Linear and nonlinear state-space controllers for magnetic levitation

The problem of precisely controllimg (within sensor resolution) the height qf’a steel ball ahoae the ground hi) levitating it against the force of yrat:ity using an electromagnet is considered. The state variables used to model the system are the hall’s position below the magnet, the ball’s speed and the current in the electromagnet. Two state-space controllers are compared in terms of their perfi,rmance in controlling the hall’s position. The Jirst controller is based on feedback linearization where a nonlinear state-space tran$vmation along with nonlinear state ,ftiedback is used to linearize the system exactly. A linear controller is then used on the resulting system to control the ball’s position. As a direct measurement OJ’ball speed is not auailahle, a nonlinear observer with linear error dynamics is used to estimate the speed. The second controller is a standard linear statefkedhack controller whose design is based on a linear model,fi,und by perturbing the nonlinear system model about an operating point. A linear observer is used to estimate the ball’s velocity. Experimental results are presented to compare the <flecticeness of the two controllers in terms of their ability to respond to step inputs and to track sinusoidal reference trajectories.