Nonlinear control of a semi-active suspension system considering actuator and state constraints using methods of optimal control

Two optimal control methods for a nonlinear semi-active suspension system subject to state and actuating constraints are presented and compared with LQR and skyhook control. Nonlinearities in the suspension system are considered in terms of variable kinematic transmission factor, bump stops and asymmetric and degressive continously variable damper characteristics. The first approach incorporates the state inequality constraint as well as the state-dependent actuating variable constraints due to the working range of the damper characteristics by applying the method of nonlinear programming. In the second strategy, the optimal control problem is formulated as an optimal switching problem between nonlinear subsystems defined by the valve current depending damper characteristics. This enables a recurrent problem formulation and thus the application of Dynamic Programming. Both approaches lead to a state-dependent control law, which is integrated in the feedback loop. The performance of the proposed approaches is analyzed in simulations based on the nonlinear model of a quarter-car test rig.