Stability analysis of real time hybrid simulation under coupled actuator delay and nonlinear behavior

Abstract

Stability of real time hybrid simulation (RTHS) has attracted considerable attention since actuator delay would deviate experiment results or even destabilize the real-time test. Previous studies have extensively investigated stability of RTHS for linear systems, while stability of RTHS for nonlinear system remains unclear. This study introduces the Takagi-Sugeno (T-S) method to describe the nonlinear behavior in a piecewise linear way, then investigates the stability of nonlinear system with time delay through the Lyapunov-Krasovskii (L-K) theory.Such approach successfully solves the stability problem of RTHS with coupled bilinear-hysteresis substructure and actuator delay, and proposes a stability criterion in the form of linear matrix inequality (LMI). It proves that the stability of RTHS is determined by the most unfavorable state of nonlinear system. In the SDOF case with stiffness softening, the initial elastic state is the most unfavorable; while for the MDOF case with multiple delays, the stability is determined by the overlap part of stable region of each nonlinear state. The computational simulation and experimental results show that the difference between linear-and nonlinear hysteretic system with time delay is that when instability occurs, latter could remain energy balanced since the time-delay energy is dissipated by hysteresis behavior, while energy accumulates in the former leading to unbounded responses. The proposed approach provides a potential tool for experimental design of RTHS before the test, the time-delay control during the test and error evaluation after the test.

Development of an explicit time integration algorithm based on optimal integration parameter updating

“…Hence, the direct integration method plays an important role in solving many complicated problems in structural dynamics, 1,2 such as the finite element analysis, 3 quasi-dynamic test 4 and real-time substructure test. [5][6][7][8][9][10] The direct integration methods can be categorized into implicit and explicit ones according to their respective characteristics. 11 For the structural response of low-order modes, the implicit method is generally preferred since it is designed to possess unconditional stability and controllable numerical dispersion.…”

“…However, when it comes to the nonlinear transient response analysis of large and complex structural systems, the direct integration method possesses more obvious applicability owing to its advantages in avoiding understanding of high‐level mathematics and easy realization in numerical computation. Hence, the direct integration method plays an important role in solving many complicated problems in structural dynamics, 1,2 such as the finite element analysis, 3 quasi‐dynamic test 4 and real‐time substructure test 5–10 …”