Nonlinear Optimal Internal-Model Control for Multiple Time-Delay Systems with Application to Vehicle Suspensions

摘要

The paper considers the nonlinear optimal vibration control problem for systems with multiple delays, i.e. control delay, state delay, and measurement delay, under reference input. The time-delay system is transformed into an equivalent delay-free one via functional transformations. The nonlinear optimal control law is designed by solving a Riccati equation, a Sylvester equation, and an adjoint differential equation. The effects generated by nonlinearity and time-delay are compensated by the nonlinear compensator and the memory terms in the designed controller. An internal model is constructed so that the disturbance will be rejected with zero steady-state error as well as the reference is tracked, through the dynamical compensator produced from the internal model. An observer is constructed to make the controller physically realizable. The result is extended to vehicle suspension systems. It is demonstrated that the road vibration that is encountered by the suspension will be canceled entirely by the proposed control. Numerical simulations illustrate the effectiveness of the presented controller.