Modeling and Control of Rotor Oscillations in Active Magnetic Bearings Using a Generalized Pole-Pair Approach

Abstract This paper proposes a generalized number of pole pairs in the model of active magnetic bearings (AMBs). The rotor’s oscillations are controlled using the conventional proportional-derivative (PD) controller. The controlled oscillations are governed by a system of nonlinear differential equations, with the equilibrium solution derived using the harmonic balance method. Moreover, a stability test is conducted using Floquet theory. The derived and studied restoring magnetic force concludes the conditions for attaining its maximal value. Furthermore, a suggestion for a high number of pole pairs is recommended to examine the rotor’s steady-state oscillations thereafter. Various responses are illustrated to examine the influence of the number of pole pairs on the rotor’s dynamic behavior. In addition, the rotor can transition between a zero-stiffness state and a positive-stiffness state by modifying the control parameters. Also, the AMBs model with a high (or low) number of pole pairs is appropriate for low-speed (or high-speed) rotary hubs.