Optimal control and parameters design for the fractional-order vehicle suspension system

Abstract

In this paper the optimal control and parameters design of fractional-order vehicle suspension system are researched, where the system is described by fractional-order differential equation. The linear quadratic optimal state regulator is designed based on optimal control theory, which is applied to get the optimal control force of the active fractional-order suspension system. A stiffness-damping system is added to the passive fractional-order suspension system. Based on the criteria, i.e. the force arising from the accessional stiffness-damping system should be as close as possible to the optimal control force of the active fractional-order suspension system, the parameters of the optimized passive fractional-order suspension system are obtained by least square algorithm. An Oustaloup filter algorithm is adopted to simulate the fractional-order derivatives. Then, the simulation models of the three kinds of fractional-order suspension systems are developed respectively. The simulation results indicate that the active and optimized passive fractional-order suspension systems both reduce the value of vehicle body vertical acceleration and improve the ride comfort compared with the passive fractional-order suspension system, whenever the vehicle is running on a sinusoidal surface or random surface.