Effects of delayed time active controller on the vibration of a nonlinear magnetic levitation system to multi excitations

Abstract

In this paper, a time-delayed positive position feedback controller is proposed to reduce the horizontal vibration of a magnetically levitated body subjected to multi force excitations. This controller is coupled to the main system with 1:1 internal resonance. The method of multiple scales perturbation technique is employed to obtain an approximate solution which clarifies the nonlinear behavior for both amplitude and phase of the whole system. The effects of time delay magnitude are investigated to indicate the safe region of operation. Validation curves are involved to compare the approximate solution with the numerical simulation.