Delay-Dependent Sliding Mode Variable Structure Control of Vehicle Magneto-Rheological Semi-Active Suspension

The vehicle semi-active suspension with Magneto-Rheological Damper (MRD) has been a hot research topic of this decade, featuring the challenging task of the robust control with actuator time delay considerations. In this study, a delay dependent sliding mode variable structure control, based on the Linear Matrix Inequality (LMI), is proposed to suppress the vibration of the Magneto-Rheological Semi-Active Suspension (MRSS) control system. In accordance with the nonlinear characteristics of MRD, a dynamic model of automotive semi-active suspension system, considering time delay, is established. By defining a parameter-dependent Lyapunov switching functional, the conditions for asymptotic stability of closed-loop time delay system are derived, while the sliding mode variable structure control with reduced conservatism is designed. According to the method of LMI, the asymptotic stability problem of sliding mode is transformed into a feasibility problem, which can be solved by the solver 'feasp' in LMI toolbox. In addition, the calculation of the critical time delay of MRSS is expressed as a generalized eigenvalue optimization problem. For comparison purposes, three representative controllers, including a conventional sliding mode controller, a delay dependent controller, and a smith compensation, are studied. Simulation and real vehicle testing on bump and random road responses show that, the designed delay dependent controller can ensure the stability of the suspension system, weaken the influence of time delay on the control performance and effectively improve the ride comfort of the vehicle.