Electromagnetic design of a magnetic suspension system

Magnetic levitation of a metallic sphere provides a high-impact visual demonstration of many principles in undergraduate educational programs in electrical engineering, e.g., electromagnetic design, compensation of a unstable control system, and power amplifier design. This paper deals with the electromagnetic and dynamic analysis of the levitation system and it has design formulas which are derived from first principles. This analysis leads to a plant transfer function which is used to implement a proportional plus derivative (PD) compensation strategy. Issues covered include coil and wire sizing for a given temperature rise. The paper shows that the electromagnet can be optimized for a given sphere. An experimental system is described which levitates a 6-cm, 0.8-kg sphere.