Nonlinear dynamics, stability, and vibration suppression of magnetically levitated systems under a combined control strategy

This study investigates a non-ideal magnetic levitation system (NIMLS) for energy harvesting, with particular emphasis on the influence of the oscillating core mass. The system is excited by an electrodynamic shaker, leading to strongly nonlinear oscillatory behavior governed by a coupled equation resembling the Duffing oscillator. Perturbation techniques are employed to analyze the system dynamics under the combined action of a negative velocity and negative acceleration controller (NVC+NAC), focusing on primary resonance and 1:1 internal resonance condition. Analytical solutions are derived to describe the system response, while MATLAB-based numerical simulations are used to validate the theoretical results. The stability of the system under primary resonance is examined using the Routh–Hurwitz criterion. Furthermore, the effects of structural constraints and system parameters on the dynamic performance of the primary system equipped with the NVC+NAC controller are investigated. A comparative analysis between analytical and numerical solutions confirms the accuracy of the perturbation-based approximations and demonstrates the effectiveness of the proposed controller in suppressing vibration amplitudes.