Stability analysis of optimal time-delayed vehicle suspension systems

A realistic form of active suspension system incorporating the effect of actuator time delay is considered. The resulting time-delayed system is optimized by minimizing the sprung mass maximum peak frequency response. Due to the dynamical behavior of the actuator, the characteristic equation of system is transcendental and the order of equations shall increase. Using a simple quarter-car model, the control parameters are optimally determined by solving a constrained optimization problem. The constraints are dictated by both the vehicle stability characteristics and the physical bounds placed on the feedback gains. A new method of the stability chart strategy, with fixed time delay, is introduced in order to address the stability issue. Results demonstrate that, for a given set of feedback gains, larger values of the actuator time delay reveals to higher values of the peak response of the sprung mass acceleration