Stability constraints of active magnetic bearing control systems

Abstract

Direct Lyapunov stability method is employed to analyse the closed-loop stability of an electromagnetically suspended rotor system in which non-linearity and singular perturbation nature are embedded. Five explicit sets of stability constraints are proposed so that the state feedback loop is not over-designed. Under impact of modeling inaccuracy, due to neglected higher-order terms, stability conditions for equilibrium point, slow-mode manifold and boundary layer are studied. In addition, the singular perturbation order-reduction technique is used to simplify the feedback loop and reduce the order of a state feedback controller. The stability margin can be numerically evaluated as long as the upper bound of the singular perturbation parameter is available. The proposed state feedback controller is verified by intensive computer simulations such that superior performance in terms of stiffness, rise time and overshoot is illustrated, in comparison to output feedback law and deadbeat control. The reported state feedback loop not only stabilizes the inherently unstable open-loop system, but also preserves the robustness with respect to the parasitic parameter variation and modeling error due to neglected higher-order terms of magnetic control force.