Imbalance compensation of active magnetic bearing systems using model predictive control based on linear parameter-varying models

Active magnetic bearing (AMB) is a suspension system to levitate a rotating shaft freely without any physical contact which allows extremely fast rotation speeds. One big control challenge of the AMB systems, which appears during high rotation speeds, is the non-uniform distribution of the rotor weight about its rotating axis. This is usually referred to as the rotor imbalance problem which produces sinusoidal disturbance forces. These disturbances lead to undesirable vibrations and large deviations of the rotor shaft from its desired trajectories. We adopt in this work model predictive control (MPC) to reduce the effect of these sinusoidal disturbances and to achieve a stable levitation of the rotor shaft while tracking a reference trajectory. Owing to the MPC capability of handling constraints in an optimal manner, physical input constraints can be committed. Moreover, state constraints can be imposed to ensure safety of operation. For tractable implementation, we embed the nonlinear dynamics of the system in a linear parameter-varying (LPV) representation. To guarantee stability of the closed-loop system, a terminal cost and a terminal constraint set are included in the MPC optimization problem. For tractable computations of these terminal ingredients, a reduced LPV model is considered. The performance of the proposed LPV-MPC scheme is validated via simulation on the nonlinear model of an experimental setup of an AMB system and it is compared with two other classical controllers commonly used for these AMB systems in practice.