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Active magnetic bearing (AMB) system has been recently employed widely as an ideal equipment for high-speed rotating machines. The inherent challenges to control the system include instability, nonlinearity and constricted range of operation. Therefore, advanced control technology is essential to optimize AMB system performance. This paper presents an application of model predictive control (MPC) based on linear parameter-varying (LPV) models to control an AMB system subject to input and state constraints. For this purpose, an LPV model representation is derived from the nonlinear dynamic model of the AMB system. In order to provide stability guarantees and since the obtained LPV model has a large number of scheduling parameters, the parameter set mapping (PSM) technique is used to reduce their number. Based on the reduced model, a terminal cost and an ellipsoidal terminal set are determined offline and included into the MPC optimization problem which are the essential ingredients for guaranteeing the closed-loop asymptotic stability. Moreover, for recursive feasibility of the MPC optimization problem, a slack variable is included into its cost function. The goal of the proposed feedback control system is twofold. First is to demonstrate high performance by achieving stable levitation of the rotor shaft as well as high capability of reference tracking without violating input and state constraints, which increases the overall safety of the system under disturbances effects. Second is to provide a computationally tractable LPVMPC algorithm, which is a substantial requirement in practice for operating the AMB system with high performance over its full range. Therefore, we propose an LPVMPC scheme with frozen scheduling parameter over the prediction horizon of the MPC. Furthermore, we demonstrate in simulation that such frozen LPVMPC can achieve comparable performance to a more sophisticated LPVMPC scheme developed recently and a standard NL MPC (NMPC) approach. Moreover, to verify the performance of the proposed frozen LPVMPC, a comparison with a classical controller, which is commonly applied to the system in practice, is provided.INDEX TERMS Model predictive control, linear parameter-varying models, magnetic bearing systems, parameter set mapping, asymptotic stability.

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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.