# Design of a Lorentz Force Magnetic Bearing Group Steering Law Based on an Adaptive Weighted Pseudo-Inverse Law

## TL;DR

This paper introduces a new control method for magnetic bearings in spacecraft to improve precision and avoid performance issues.

## Contribution

A novel adaptive weighted pseudo-inverse control law is proposed to enhance torque distribution and reduce energy consumption in magnetic bearing systems.

## Key findings

- The adaptive weighting matrix reduces residual saturation effects on attitude control speed and accuracy.
- The proposed method reduces total energy consumption by 22% in simulations.
- Optimal mounting configurations improve attitude control accuracy and performance.

## Abstract

Aiming at the high-precision torque output and saturation singularity avoidance problems in Lorentz force magnetic bearing (LFMB) swarms for magnetic levitation spacecraft, this study designs a manipulation law based on an adaptive weighted pseudo-inverse law. The system monitors each magnetic bearing’s working state in real time using high-precision position and current sensors. As the key input for the adaptive weighted pseudo-inverse control law, the sensor data’s measurement accuracy directly determines torque distribution effectiveness and attitude control precision. First, considering electromagnetic back-EMF effects, individual LFMB dynamics are modeled via the equivalent magnetic circuit method, with working principles elucidated. Subsequently, saturation coefficients for LFMB swarms are designed. Incorporating spacecraft maneuvering requirements, a genetic optimization algorithm establishes the optimal mounting configuration under task constraints. Considering the LFMB swarm configuration characteristics, this study proposes an adaptive weighted pseudo-inverse maneuvering law tailored to operational constraints. By designing an adaptive weighting matrix, the maneuvering law adjusts each LFMB’s torque output in real time, reducing residual saturation effects on attitude control speed and accuracy. Simulation results demonstrate that the proposed mounting configuration and adaptive weighted pseudo-inverse maneuvering law effectively mitigate saturation singularity’s impact on attitude control accuracy while reducing total energy consumption by 22%, validating the method’s effectiveness and superiority.