Magnetic levitation using feedback

Abstract

Consider a steel ball being levitated. There are two forces acting on it: one is its weight and the other is the magnetic force (force of attraction by the magnet). The former can be assumed to be a constant-acting force, while the latter is a function of the distance between the ball and the magnet and also the square of the coil current. It would seem that if along the vertical axis of the magnet and within its magnetic field a position is found where the gravitational force balances out the magnetic force, an equilibrium position can be said to be obtained. It might also be expected that if the ball is placed exactly at this position, the ball would just float there. Without feedback this ball is unable to float there - the ball falls to the ground as soon as it is released. This equilibrium position is clearly UNSTABLE. In order to achieve the desired stability, it is required that the coil current (and therefore, the force of attraction) be adjustable in the face of the changing separation between the magnet and the ball. One method of doing this is to use an optical sensing unit to closely monitor the ball position and, through an appropriate feedback network, to relay the ball position information to the amplifier feeding the coil so that the coil current can be adjusted. In this way the ball is prevented from moving very far from the desired equilibrium position ... The central issue in this piece of work is the stabilization of an unstable plant using a proportional plus derivative feedback control as provided by the analog controller