Stability and Hopf bifurcation of the maglev system with delayed position and speed feedback control

In this paper, the dynamic behavior of suspension system of maglev train with time-delayed position and velocity feedback signal is considered with rigid guideway. The stability conditions of the system are obtained with characteristic root method. The Hopf bifurcation direction and stability of the system at the critical point are also investigated. Based on center manifold reduction and Poincaré normal form theory, the general formula for the direction, the estimation formula of period and stability of Hopf bifurcating periodic solution are also given. It is shown that time delays can change the current complicated dynamic behavior. And the condition that the bifurcation may occur is given to restrain the dynamic response and vibration between vehicle and guideway of the system with time-delayed position and velocity signal.