Robust H∞ control for Active Magnetic Bearing system with imbalance of the rotor

Abstract

This paper proposes design of a robust H∞ controller for Active Magnetic Bearing (AMB) system. In this paper, the rotor of AMB has both static and dynamic imbalance. AMB system is affected by gyroscopic effect and imbalance of the rotor. Gyroscopic effect depends on angular velocity of the rotor. The H∞ controller is designed to suppress the vibration caused by imbalance and gyroscopic effect. The purpose of this study is to control attitude of the rotor. In order to control the attitude of the rotor, the perturbation of the rotor from equilibrium point is decreased by the state-feedback control. Mathematical model of AMB has first and second order terms of the angular velocity. In attempt to guarantee the robust stability for a prescribed range of angular velocity with lower conservativeness, the second order terms of angular velocity are changed into first order terms by using linear fractional transformation (LFT) and descriptor representation. Polytopic representation is applied to the system matrices which has only the first order terms of the varying parameter. H∞ controller is obtained by solving a finite set of linear matrix inequality (LMI) conditions at the vertex matrices of the polytope. Furthermore the effectiveness of the proposed controller is illustrated by simulations comparing with robust linear quadratic controller (RLQ).