Optimal Vibration Control for Vehicle Active Suspension Discrete‐Time Systems with Actuator Time Delay

This study researches the vibration control approach for vehicle active suspension discrete-time systems with actuator time delay under road disturbances. First, the discrete-time models for the quarter vehicle active suspension system with actuator time delay are presented, and road disturbances are considered as the output of an exosystem. By introducing a discrete variable transformation, the discrete-time system with actuator time delay and the quadratic performance index are transformed into equivalent ones without the explicit appearance of time delays. Then, the problem of original vibration control with actuator time delay is transformed into the optimal vibration control for a non-delayed system with respect to the transformed performance index. Based on the maximum principle, the feedforward and feedback optimal vibration control law is obtained from Riccati and Stein equations. The existence and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator. Finally, the feasibility and effectiveness of the proposed approaches are validated by a numerical example.