Feedback Stabilization of a Permanent Magnet Levitation System

A magnetic levitation system consists of a magnet facing groundward to attract a magnetic object against gravity and levitate it at a distance from the face of magnet. Due to the unstable nature of this system, it must be stabilized by means of feedback control, which adjusts the magnetic force applied to the levitating object depending on its measured position and possibly velocity. Conventionally, electromagnets have been used for magnetic levitation, as they can be simply controlled via their terminal voltages. This paper, however, studies a levitation system relying on a permanent magnet and a linear servomotor to control the applied magnetic force by changing the distance between the magnet and the levitating object. For the proposed system, which is highly nonlinear, a stabilizing feedback control law is developed using feedback linearization and other control design tools. Then, the closed-loop stability is examined against system parameters such as the size of the levitating object, the viscosity of the medium it moves in, and certain characteristics of the magnet in use. The emphasis here is on understanding the impact of intrinsic servomotor limitations, particularly its finite slew rate (cap on its maximum velocity), on the ability of feedback control to stabilize the closed-loop system. This particular limitation seems to be a major concern in utilizing permanent magnets for noncontact actuation and control.