Single magnet levitation by repulsion using a planar coil array

This paper describes the controlled levitation of a single disk magnet above an array of cylindrical coils, using electromagnetic repulsion to generate actuation forces and torques from coil currents, and an optical motion tracking system to provide realtime position and orientation measurements for feedback control. Our method is to measure the electromagnetic forces and torques generated from a single cylindrical coil current on a disk magnet as a function of their relative positions beforehand, then combine the forces and torques from multiple identical coils in a planar array to derive matrix transformations from coil currents to forces and torques, given the position of the magnet during levitation. If the transformation matrix is invertable, then the coil currents necessary to generate forces and torques for feedback control can be calculated. With our setup, proportional-derivative feedback control applied in each direction of motion is sufficient for stable magnetic levitation. Experimental results for levitation of a single magnet are given for a simplified case with 3 coils with the magnet motions partially constrained by an attachment to a ball joint, and for 5 coils with the rotation of the magnet about its vertical axis left uncontrolled to rotate freely.