Optimal and Robust Damping Control for Semi-active Vehicle Suspension

The paper focusses on optimal control issues arising in semi-active vehicle suspension motivated by the application of continuously controllable ERF-shock absorbers. Optimality of the damping control is measured by an objective consisting of a weighted sum of criteria related to safety and comfort which depend on the state variables of the vehicle dynamics model. In the case of linear objectives and linear quarter or half car dynamics models the well-known linear quadratic regulators can be computed. However, to account for maximum robustness with respect to unknown perturbations, e.g., by the ground, linear robust-optimal H-infinity controllers are investigated which can be computed iteratively. The linear H-infinity controller can be viewed as the solution of a linear dynamic zero-sum differential game. Thus, a nonlinear H-infinity controller can be obtained in principle as the solution of a nonlinear zero-sum dynamic game problem. Such a problem formulation enables to consider nonlinear vehicle dynamics as well as nonlinear objectives and constraints. A computational method is discussed which computes approximations of robust-optimal trajectories for nonlinear damping control. The method is based on a reformulation of the dynamic game and the application of a control and state parameterization approach in combination with sparse nonlinear programming methods. Numerical results for the different approaches and their validation by software-in-the-loop simulation using a full motor vehicle dynamics model are presented.