Back-EMF and rotor angular velocity estimation for a reaction sphere actuator

This paper presents a procedure to estimate the back-EMF voltages and the rotor angular velocity of a reaction sphere actuator for satellite attitude control. The reaction sphere is a permanent magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. The developed technique to measure the back-EMF voltages is based on Faraday´s law, in which the magnetic flux density is decomposed on a spherical harmonic basis, whose expansion parameters are derived from measurements of the radial component of the field collected from at least seven locations. Then, given the back-EMF voltages, the rotor angular velocity is derived employing the energy conservation principle. The resulting expressions are linear and are expressed in closed-form. Finally, the proposed method is validated numerically with finite element simulations and experimentally using a developed laboratory prototype.