Discrete approximate optimal vibration control for nonlinear vehicle active suspension

This paper presents the approximate optimal vibration control methodology for discrete nonlinear vehicle active suspension subject to persistent road disturbances. Based on a dynamic model of nonlinear vehicle active suspension and a linear exogenous system model of the persistent road disturbances, a nonlinear two-point boundary value (TPBV) problem is introduced. By introducing a sensitive parameter, the original TPBV problem is reformed as a series of TPBV problems without nonlinear items. A discrete approximate optimal vibration controller (DAOVC) can be obtained by solving a Riccati equation, Stein equation, and nonlinear compensation item, respectively. An iteration algorithm is designed to realize the computational realizability of DAOVC based on the control performance. It is demonstrated that the control performance of ride comfort, road holding ability, and suspension deflection under the DAOVC are much smaller than the ones under the classical feedforward and feedback optimal vibration controller (FFOVC) and open-loop vehicle suspension system