Hopf bifurcation of the maglev time-delay feedback system via pseudo-oscillator analysis

Abstract

This paper investigates the local dynamics around the trivial solution of suspension system of maglev train with time-delayed feedback signals. With characteristic root method, the linear stability analysis of the maglev system is obtained, which implies that a Hopf bifurcation may occur when time delay exceeds a critical value. To gain insight into the periodic motion, the pseudo-oscillator analysis is used to calculate the bifurcated periodic solution, and to determine the direction of the bifurcation. Unlike the widely used methods such as manifold reduction, the pseudo-oscillator analysis involves simple computation and gives prediction of the local dynamics with high accuracy. Numerical simulation results show that the existence of the Hopf bifurcation and the amplitude of the periodic solution can be determined by time delay and control parameters. So appropriately selecting them can restrain vibration between vehicle and guideway of the system effectively.