Robust magnetic bearing control via eigenstructure assignment dynamical compensation

This paper deals with the robust control of a basic current-controlled magnetic bearing by an output dynamical compensator. Based on a parametric approach for eigenstructure assignment and a linearized model of the magnetic bearing system, a general explicit parametric expression for all the first-order dynamical compensators assigning desired nondefective closed-loop eigenstructure is obtained. This parametric expression is expressed in terms of the closed-loop eigenvalues and a free parameter. Through optimizing this free parameter and the closed-loop eigenvalues, a dynamical compensator is obtained which gives insensitive closed-loop eigenvalues, effectively attenuates the effect of the disturbance, and uses small control effort. To ensure desired closed-loop dynamical performance, the closed-loop eigenvalues are optimized within some desired regions on the left-half complex plane. Measures are also taken to ensure the robust stability of the closed-loop system in the case of large system parameter perturbations. The proposed approach is applied to a flywheel which is supported by four current-controlled active magnetic bearings. Nonlinear simulation and experimental results show the effect of the proposed approach.