An optimal sensor placement strategy for force and torque analytical models of a reaction sphere actuator for satellite attitude control

This article presents an optimization strategy to position magnetic flux density sensors in a reaction sphere actuator. The reaction sphere consists in a magnetic bearings spherical rotor whose rotation axis can be electronically controlled. The actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. Force and torque analytical models of the actuator are parameterized using 7 decomposition coefficients that deliver to the models all the necessary information relative to the orientation of the rotor inside the stator. These coefficients are determined non-iteratively and in a linear fashion by measuring the radial component of the magnetic flux density from at least 7 different locations. The proposed optimization procedure consists in minimizing the condition number related to the linear estimation problem of the coefficients so as to minimize the influence of the measurement noise on force and torque relative errors. Finally, numerical simulations confirm the effectiveness of the proposed optimization strategy.