Non-Linear Control of a Magnetic Levitation System of a Flexible Beam Based on Passivity : Stability Analysis and Experiment

This paper presents a non-linear control for a magnetic levitation system of a flexible object based on passivity of the system. There are many researches on a passivity-based controller for the flexible manipulators. In these researches, controllers are designed without approximating flexible links into finite order model by truncating higher order vibration modes and linearizing non-linear terms in a neighborhood of an equilibrium point. Such linear finite controllers do not cause spillover phenomena and make wide operating area. In this paper, the magnetic levitation system is divided into two subsystems : an electrical subsystem and a mechanical subsystem. The controller for each subsystem is designed independently based on passivity. The dynamics of the flexible object are fully addressed and the results are valid for large deviations from equilibrium. The obtained controller dose not need current feedback for the electrical subsystem and consists of position, velocity and deflection rate feedback for the mechanical subsystem. It ensures asymptotic stability of the position trajectory and suppression of the elastic vibration. To illustrate the validly of our controller, some experimentals are carried out