Interpretation of Real-Time Hybrid Simulation as Neutral and Retarded Delay Systems for Its Stability Analysis

As an economical and effective testing method, real-time hybrid simulation (RTHS) can be understood as a dynamic system with substructure feedback, where the time delay in feedback caused by servo-hydraulics may destabilize the system. Existing research does not realize that the time delay in each component has a different effect on stability. This study categorizes RTHS into neutral or retarded delay systems to differentiate their pole distribution and explore how time delay affects the stability. The analysis results show that (1) time delay introduces infinite pairs of conjugate characteristic roots into both neutral and retarded systems but results in different patterns of root distribution; (2) the characteristic roots approach based on the rational function approximation is only suitable for stability analysis of a retarded delay system, not for a neutral delay system; and (3) the definite integral stability analysis approach can directly determine the stability of both retarded and neutral delay systems without solving the transcendental equation. The computational simulation demonstrated the difference between retarded and neutral delay systems and the effectiveness of the new approach. This study provides fresh insights for the dynamic analysis of RTHS system with time delay.