# Theoretical Analysis and Research on Support Reconstruction Control of Magnetic Bearing with Redundant Structure

## TL;DR

This paper studies how magnetic bearings with redundant structures can maintain stability and control when some coils fail, using theoretical analysis and simulations.

## Contribution

The paper introduces a current distribution matrix (CDM) to enable support reconstruction in magnetic bearings with up to two coil failures.

## Key findings

- The CDM allows for EMF reconstruction in magnetic bearings with up to two coil failures.
- Simulation results show that displacement disturbance during reconstruction is less than 0.28 μm.
- The proposed method maintains EMF consistency with expected values under various fault conditions.

## Abstract

At present, the redundant structures are one of the most effective methods for solving magnetic levitation bearing coil failure. Coil failure causes residual effective magnetic poles to form different support structures and even asymmetrical structures. For the magnetic bearing with redundant structures, how to construct the electromagnetic force (EMF) that occurs under different support structures to achieve support reconstruction is the key to realizing fault tolerance control. To reveal the support reconstruction mechanism of magnetic bearing with a redundant structure, firstly, this paper takes a single-degree-of-freedom magnetic suspension body as an example to conduct a linearization theory analysis of the offset current, clarifying the concept of the current distribution matrix (CDM) and its function; then, the nonlinear EMF mode of magnetic bearing with an eight-pole is constructed, and it is linearized by using the theory of bias current linearization. Furthermore, the conditions of no coils fail, the 8th coil fails, and the 6–8th coils fail are considered, and, with the maximum principle function of EMF, the corresponding current matrices are obtained. Meanwhile, based on the CDM, the corresponding magnetic flux densities were calculated, proving that EMF reconstruction can be achieved under the three support structures. Finally, with the CDM and position control law, a fault-tolerant control system was constructed, and the simulation of the magnetic bearing with a redundant structure was carried out. The simulation results reveal the mechanism of support reconstruction with three aspects of rotor displacement, the value and direction of currents that occur in each coil. The simulation results show that, in the 8-pole magnetic bearing, this study can achieve support reconstruction in the case of faults in up to two coils. Under the three working conditions of wireless no coil failure, the 8th coil fails and the 6–8th coils fail, the current distribution strategy was adjusted through the CDM. The instantaneous displacement disturbance during the support reconstruction process was less than 0.28 μm, and the EMF after reconstruction was basically consistent with the expected value.