Controlling quarter car suspension system by proportional derivative and positive position feedback controllers with time delay

The active car suspension system is presented here to suppress the vibration of the car by applying proportional derivative (PD) and positive position feedback (PPF) controllers with time delay. The control signal output of the controller is applied electrically to the magneto-rheological (MR) damper or Electrical-rheological (ER) damper which is attached parallel to the passive components to improve the suppression of the vibration. The electrical control signal is produced by electronic circuits or programmable logic controller and the two-position sensor feedback signal which are connected to the controller. The approximate solutions of PD and PPF suspension systems are obtained by applying multiple time scales perturbation method. The effects of parameters variation of both the system and the controllers are investigated to achieve the best performance. Simulation results show good performance of the designed controllers