Distributed multi-pole model for motion simulation of PM-based spherical motors

Design and control of multi degrees of freedom (DOF) electromagnetic actuators require a good understanding of the magnetic fields, and involve real-time calculation of magnetic forces. This paper presents a new method to derive closed-form solutions for characterizing the magnetic field of permanent magnets (PM), and their uses in modeling the magnetic torque of a PM-based spherical motor. The method, referred here as distributed multi-pole (DMP) model, inherits many advantages of the dipole model originally conceptualized in the context of physics, but provides an effective means to account for the shape and magnetization of the physical magnet. The DMP models have been validated by comparing the calculated fields and magnetic forces against numerical and experimental results. The comparisons show excellent agreement. We also illustrate the application of the DMP model in developing an accurate torque model to faithfully simulate the transient response of a spherical motor, and as a basis for deriving a closed-form inverse torque model for its real-time current optimization. While developed in the context of a spherical motor, the modeling techniques presented in this paper are applicable to other PM-based actuator and sensing systems.