A Lyapunov approach to controller design for magnetic suspension with two degrees of freedom.

by Thomas Thibodeau

This thesis details our work to apply a Lyapunov approach based on quadratic functions to the problem of magnetic suspension. Specifically the theory is applied to the problem of suspending an iron bar below two electromagnets. The control objective is to suspend the bar at a given location and to maintain this position in a stable manner. This is achieved by first measuring the displacement of the bar with two proximity sensors and then adjusting the strength of the two electromagnets with a properly designed controller.;This problem is a good application of the Lyapunov approach to controller design for three reasons. Firstly the force produced by the magnets is inherently nonlinear with respect to the coil current, which can be directly controlled. Therefore classical linear system design approaches can not be applied to the problem. Secondly it is impossible to accurately determine the parameters used to describe the properties of the electromagnets, so the system model needs to include a range of parameters to account for the uncertainty. The third reason is that the system is subject to both input and state constraints: the coil currents are within 2.5A and the motion of the bar is restricted within 4mm. All these nonlinearity, uncertainty and constraints will be effectively handled under the Lyapunov framework.

64 pages, NOOKstudy eTextbook