@article{Bauomy2025, 
author = {Hany Bauomy},
title = {Control and optimization mechanism of an electromagnetic transducer model with nonlinear magnetic coupling},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {2},
pages = {2891-2929},
keywords = {mixed excitations, electromagnetic transducer, perturbation, stability, NPDCVF controllers},
url = {https://www.sciopen.com/article/10.3934/math.2025135},
doi = {10.3934/math.2025135},
abstract = {This paper presents a novel nonlinear proportional-derivative cubic velocity feedback (NPDVF) controller for controlling vibrations in systems with both mechanical and electrical components subjected to mixed forces. The proposed controller aims to address the challenges posed by nonlinear bifurcations, unstable motion, and vibrations. The effectiveness of the controller demonstrated through numerical simulations, where it shown to significantly reduce harmful vibrations and stabilize the system under varying operating conditions. To analyze the system, a perturbation technique employed to derive approximate solutions to the system's equations up to the second order at simultaneous resonance case (             Ω              2        ≅            ω              1        ,            Ω              4        ≅            ω              2      ). A comparative analysis with other control strategies, such as proportional-derivative (PD) control, sliding mode control (SMC), and model predictive control (MPC), the superior robustness, computational efficiency, and control signal amplitude of the NPDVF controller. Results indicate that the proposed approach not only outperforms traditional methods in terms of energy efficiency and computational cost but also maintains robust performance even in the presence of nonlinearities and parameter uncertainties. The findings support the potential application of the NPDVF controller in real-time vibration control systems.}
}