Passivity based control for a magnetically levitated flexible beam with rate estimation via the extended Kalman filtering technique

Abstract

This paper presents a passivity based control method combined with velocity estimation by an extended Kalman filter for a magnetically levitated flexible beam with both ends free by two electromagnets. An energy-based analysis concludes that the system can be decomposed into two passive subsystems: a mechanical subsystem consisting of the flexible beam and an electrical subsystem consisting of the electromagnets. We designed a passivity based controller independently for each subsystem. An output feedback controller for the mechanical subsystem computes the desired force that is required to achieve position convergence and vibration suppression of the flexible beam. A feed forward controller for the electrical subsystem computes the input voltage for the electromagnets to generate the desired force. In a practical point of view, structural and economic considerations restrict simultaneous usage of both position sensors and velocity sensors while the control strategy requires accurate measurements of the position and velocity of the flexible beam. We employ the extended Kalman filtering technique in order to estimate the velocity of the flexible beam from the measured micro-displacement vibration at a high sampling frequency. Effectiveness of the proposed controller and velocity estimator is demonstrated by a numerical simulation.