Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Abstract

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

A state-of-the-art review on uncertainty analysis of rotor systems

“…Wang et al [64] established a two-degree-of-freedom AMB model with uncertain parameters induced by the environment and materials, such as magnetic permeability.…”

“…However, the required rewriting of the equations of the problem can sometimes be complicated and the modifications to a numerical solver are painful. Even if this does not represent a major theoretical problem in terms of mathematical rewriting [48,64,75], it can be quite complicated to set up when many uncertainties are considered. For a better illustration, the differences between intrusive and non-intrusive UQ approaches in rotor dynamic analysis are depicted in Fig.…”

“…The research on nonlinear rotordynamics under uncertainty is more difficult than the linear studies since there are interactions between nonlinearities and uncertainties. Some papers investigated the nonlinear dynamics of the rotor-AMBs systems [64,225,226] and cracked rotor systems [47,75,76,115,227,228]. Nonlinear analysis techniques, such as the alternating frequency/time technique (HB-AFT), orthogonal polynomial approximation and linearization, are used to deal with nonlinearities.…”

“…Simulation and experiment results proved its efficacy. Wang et al [64] investigated the uncertain magnetic permeability in an AMB and found that this random uncertainty affects the Hopf bifurcation of the rotor-AMB system shown in Fig. 17(a).…”