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In this paper, a new analytical method using Lagrange equations for the analysis of magnetic levitation (MagLev) systems is proposed, using Thomson’s jumping ring experiment. The method establishes the dependence of the primary and induced currents, and also the equilibrium height of the levitating object on the input voltage through the mutual inductance of the system. The mutual inductance is calculated in two ways: (i) by employing analytical formula; (ii) through an improved semi-empirical formula based on both measurements and analytical results. The obtained MagLev model was analyzed both analytically and numerically. Analytical solutions to the resulting equations were found for the case of a dynamic equilibrium. The numerical results obtained for the dynamical model under transient operation show a close correspondence with the experimental results. The good precision of the analytical and numerical results demonstrates that the developed method can be effectively implemented.
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A dynamic model of the vehicle/guideway coupled with a controller is developed for the maglev demonstration system currently being developed at ODU, using the MAthematical DYnamic MOdeling software MADYMO. The fundamental characteristics of the vehicle and guideway are obtained from detailed finite element analyses using MSC-NASTRAN. As a result, the vehicle is modeled in MADYMO as a 21degree-of-freedom spring-mass-damper system. A three span concrete guideway is modeled using 3D solid Hex8 elements. The air gap is modeled as a penetration of the magnets into the guideway. Decentralized colocated PD controllers are used for controlling the penetration of each magnet at steady state levitation. The PD controllers aim at achieving constant penetration (i.e. constant desired air gap) for all magnets.
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