Abstract
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.
Highlights
Active magnetic bearing (AMB) systems are used in verity of industrial high-speed rotating machines including linear induction motors, compressors, flywheel storage systems, The associate editor coordinating the review of this manuscript and approving it for publication was Bohui Wang .wind turbines, etc. [1]–[3]
For practical implementation of the model predictive control (MPC) based linear parameter-varying (LPV), we propose a frozen LPVMPC scheme, where, at every sampling time of the MPC problem, the scheduling parameter is frozen at its current value and over the prediction horizon
Disturbance rejection, and we compare the proposed frozen LPVMPC with a classical lead-lag controller developed by the manufacturer of the AMB experimental setup (MBC500) [25]
Summary
Active magnetic bearing (AMB) systems are used in verity of industrial high-speed rotating machines including linear induction motors, compressors, flywheel storage systems, The associate editor coordinating the review of this manuscript and approving it for publication was Bohui Wang .wind turbines, etc. [1]–[3]. Active magnetic bearing (AMB) systems are used in verity of industrial high-speed rotating machines including linear induction motors, compressors, flywheel storage systems, The associate editor coordinating the review of this manuscript and approving it for publication was Bohui Wang. AMB is used in medical applications, e.g., as a suspended rotor in ventricular assist devices for heart failure replacement in humans [4]. The electromagnetic forces generated in the AMB system provide contact-less suspension of its rotatory component, which allows for very high rotational speeds without mechanical frictions. A. Morsi et al.: Model Predictive Control Based on Linear Parameter-Varying Models of Active Magnetic Bearing Systems
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