Optimization of the Four Coil Configuration for Single Magnet Levitation from Below

Magnetic levitation systems have the capability to provide six degree-of-freedom rigid-body motion control with high precision in translation, rotation, force, and torque in all directions with only a single moving part and noncontact actuation and sensing. This means of motion control eliminates deleterious effects on performance from mechanical contact such as friction, hysteresis, backlash, and vibration. These motion control capabilities have applications in precision fabrication and manipulation, medical interventions, and haptic human-machine interaction. In this work we investigate a specific system configuration which uses four cylindrical coils to levitate a magnet. The notable features of this configuration are that only four coils and two Hall effect sensors are needed to levitate a single magnet from underneath, and simple linear proportional-derivative (PD) controllers are sufficient to stabilize both translation and rotation in both planar directions in a small motion region. Translation in the vertical direction is stable and rotation about the vertical axis is neutrally stable and uncontrolled, allowing a disk magnet to rotate freely. Optimized parameters are presented for sample values of levitation height, mass, and maximum current, and disturbance response experimental results will be shown for the implemented levitation system with optimized dimensional values.