Gain-margin based discrete-continuous method for the stability analysis of real-time hybrid simulation systems

Abstract

Stability prediction is a key step to implement a real-time hybrid simulation (RTHS) testing successfully. There are two kinds of stability prediction methods based on continuous and discrete transfer function. In the family of continuous transfer function based methods, the numerical and physical substructures are seen as continuous systems together with loading system. In discrete family, all subsystems in RTHS are regarded as discrete systems. Actually, in a real RTHS, the numerical substructure is discrete; the physical substructure is continuous. Meanwhile, the signal coordination is needed to balance the sampling interval between numerical solution and physical loading, which is ignored in the reported methods. In order to predict the stability of RTHS system more accurately, this work develops a discrete-continuous stability analysis method through the concept of gain margin, which can consider the performance of numerical substructure, physical substructure, loading system and signal coordination comprehensively. And the accuracy of the method is verified by SIMULINK simulation and experimental testing. Based on shaking table and actuator RTHS systems, the performance of continuous and discrete methods is compared with the proposed method analytically. The results show that the discrete method and continuous method have slight influence on the stability prediction with a small integration step (e.g 1 ms). However, with the increase of integration step, compared with the discrete-continuous method, the discrete method and continuous method may overestimate or underestimate the stability of a real RTHS system.