Model predictive control of a magnetic levitation system with prescribed output tracking performance

To guarantee the safe and dependable operation of a magnetic levitation train, the distance between the magnet and the reaction rail needs to be kept within a given range. In this work, we design model predictive controllers which, in addition to complying with these constraints, provide a favorable behavior with regard to performance criteria such as travel comfort and control effort. For this purpose, we present a model of the system and the disturbances affecting it. Several results regarding the mathematical properties of this model are proven to gain insight for controller design. Finally we compare three different controllers w.r.t. performance criteria such as robustness, travel comfort, control effort, and computation time in an extensive numerical simulation study: a linear feedback controller, a model predictive control (MPC) scheme with quadratic stage costs, and the recently-proposed funnel MPC scheme. We show that the MPC closed loop complies with the constraints while also exhibiting excellent performance. Furthermore, we implement the MPC algorithms within the GRAMPC framework. This allows us to reduce the computational effort to a point at which real-time application becomes feasible.