H∞-PD controller for suspension systems with MR dampers

In this paper, we consider the implementation of a static H_∞ output feedback controller to a quarter vehicle suspension system with a semi-active magnetorheological fluid (MRF) damper. Unlike most of the existing literature, all the states in the equation of motion are relative displacements and velocities between sprung, unsprung masses and road disturbance instead, in addition the input to the system is the acceleration of road disturbance. The measurements of the system are the relative displacement and velocity between sprung and unsprung masses only, which makes the practical implementation feasible. The controller of the system is composed of the H_∞-PD controller, which serves as a system controller to provide the desired damping force with the necessary robustness, and a modified version of the clip-optimal controller, which serves as a damper controller to track the the desired damping force. Satisfactory results are obtained through numerical simulations. To obtain the damper controller adopted in this work, an assumption regarding the dynamics of the MR damping force is verified through several numerical experiments. This dynamic equation indeed can also be served as an estimator of the magnetorheological damping force.