Dual time-delay vibration control and stability analysis for an automotive active suspension system

This paper proposes a dual time-delay control (DTDC) analysis and optimization method for vehicle active suspension systems (ASS) to address the challenges of parameter coupling, stability analysis, and performance coordination in dual time-delay systems. A half-car dualtime-delay ASS model is established to analyze the coupled effects of feedback gains and timedelay parameters on the vehicle's vertical and pitch dynamics. Then, a stability analysis framework based on the cluster treatment of characteristic roots (CTCR) method is developed to accurately determine the stability region of the dual time-delay system. By considering timedelay parameters as independent design variables, the relationship among external excitations, control parameters, and system dynamics is established, enabling the coordinated optimization of stability margins and vibration attenuation performance. Numerical results show that, under harmonic excitation, compared with the multi-objective fuzzy weighted linear quadratic regulator (MOFWLQR), DTDC reduces the root mean square (RMS) values of body vertical acceleration and pitch angular acceleration by 97.86% and 78.27%, respectively. Under ISO class B and class C random road excitations at vehicle speeds of 10-30 m/s, DTDC reduces these two indicators by 3.18% and 2.99% on class B roads, and by 3.05% and 2.93% on class C roads, compared with the passive suspension system (PSS). The results demonstrate that DTDC effectively utilizes the independent regulation capability of dual time-delay feedback to suppress vertical and pitch vibrations while maintaining stability.