Modified Runge-Kutta Integration Algorithm for Improved Stability and Accuracy in Real Time Hybrid Simulation

Abstract

Stability in Real Time Hybrid Simulation (RTHS) has been shown to be largely affected by system dynamics and associated phase lags. This lag typically originates in the physical components and considerable research has been conducted to compensate for it. Within the computational component of RTHS, different time integration algorithms are employed to achieve a more stable and accurate solution, mostly focusing on dissipating the high frequency content in the model. However, in RTHS, an inherent computational delay exists in the force measurement due to the sequential nature of communication between the numerical and experimental sub- structures. In this article, it is demonstrated that this computational delay affects performance and stability of closed loop RTHS even when no other delays or phase lags are present. This finding is validated through theoretical derivation and simulation results. A modified Runge-Kutta (MRK) integration algorithm is proposed to reduce the effect of computational delay.The MRK integration involves a three-stage computation: (1) the pseudo response is calculated using the delayed force measurement; (2) feedback force from the physical component for the next step is predicted using the pseudo response; and (3) the corrected structural response is then computed using the predicted feedback force. Both analytical and simulation results confirm that the MRK integration scheme is stable and accurate for a wide range time steps and is robust with respect to modeling error and nonlinearity in the experimental substructure. A moment-resisting frame is used as the experimental substructure in different cases of RTHS to validate the MRK integration method. This approach can also be adapted to other existing numerical integration schemes by applying the proposed three-stage computation process approach.