A robust stability and performance analysis method for multi-actuator real-time hybrid simulation

Real-time hybrid simulation (RTHS) is a relatively new method of vibration testing for characterizing the system-level dynamic response of physical hardware components or substructures. With RTHS, a structural dynamic system can be partitioned into separate physical and numerical substructures and interfaced together in real time as a cyber-physical system similar to hardware-in-the-loop testing. Control actuation and sensing are used to enforce the compatibility and equilibrium conditions between the physical and numerical substructures. Since RTHS involves a feedback loop, the frequency-dependent dynamics of the actuator transfer system can introduce inaccuracy and potential instability during closed-loop testing. This paper presents a robust stability and performance analysis method for multi-actuator RTHS based on concepts from robust stability theory for multiple-input multiple-output (MIMO) feedback control. This method involves casting the actuator dynamics as a multiplicative uncertainty and applying the small gain theorem to derive the sufficient conditions for robust stability and performance. The attractive feature of this method is that it accommodates linearized modeled or measured frequency response functions for the physical substructure and actuator dynamics. The method is demonstrated using Network for Earthquake Engineering Simulation (NEES) experimental data from a two-actuator RTHS test of a seismically excited two-story steel frame structure. Results show that the robust stability and performance analysis method provides a versatile and useful tool for pre-test planning and post-test diagnostics of RTHS tests involving multiple actuators.