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Nonlinear modeling and experimental validation of a magnetic levitation system using a proportional-derivative 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 nonlinear modeling and experimental evaluation of a two-electromagnet magnetic levitation system controlled by a fixed-gain proportional-derivative (PD) controller. A nonlinear mathematical model was developed from Newton’s second law and the electrical dynamics of both electromagnets, including the dependence of electromagnetic force on coil current and sphere position. The model was implemented in MATLAB/Simulink and compared with experimental recordings for corresponding disturbance amplitudes and reference air gaps. Two scenarios were investigated: varying disturbance amplitude and varying reference position. Agreement was assessed using position RMSE and MAE, supplemented by comparisons of velocity, coil currents, and control voltage. For a disturbance amplitude of 0.2 V and a reference upper air gap of 0.009 m, the position RMSE and MAE over 10 s were 0.0824 mm and 0.0496 mm, respectively. Discrepancies increased with disturbance amplitude. The model reproduced the principal response trends but did not consistently reproduce the magnitude and oscillatory behavior of the experimental responses. The fixed-gain PD controller maintained levitation in a limited subset of the tested conditions, while changes in operating point produced steady-state tracking errors. Validation was restricted to intervals preceding the geometric boundary. These findings support further investigation of improved models and control strategies.
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