Stability Analysis of Real-Time Hybrid Simulation with a Tuned Liquid Damper

Real-time hybrid simulation (RTHS) is a form of testing where the physical component of structure communicate with numerical model which simulates the behavior of the rest of the structure. Interface forces between the experimental and computational substructure are imposed by an actuator. The resulting displacement and velocity of the experimental substructure are fed back to the computational engine to determine the interface forces applied to the computational and experimental substructures for the next time step. In this paper, the RTHS technique is used to conduct experiments with a numerically simulated structure and physically tested tuned liquid damper (TLD). One very important factor which causes instability in RTHS is the actuator's inability to perform the commands from the simulator in real-time. In RTHS, an actuator dynamic is approximated by a pure time-delay, and the time-delay in the closed loop system causes inaccuracy results or even instability. Therefore, Delayed Differential Equation (DDE) is used to determine the critical time-delays depending on the TLD parameters. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio has a lower limit for low delays and upper limit for high delays to remain stable. As frequency and amplitude ratios increase, the margin of stability for the mass ratio increases.