Optimal vibration control for vehicle active suspension systems with controller delays

The optimal vibration control for vehicle active suspension systems with controller delay is considered. The time delay for the controller is assumed as uncertain time-invariant but has a known constant bound, and the dynamic models for the 2-degree-freedom quarter-car suspension system and the time domain model for the road roughness stochastic power input are established. Then, according to the standards of road comfort and road holding the optimal state feedback vibration control law is designed, which can be obtained optimally through Riccati and Sylvester equations. The optimal vibration control law is proved to be unique. It is confirmed by the simulations that the designed controller can not only preserve the closed-loop stability in spite of the existence of the actuator time delay within allowed bound but achieve a better performance enhanced by 50% than the delay-independent controller.