A new approach to optimal control of vehicle suspension systems, incorporating actuator time delay, is presented. The inclusion of time delay provides a more realistic model for the actuators, and the problem is viewed from a different perspective rather than the conventional optimal control techniques. The objective here is to select a set of feedback gains such that the maximum vertical acceleration of the sprung mass is minimized, over a wide band frequency range and when subjected to certain constraints. The constraints are dictated by the vehicle stability characteristics and the physical bounds placed on the feedback gains. Utilizing a Simple Quarter Car model, the constrained optimization is then carried out in the frequency domain with the road irregularities described as random processes. Due to the presence of the actuator time delay, the characteristic equation is found to be transcendental rather than algebraic, which makes the stability analysis relatively complex. A new scheme for the stability chart strategy with fixed time delay is introduced in order to address the stability issue. The stability characteristics are also verified utilizing other conventional methods such as the Michailov technique. Results demonstrate that the suspension system, when considering the effect of the actuator time delay, exhibits a completely different behavior.
Sum-of-squares based observer design for polynomial systems with a known fixed time delay
