Back-Stepping Sliding Mode Controller Design for Vehicle Seat Vibration Suppression Using Magnetorheological Damper

Purpose This paper presents a back-stepping sliding mode control method for vehicle suspension system with magnetorheological damper to obtain both the true nominal optimal suspension performance and better robustness. Through the study of control method, the acceleration of sprung mass is reduced, that is, the vertical vibration of vehicle is suppressed. Methods A back-stepping sliding mode controller based on the establishment of the quarter-body MR suspension dynamic model, and it used the approximate skyhook-damping system as the reference model. The error dynamic equation is obtained through the MR suspension model and the reference model, and the error dynamic component is used as the back-stepping control parameter. On the premise of ensuring the system is asymptotically stable, adding the sliding mode surface to the dynamic equation of the third error subsystem can complete design of the back-stepping sliding mode controller. By constructing a magnetorheological damper experimental platform and then collecting the measured data, the improving hyperbolic tangent model of MR damper is presented. Furthermore, the Particle Swarm Optimization (PSO) method is proposed to find the improving hyperbolic tangent model's optimal parameters to get the MR damper models. Results The proposed semi-active suspension control system is rigorously proven to be input-to-state stable by virtue of Lyapunov stability theory. Through the simulation and experimental verification, it is proved that back-stepping sliding mode controller can reduce the acceleration of the sprung mass, that is, suppress the vertical vibration of the vehicle. At the same time, it is proved that the forward and inverse model of MR damper is effective, and can be applied to the hardware in the loop control experiment. Conclusion The back-stepping sliding mode proposed in this paper is better than the seat suspension under other control and passive systems, which proves that the back-stepping sliding mode controller is effective. It also shows that the forward and inverse model of MR damper is effective.