Active vibration control of a nonlinear magnetic levitation system via Nonlinear Saturation Controller (NSC)

Abstract

In this paper, a nonlinear saturation controller (NSC) is proposed to reduce the horizontal vibration of a magnetically levitated body described by a nonlinear differential equation. An approximate solution is obtained applying the multiple scales perturbation technique to analyze the nonlinear behavior of this model. Based on the quadratic coupling, the energy transfer between the main system and the controller is achieved by designing the natural frequency of the NSC to be close to one half of the natural frequency of the main system. Time histories of the main system and the controller are included to show the response with and without control. Validation curves are included to show the closeness between the perturbation solution and the numerical one. A comparison with previously published work is included.