Sup-Resonant Response of a Nonautonomous Maglev System With Delayed Acceleration Feedback Control

A Maglev system with delayed acceleration feedback control is disturbed by the deflection of flexible guideway, and resonant response may take place. We have investigated sup-resonant response of the Maglev system by employing center manifold reduction and the method of multiple scales. We present the dynamic model and expand it to a third-order Taylor series. Taking time delay as its bifurcation parameter, we discuss the condition for the occurring of Hopf bifurcation. We apply center manifold reduction to get the Poincare normal form of the nonlinear system and employ the perturbation technique to study sup-resonant response of the system. This yields the sup-resonant periodic solution of the normal form. We analyze the stability condition of the free oscillation in the solution and discuss the relationship between guideway excitation and periodic solution. Finally, numerical results show how time delay, control, and excitation parameters affect the system response. With the proper system parameter, the free oscillation may vanish and only the periodic solution plays a part. Time delay can control amplitude of the forced oscillation. The appearance of the chaos phenomenon can also be governed by regulating time delay. And judiciously selecting a control parameter makes it possible to suppress the response.