Robust Stability and Performance Analysis for Multi-actuator Real-Time Hybrid Substructuring

Real-time hybrid substructuring (RTHS) is a relatively new method of vibration testing for characterizing the system-level performance of physical components or substructures. With RTHS, the coupled system is partitioned into physical and numerical substructures and interfaced together in real-time as cyber-physical system similar to hardware-in-the-loop testing. Control actuation and sensing is used to enforce the compatibility and equilibrium conditions between the physical and numerical substructures. Since RTHS involves a feedback loop, the frequency-dependent magnitude and inherent time delay of the actuator dynamics can introduce inaccuracy and instability. This paper presents a robust stability and performance analysis method for multi-actuator RTHS based on robust stability theory for multiple-input-multiple-output (MIMO) feedback control. This analysis 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 robust stability and performance analysis method is that it accommodates linearized modeled or measured frequency response functions for both the physical substructure and actuator dynamics.