H∞ Control of a Rotor-magnetic Bearing System Based on Linear Matrix Inequalities

Abstract

In this paper, H∞ robust control based on a linear matrix inequality is designed for controlling the motion of a 4-axis unbalanced rigid asymmetric rotor supported by two active magnetic bearings. To this end, the equations of motion of the system are derived via Hamilton’s variational principle and they are transformed to a state-space form for the standard H∞ control problem. An LMI-based controller, which does not require additional assumptions beyond stabilizability and detectability, is designed on the basis of the pole placement weighting function and the loop-shaping technique. The obtained results are compared with the results obtained in the case of the LQR scheme reported in the available literature, and the efficiency of the proposed LMI-based H∞ control is revealed.