Periodic Response and Stability of a Maglev System with Delayed Feedback Control Under Aerodynamic Lift

Abstract

In this research, the periodic response and stability of a nonlinear maglev system under the combined effects of steady and unsteady aerodynamic lifts is investigated, considering time delay in the feedback control loop. First, a nonlinear maglev system with a single levitation point that accounts for the nonlinearity of the electromagnetic force, time delay in the feedback control loop, and effect of aerodynamic lift is established. Then the periodic solutions of the maglev system with aerodynamic lift and time delays are obtained by an incremental harmonic balance analysis, in which the explicit time-delay action matrices used indicate that the effect of time delay on the response of the maglev system is periodic. The stability of the periodic solutions based on a finite difference continuous time approximation method and Floquet theory is studied, from which the critical time delay is obtained. Also, the relationship between the periodic vibration amplitude and the time delay is examined, along with the steady aerodynamic lift coefficient, and frequency of the unsteady aerodynamic lift, as well as the variation of critical delay with respect to the position feedback and velocity feedback with the control gain parameters. In addition, the stability boundary for the simultaneous time-delayed position and velocity feedback is obtained.