Bifurcation analysis of a wheel‐slip control loop under low wheel‐slip regulation considering time‐delay

Abstract

Safety and efficiency are key aspects of research and development in the automotive industry, especially in the field of safety‐critical subsystems, such as brake systems. The effect of time delay arise in brake systems, this adverse effect can cause performance degradations or make the brake system unstable. In this study, the bifurcation analysis of a wheel slip control feedback loop is presented. The control system consists of a wheel and a tyre, delayed actuator dynamics, and an LQR (linear quadratic regulator) that is designed to operate under relatively low wheel slip, during service braking. As a result, it is shown, that if time delay is neglected, the steady‐state solution of the model is globally stable using the LQ optimal controller gains. However, considering nonzero time‐delay may cause a subcritical Hopf‐bifurcation, and an unstable limit‐cycle exists around the steady‐state solution in a large domain of time‐delay parameters. Critical bifurcation maps and simulation results with more detailed system models are generated and shown in the study.