Relative stability analysis for robustness design of real-time hybrid simulation

Stability is a prerequisite of a successful real-time hybrid simulation (RTHS), which depends on the timeintegration algorithm, the delay-compensation method, the loading system dynamics (mostly characterized as a time delay), and the nonlinearity of the structures being tested. The existing stability analysis methods generally provide a qualitative judgement based on one or some of the factors above, without considering all these factors to estimate quantitative stability margin. However, it is critical to design a robust RTHS system with enough stability margin (i.e., robust RTHS system) to ensure the success of the actual test with inescapable uncertainties. To this end, a relative stability analysis method for robustness design of RTHS systems is proposed. In this method, the critical gain of the stiffness of an experimental substructure is used to quantify the stability limit, and the critical delay is used to quantitatively represent the sensitivity of an RTHS system to the phase discrepancy at the interface. The RTHS system with a nonlinear experimental substructure is modeled by a discrete transfer function in an incremental form, wherein the time-integration algorithm, the delaycompensation method, the loading system dynamics, and the nonlinearities of the experimental substructure are considered. The critical delay and gain are obtained from the discrete transfer function. Two relative stability criteria are proposed based on the critical delay and the critical gain of an RTHS system to facilitate the evaluation of the system's stability performance and the design of a robust RTHS system. To verify the critical delay and gain estimated using the proposed method, numerical simulation of RTHS systems was carried out first. Then RTHS experiments of single-degree-of-freedom models with experimental substructures consisting of a linear spring and a nonlinear stiffness hardening specimen were conducted. The consistent results of the numerical simulation and the physical RTHS tests with those derived from the proposed relative stability analysis method demonstrate its effectiveness and accuracy in determining the stability properties of RTHS systems, which can be further utilized in designing more robust RTHS testing systems.