As a new approach to magnetic levitation by permanent magnet envisioned in 1990s, the concept of Inductrack has been applied to designs of various Maglev systems, including rocket launchers, Maglev trains, and the Hyperloop system as a conceptual future transportation tool. In such a system, the interaction forces between the source and induced magnetic fields are motion-coupled, and inevitably complicated with transient responses. Most previous investigations have mainly relied on the assumptions of ideal magnetic field, steady-state response and averaged magnetic force. Although these analyses provide some useful information for system design, due to limited understanding of the magnetic field-motion coupling and transient responses, they cannot predict the dynamic behaviors of an Inductrack system with fidelity and accuracy. Presented in this paper is a new transient model of Inductrack dynamic systems that is derived from fundamental physics laws, with the interactions of magnetic forces and motion in consideration. In the development, a state space representation of the transient model is established for numerical simulations. As verified in numerical examples, a benchmark 2-DOF transient model not only is able to reproduce the “steady-state” results reported in the literature, but also can exhibit the transient behaviors of Inductrack systems in longitudinal and vertical motion, which otherwise may not be possible by the existing models. The modeling approach presented in this paper is extendible to multi-degree-of-freedom (M-DOF) cases and it provides a foundation for stability analyses and feedback control of Inductrack systems.

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