Nonlinear analysis of a maglev system with time-delayed feedback control

Abstract

This paper undertakes a nonlinear analysis of a model for a maglev system with time-delayed feedback. Using linear analysis, we determine constraints on the feedback control gains and the time delay which ensure stability of the maglev system. We then show that a Hopf bifurcation occurs at the linear stability boundary. To gain insight into the periodic motion which arises from the Hopf bifurcation, we use the method of multiple scales on the nonlinear model. This analysis shows that for practical operating ranges, the maglev system undergos both subcritical and supercritical bifurcations, and which give rise to unstable and stable limit cycles respectively. Numerical simulations confirm the theoretical results and indicate that unstable limit cycles may coexist with the stable equilibrium state. This means that large enough perturbations may cause instability in the system even if the feedback gains are such that the linear theory predicts that the equilibrium state is stable.

Stability and Bifurcation Analysis in a Maglev System with Multiple Delays

“…If τ 2 is fixed and τ 1 changes, the branching structure of the Hopf bifurcation is the same as in Fig. 4(c) of paper [Zhang et al, 2011].…”

“…The Maglev model we study is similar to that presented in Zhang et al, 2011;Zhang et al, 2012]. Mg represents the weight force of the electromagnet respectively, and z denotes the absolute vertical displacement of the electromagnet.…”

“…Wang L. L. Zhang et al investigated the stability and Hopf bifurcation of the Maglev system with delayed speed feedback control . Papers [Zhang et al, 2011;Zhang et al, 2012] took on a nonlinear analysis of a model for a Maglev system with timedelayed feedback. Zhang et al [2011] determined constraints on the feedback control gains and the time delay which ensure the stability of the Maglev system.…”

“…Papers [Zhang et al, 2011;Zhang et al, 2012] took on a nonlinear analysis of a model for a Maglev system with timedelayed feedback. Zhang et al [2011] determined constraints on the feedback control gains and the time delay which ensure the stability of the Maglev system. Using the method of multiple scales, this analysis showed that for practical operating ranges, the Maglev system undergoes both subcritical and supercritical bifurcations.…”

Motion stability of high-speed maglev systems in consideration of aerodynamic effects: a study of a single magnetic suspension system

“…The relationship between the periodic solution and the excitation and control parameters was also examined. The stability and the Hopf bifurcation of a rigid guideway maglev train with position-delay and speed-delay feedback and an elasticguaideway maglev train with position-delay feedback were discussed by Zhang et al [13][14][15] using center manifold and normal form theory. The normal equation was obtained, and the stability of the limit cycle was determined.…”