Magnetic Levitation of Permanent Magnet Spheres: Modeling and Simulation

The study of magnetic levitation systems has attracted significant attention due to their energy efficiency and minimal friction attributes that are deemed essential in various industries. These systems are characterized by inherent non-linearity and open-loop instability, primarily due to the dynamics of magnetic forces. This paper introduces a comprehensive approach to modeling and controlling a magnetic levitation system that levitates a permanent magnet sphere. The developed non-linear model realistically accounts for various system parameters including the length of the electromagnet, coil diameter, and number of turns. Additionally, the magnetic permeability of the electromagnet core is factored into the calculation of the system's magnetic force. Finally, the model also accounts for the magnetic field due to the permanent sphere. For control purposes, a linearized version of the system model is employed to design a proportional-integral-derivative (PID) controller. The efficacy of the derived model is demonstrated through comparison with experimental measurements of a magnetic levitation system that utilizes a Hall effect sensor. The findings of the comparison underscores the model's accuracy, confirming its viability for designing controllers for magnetic levitation systems.