful STST is to coordinate among the substructures, specifically, to satisfy compatibility, equilibrium, and synchronization at the boundary between numerical and experimental substructures. A number of studies have focused on the essential techniques of STST, and several applications have been carried out. Nonetheless, its progress is still in the preliminary stage, because of the limited applications using multi-directional shaking tables on large-scale specimens. This paper reviews a series of STSTs and their associated implementation aspects including hybrid testing frameworks, time integration algorithms, delay compensation methods, shaking table and actuator control schemes and boundary force measurement methods. The key techniques required for a successful test are also stressed, such as the force control of actuators to coordination among the substructures. Finally, challenges for future studies and applications are identified and presented.