Vibration suppression of a nonlinear magnetic levitation system via time delayed nonlinear saturation controller

• Actively controlling the vibration of a nonlinear magnetic levitation system.
• Applying multiple scales perturbation method to analyze its nonlinear dynamics.
• Investigating the effects of time delay on its behavior.
• Extracting the optimum conditions for the best performance.
• Validating the results with numerical simulation.

In this paper, a time delayed nonlinear saturation controller is proposed to reduce the horizontal vibration of a magnetically levitated body described by a nonlinear differential equation subjected to both external and modulated forces. An approximate solution is obtained applying the multiple scales perturbation technique to analyze the nonlinear behavior of this model. Based on the quadratic coupling, energy transfer from the main system to the controller is achieved by selecting the natural frequency of the controller to be approximately half that of the natural frequency of the main system. The effects of time delay are investigated to indicate the operation safe region. Time histories of the main system and the controller are illustrated to show the response with and without control. Validation curves are also included to show the closeness between the perturbation solution and the numerical one. A comparison with previously published work is included by the end.