A magnetic flux model based method for detecting multi-DOF motion of a permanent magnet spherical motor

This paper presents a new method, referred to here as back-EMF method, for sensing the multi-DOF motion of a permanent magnet spherical motor (PMSM). With an explicit model characterizing the magnetic flux in the PMSM, a relationship between the electromotive force (EMF) induced in the winding of electro-magnets and the motion of the rotor permanent magnets is derived; and closed-form solutions that solves for multi-DOF Euler angles and angular velocities of the rotor are presented. This method allows for simultaneous estimation of both quantities in real-time by only measuring the voltages across the electro-magnets. Requiring no installation of additional sensors or fixtures on the rotor, the back-EMF method retains the structural simplicity of the PMSM. This method has been experimentally investigated on a prototype PMSM; the estimated Euler angles and angular velocities compare favorably with measurements from a commercialized gyroscope. As an immediate application, the motion states acquired using the back-EMF method are used for parameter estimation of the PMSM.