Generalized first-principle model of magnetic levitation

Abstract

Since its first demonstration more than a half century ago, magnetic levitation (MagLev) has gained eminent scientific attention from both the fundamental and applied points of view. In essence, MagLev shows highly nonlinear dynamics, described with nonlinear differential equations. Thus, in order to exploit the MagLev phenomenon, both mathematical models and control algorithms must be constructed. Frequently authors use simplifications of the model, and in doing so, limit the application of the MagLev model around a nominal operating point. In these simplified cases, the MagLev models may contain parameters that are not represented by proper physical quantities. Thus, in this work, we revised the issue of MagLev modelling from the first-principle approach. More specifically, we theoretically derived expressions for the interaction between the magnetic fields of the solenoid and a small magnetic object. The behaviour of the inductance on a distance from the solenoid was then described. The suggested MagLev modelling concept was verified experimentally, confirming the validity and correctness of the proposed MagLev mathematical model. The results presented here could thus be regarded as highly beneficial for formulating more complex MagLev designs exploitable in the field of model predictive control of the position of a levitating object.