Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Jing Wang,Peng Hao,Shaojuan Ma,Hehui Yuan

doi:10.1155/2019/1641953

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.

Highlights

One of the most innovative developments involves the use of magnetic bearings. ey are being used widely in rotating machinery because of their advantages, including very low friction, no wear, and high rotor speed. e application of magnetic bearing technology has experienced substantial growth since the First International Symposium on Magnetic Bearings was held in 1988
Most of the components are of nonlinear characteristics; the entire system becomes inherently nonlinear
The bifurcation diagram, the power spectrum, and Poincaremapping were used in [8] to identify the main factors a ecting the dynamic characteristics of an AMB system

Summary

Introduction

One of the most innovative developments involves the use of magnetic bearings. ey are being used widely in rotating machinery because of their advantages, including very low friction, no wear, and high rotor speed. e application of magnetic bearing technology has experienced substantial growth since the First International Symposium on Magnetic Bearings was held in 1988. References [8, 9] utilized numerical simulation methods to analyze the bifurcation phenomena in active magnetic bearing systems. Zhe et al studied nonlinear dynamic characteristic analysis of the magnetic bearing system based on the cell mapping method [13]. Kiani et al [16] designed a segmented linear form of hybrid controller to stabilize the magnetic bearing system Shrivastava and his team proposed a model-based method to estimate unbalanced rotor plane parameters, using Kalman filter and recursive least squares input force estimation technique in [17]. E model consists of a mass with two degrees of freedom, and the equations of motion governing the unbalance of the magnetic bearing can be written as mx€ fx − cx_ + meΩ2 cos Ωt, my€ fy − cy_ + meΩ2 sin Ωt.

Hopf Bifurcation Analysis of Equivalent Deterministic Magnetic Bearing System

Hopf Bifurcation Control