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Research on the Dynamical Stability of Maglev System

Author: ShenFei
Tutor: WuJianJun
School: Lanzhou University
Course: Solid Mechanics
Keywords: maglev stability Hopf bifurcation feedback control gain periodic oscillation delayed feedback control
CLC: U266.4
Type: Master's thesis
Year: 2009
Downloads: 105
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Abstract


One of the most serious problems in the maglev train is the vibration of the system which exists in all the maglev trains from the first one TR1 built in 1960s to the latest one TR8 running in Shanghai City. Therefore, the process of the development of maglev train has always gone with the process of searching for the keys to this problem. In order to go deep into the origin of the problem, it is necessary to theoretically analyze the dynamic characteristic of the maglev train.In this dissertation, focusing on the second order model of a maglev vehicle, the influences of the feedback control gains and the delay time on the stability of the maglev system are investigated, respectively. The main achievements are as follows:1. The influence of the feedback control gains on the stability of the maglev system is discussed. A test function for Hopf bifurcation is introduced to analyze the formation condition of the Hopf bifurcation. In this way, the time-consuming of eigenvalue computation in the process of analyzing system stability is avoided. With the velocity feedback control gains as the bifurcation parameter, the normal form theory and center manifold argument are applied to derive the explicit formulae, which determine the direction of Hopf bifurcation and the stability of periodic solutions bifurcating from trivial equilibrium.2. The influence of the delay time on the stability of the maglev system with delayed feedback control is investigated. The stable regions of some system parameters are gained by numerical methods, and the dynamic responses of maglev system are numerically simulated by using various parameters.3. Taking the time delay as the bifurcation parameter, the condition on which the Hopf bifurcation may occur is investigated. The explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the theory of normal form and center manifold. Meanwhile, the results of numerical simulations are given to support the above theoretical predictions. It can be seen obviously from the analysis that when the delay reaches the critical value, the maglev system will undergo a supercritical Hopf bifurcation and generate stable periodic oscillation. If the time delay is fixed and exceeds the critical value, then taking the feedback control gain as the bifurcation parameter, the asymptotically stable system can be regained by adjusting the feedback control gain in the direction opposite to that of the Hopf bifurcation.

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CLC: > Transportation > Rail transport > Locomotive works > EMU,EMU (power train ) > Non- wheel rail Department of locomotives, Maglev,gas floating car
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