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

Abstract

This paper presents a passivity based control combined with velocity estimation by the extended Kalman filter for a magnetically levitated flexible beam with both ends free. Passivity analyses result in that the system can be decomposed into two passive subsystems: a mechanical subsystem that consists of the flexible beam with both ends free and an electrical subsystem that is comprised of electromagnets. An output feedback controller combined with velocity estimation by the extended Kalman filter for the mechanical subsystem computes desired force required to achieve position convergence and vibration suppression of the flexible beam. In a practical point of view, economic considerations restrict accurate measurements of both position and velocity of the supporting object while the control strategy requires accurate measurements of them. Thus, we employ the extended Kalman filtering technique in order to reject noise in the velocity signals at high sampling frequencies and/or micro-displacement vibrations. A feed forward controller that generates the desired force is designed for the electrical subsystem. Effectiveness of the proposed controller and velocity estimator is demonstrated by a numerical simulation.