An Accurate Linearization of Electromagnetic Force of Heteropolar Magnetic Bearings With Redundant Structures

Abstract

Fault tolerance is one of the practical and effective approaches to improve the reliability of magnetic bearings. The linearization of the electromagnetic force (EMF) from the redundant structures is the crucial basis of the design of a fault-tolerant controller. In this paper, we propose an accurate linearization approach for the heteropolar magnetic bearings with redundant structures by solving the Taylor series expansion equation of the current distribution matrix (W) in the nonequilibrium position and introducing a set of displacement compensation matrices to establish a unified accurate EMF model including the controlled current and rotor position. The proposed approach can effectively decrease the EMF error between the actual physical model and the linearized model compared with the existing methods for the consideration of the rotor position. Moreover, the solutions of the current distribution matrix and the relevant optimization approach have been presented on the basis of the proposed approach to help to design a high-performance fault-tolerant controller in the entire rotor displacement range. The numerical results demonstrated the noticeable accuracy advantages of the proposed EMF model.