Sub-optimal recursively feasible Linear Parameter-Varying predictive algorithm for semi-active suspension control

This study proposes an algorithm to enhance the comfort of passengers in a vehicle with semi-active suspensions. The vertical dynamics of the car are represented through a quasi-linear parameter-varying (qLPV) model. The scheme resides in solving a set-constrained model predictive control (MPC) problem, embedding a comfort performance index to the MPC optimisation function. Its sub-optimality resides in the fact that the MPC is synthesised considering a frozen guess for the evolution of the qLPV scheduling parameters along the horizon. Assuming bounds on the variation rates of the qLPV scheduling parameters, the method enables a replacement of the original complex non-linear optimisation by a much simpler quadratic program (QP). This QP uses a Lyapunov-decreasing cost and set-based terminal ingredients, which guarantee that the domain of attraction of the controller is enlarged and that recursive feasibility can be maintained. The study ends with successful realistic non-linear simulations of a one-fifth-scaled car with electro-rheological suspensions, for which the proposed method is tested and compared with other optimal controllers (Linear Quadratic Regulator (LQR) and linear MPC). The results illustrate the overall good operation of the vehicle; the comfort of the passengers is substantially improved, as measured through time- and frequency-domain indexes.