H∞ control of multiple model subject to actuator saturation: application to quarter-car suspension system

Abstract

This paper deals with the H∞ control of nonlinear systems in multiple model representation subject to actuator saturation. An application to Quarter-Car suspension system under actuator saturation is then given using the multiple model approach. The concept of so-called parallel distributed compensation (PDC) is employed for designing control system. The idea of this controller consists in designing a linear feedback control for each local linear model. To address the input saturation problem in this paper, both constrained and saturated controls input cases are proposed. In the two cases, H∞ stabilization conditions in the sense of Lyapunov method are derived. Moreover, a controller design with larger attraction domain is formulated and solved as a linear matrix inequality (LMI) optimization problem. Our simulation results show that both the saturated and constrained controls can stabilize the resulting closed-loop suspension system and eliminate the effect of external disturbances. Indeed, the main roles of car suspension systems, which consist on improving ride comfort of passengers and the road holding capacity of the vehicle, are achieved.