Transient Vibration and Feedback Control of an Inductrack Maglev System

As a new strategy for magnetic levitation envisioned in 1990s, the Inductrack system with permanent magnets aligned in Halbach arrays has been intensively studied and applied in many projects in different countries. To analyze such a system, most previous investigations have utilized steady-state Inductrack models, which commonly assume ideal sinusoidal magnetic field, fixed levitation gap, constant traveling speed, steady-state induced current and averaged magnetic force. However, due to the nonlinear, time-varying and motion-dependent electro-magneto-mechanical coupling in an Inductrack Maglev system, the dynamic behaviors are naturally complicated with transient responses, which in most cases can hardly be predicted with accuracy and fidelity by a steady-state Inductrack model.

Presented in this paper is a benchmark 2-DOF transient Inductrack model that is derived from the first laws of nature, without any assumption of the above-mentioned steady-state quantities. The model is built based on general transient response scenarios and with the consideration of practical issues, such as the finite dimensions of the on-board magnet arrays, the transient effects of the induced currents in the coils on the track, and the interaction forces between each magnet block and each track coil. It is found from thorough derivation that the Inductrack dynamic system is governed by a set of nonlinear integro-differential equations. As demonstrated by numerical simulations with the transient model, unstable vibrations in the levitation direction can occur, particularly when the vehicle is coasting at low traveling speeds. This phenomenon is accordance with the well-known “negative damping” effect discovered in traditional electrodynamic suspension systems for Maglev transportation.

To resolve the issue of instability, feedback control is implemented in the Inductrack Maglev system. In the development, active coils are wound around the on-board permanent magnets to generate an added and controllable source magnetic field. In this preliminary investigation, the proposed controller design process takes two main steps. First, a simple PID controller is set and tuned based on the basic lumped-mass dynamic system, which computes the required control force. Second, the nonlinear current-force correlation is obtained from a lookup table that is pre-calculated by a truncated version of the full transient Inductrack model, and this output current is served as the actual input of the entire Inductrack dynamic system. With the implemented feedback controller, the numerical examples show that the vertical oscillation of the vehicle can be effectively stabilized in a short time at various traveling speeds. Although only a 2-DOF transient model is used here, the modelling technique and the feedback control method developed in this work are potentially applicable to more complicated Inductrack Maglev systems.