Static and Dynamic Modeling of the Electromagnets of the Maglev Vehicle Transrapid

This work provides a new approach for modeling the electromagnets of the magnetic levitation (Maglev) vehicle Transrapid intending to effectively and efficiently represent the statics and the dynamics in a frequency range relevant for Maglev control design and for the use in mechatronic simulation models. It includes the effects of magnetic reluctances, fringing and leakage flux, magnetic saturation, and eddy currents. The modeling follows a systematic approach by setting up the equivalent magnetic and electric circuits, and coupling the equations using Ampère's circuital law and Faraday's law of induction resulting in a system of differential algebraic equations. It allows to study effects occurring in the magnet design process or different operating points, resulting, e.g., from aerodynamic uplift, for which an extended validity range is needed. Since the computational effort of such models is significant, additionally, a numerical procedure for model reduction is presented yielding a simplified version, which possesses a nearly identical input-output behavior and is usable for control design or in large vehicle models. The proposed approach can be applied to any levitation or guidance magnet of the vehicle and is shown exemplarily for a Transrapid's levitation magnet. The model is validated for the parameters of the latest Transrapid vehicle, called TR09, showing good correspondence with the measured static force-current-gap characteristics and the inductance.