A Robust Compensation Strategy Combining H∞ Loop Shaping and Polynomial Extrapolation for Multi-Axial Real-Time Hybrid Simulations

Abstract

Real-time hybrid simulation (RTHS) is a promising experimental method to evaluate structural dynamics. It divides the to be simulated structure into a numerical substructure (NS) and a physical substructure (PS), and has been lauded for its versatility and cost-effectiveness. In RTHS, a transfer system is used to guarantee synchronization among substructures, resulting in the fact that the actuator control scheme plays a vital role in attaining high accuracy and stability. This is particularly true for multi-axial RTHS (maRTHS), where several actuators are used to impose precise controls on the PS. In maRTHS, internal coupling issues are more troublesome, and the control-structure interactions and servo-actuator dynamics are more complicated than in single axial RTHS, making actuator control more challenging. With this in mind, we propose a robust compensation strategy, combining H_∞ loop shaping theory and polynomial extrapolation, to tackle servo-hydraulic dynamics issues for maRTHS problems. The proposed method consists of an H_∞ loop shaping feedback controller and polynomial extrapolation. The former can stabilize the servo-hydraulic actuator and PS dynamics and achieve approximate decoupling among the actuators, while the latter will further reduce the time delay as well as amplitude discrepancies. The integration of these control strategies facilitates a flexible design scheme that handles various uncertainties and has high stability. Initially, a comprehensive design procedure of the proposed method is provided. Subsequently, the effectiveness of this method is demonstrated through a series of virtual RTHSs, using a recently established maRTHS benchmark model. The simulated results indicate that the proposed approach holds considerable promise for high-precision experiment synchronization, and robustness in the face of uncertainties, including numerical structure variability, seismic excitations, and multiple-actuator properties.