Analytical Design of Constrained Nonlinear Optimal Controller for Vehicle Active Suspension System considering the Limitation of Hydraulic Actuator

In this paper, a constrained nonlinear optimal control law is analytically developed for vehicle active suspension system considering the limitation of hydraulic actuator. In the design of the controller, the nonlinear characteristics of spring and damper forces and hydraulic actuator are considered. The control input is the displacement of the hydraulic valve spool which is bounded in practice and its constraint should be considered in the design process. In the proposed method, the control problem is firstly transformed to a constrained nonlinear optimization problem by performing a performance index defined as a weighted combination of predicted responses of nonlinear suspension system and control input. Then, this equivalent constrained optimization problem is solved using Kuhn-Tucker theorem to find the constrained optimal control law. The derived control law is in the closed form which is easy to solve and implementation. The controller performance is evaluated through computer simulation of the vehicle suspension model excited by a random road input. The obtained result indicate a remarkable decrease of the body acceleration which leads to the ride comfort. Meanwhile, other suspension responses including suspension and tire deflections are in suitable ranges.