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

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 undergoes both subcritical and supercritical bifurcations, 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.

► We study a nonlinear model for a maglev system with time-delayed feedback control.
► We give constraints on the feedback gains and delay to ensure that the control stabilizes the equilibrium.
► We show that a Hopf bifurcation occurs when the equilibrium loses stability.
► Using the method of multiple scales, we show that the Hopf bifurcation may be subcritical or supercritical.
► We show that nonlinear instability exists—the equilibrium may only be stable to small perturbations.