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Nonlinear modeling and experimental validation of a magnetic levitation system with PD controller
 
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Faculty of Mechanical Engineering and Ship Technology, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-222, Gdańsk, Poland
 
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Kacper Falkiewicz   

Faculty of Mechanical Engineering and Ship Technology, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-222, Gdańsk, Poland
 
 
 
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ABSTRACT
This paper presents the identification, modeling, and experimental validation of a nonlinear magnetic levitation system. A mathematical model of the system was developed based on Newton’s second law and electrical circuit equations, taking into account the nonlinear dependence of the electromagnetic force on the coil current and the position of the levitating sphere. The model was implemented in the Matlab/Simulink environment and used for the design of a PD control system. A systematic study was carried out through both simulations and real-time experiments under identical operating conditions, including variations of disturbance amplitudes in the range of 0.2–0.7 and reference position changes from 0.005 to 0.015 m. A qualitative and quantitative comparison between the simulation model and the real system was performed, focusing on system dynamics, disturbance rejection, and stability margins. The obtained results confirm the qualitative accuracy of the proposed model while revealing significant limitations of the classical PD controller when applied to a nonlinear unstable system. In particular, a strong dependence of control performance on the operating point and a noticeable degradation under high disturbances and extreme reference values were observed. The results provide a foundation for further research on advanced control strategies, including optimal and adaptive control methods.
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