Optimal vibration control of nonlinear systems with multiple time-delays: An application to vehicle suspension

Abstract

ABSTRACTThis paper addresses optimal vibration control problem for nonlinear systems with state, control, and measurement delays. By using the functional transformations, the original system is reduced to an equivalent delay-free one. The approximating sequence method is applied to simplify and solve the nonlinear optimal vibration control (NOVC) problem, which is reduced to a linear two-point boundary value problem of approximating sequences. The nonlinear optimal control law is obtained from the convergence solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. The proposed control strategy is applied to design a vibration controller for an active vehicle suspension. The nonlinear vehicle suspension system with delays is modelled, as well as the road disturbance model is established. Comparing with a passive controller and a non-delay-compensation controller (NDCC), the simulations for the designed NOVC are demonstrated. The simulation results illustrate the effectiveness and the simplicity of the proposed approach.