A study of the nonlinear response and chaos suppression in a magnetically levitated system

Abstract

This study employed a variety of nonlinear dynamic analysis techniques to explore the complex phenomena associated with a magnetically levitated system involving a suspended ferromagnetic ball. The aim was to develop a method with which to assume control over chaotic behaviour. Rich dynamics were investigated numerically using Poincare maps, phase portraits, time responses and frequency spectra. Our results reveal that the nonlinear characteristics of magnetic forces cause period-doubling bifurcations which can lead to chaotic motion. Analysis based on the largest Lyapunov exponent was also used to identify the onset of chaotic motion. Finally, a continuous feedback control method based on synchronisation characteristics was developed for the suppression of chaotic oscillations. Simulation results support the feasibility of the proposed method. Finally, some robustness analysis of parametric perturbation on a maglev system with synchronisation control is confirmed by Lyapunov stability theory and numerical simulations.