Stability analysis of MDOF real-time dynamic hybrid testing systems using the discrete-time root locus technique

摘要

The time delay resulting from the servo hydraulic systems can potentially destabilize the real-time dynamic hybrid testing (RTDHT) systems. In this paper, the discrete-time root locus technique is adopted to investigate the delay-dependent stability performance of MDOF RTDHT systems. Stability analysis of an idealized two-story shear frame with two DOFs is first performed to illustrate the proposed method. The delay-dependent stability condition is presented for various structural properties, time delay, and integration time steps. Effects of delay compensation methods on stability are also investigated. Then, the proposed method is applied to analyze the delay-dependent stability of a single shaking table RTDHT system with an 18-DOF finite element numerical substructure, and corresponding RTDHTs are carried out to verify the theoretical results. Furthermore, the stability behavior of a finite element RTDHT system with two physical substructures, loaded by twin shaking tables, is theoretically and experimentally investigated. All experimental results convincingly demonstrate that the delay-dependent stability analysis on the basis of the discrete-time root locus technique is feasible.