Passivity based control of a magnetic levitation system with two electromagnets for a flexible beam

This paper presents a passivity based control of a magnetic levitation system handling a flexible beam supported by two electromagnets. Elastic vibrations sometimes cause control failure so it is important to suppress the elastic vibrations in order to ensure stable control in case of levitating a flexible object. The system can be decomposed into two subsystems: an electrical subsystem and a mechanical subsystem. It is shown that the whole system can be regarded as a feedback connected system with these subsystems and a controller for each subsystem can be designed independently. Passivity for each subsystem is also shown and a controller for each subsystem is designed based on its passivity. A controller for the electrical subsystem generates the desired magnetic force that makes the flexible beam follows a desired trajectory. A controller for the mechanical subsystem consists of position and velocity feedback related to deflections of the flexible beam. The whole controller ensures stability of the system and suppression of the elastic vibrations by means of Lyapunov stability theory. To illustrate the validity of the controller a numerical simulation is carried out.