| High-speed railway in China has undergone rapid development in recent years.The realization of railway high-speedization not only requires improving the locomotive’s performance,maintaining the structural stability of the railway line,but also ensuring that the train has a stable energy input when running at high speed.As an important facilities of the railway transportation system,the pantograph-catenary system is the guarantee for the safe and stable operation of the railway.However,as the speed of the train increases,the flow problem of the pantograph-catenary system becomes more complicated,and the negative effect of external excitation will be intensified.Therefore,it is necessary to analyze the dynamic characteristics of the pantograph-catenary system under the influence of external excitation.In this thesis,based on the fractional-order characteristics of the air spring in the pantograph,the dynamic model of the pantograph-catenary system containing fractional-order differential terms was constructed,then the influence of forced excitation on the stability of the pantograph-catenary system was analyzed,and the effect of fractionalorder time-delay feedback control on the stability of the pantograph-catenary system was studied.The main contents of this thesis are as follows:(1)The domestic and foreign research status of pantograph-catenary system,parametrically excited system,fractional-order differential and time-delay control were expounded,and the main innovation points of this thesis were discussed.(2)Based on the fractional-order characteristics of the air spring in the pantograph,the fractional-order model of the air spring was established and introduced into the modeling of the pantograph-catenary system,the fractional-order model of the pantograph-catenary system was obtained.(3)The stability determination theorem for the non-homogeneous parametrically excited system was extended,the analytical expressions for stability boundary and periodic solutions of pantograph-catenary system were derived by using the multiplescale method combined with the perturbation method.Then,the numerical analysis was used to verify the accuracy of analytical solutions,the influence of damping and fractional-order parameters on stability boundary was discussed.Finally,by substituting pantograph parameters,the stable current collection boundary related to train running speed and catenary span were obtained.(4)The properties of unstable periodic solutions in pantograph-catenary system were studied.By studying the generation conditions of periodic solutions,it was found that the periodic solutions will resonate when disturbed by forced excitation with the same frequency,then form unstable resonance regions.In addition,the properties of resonance regions were studied by numerical analysis,and the influence of system parameters on resonance regions were discussed.Then the results were combined with pantograph parameters to obtain unstable current collection range corresponding to the locomotive speed and catenary span in the resonance regions.(5)The stability of pantograph-catenary system under fractional-order time-delay feedback control was analyzed.Based on the multiple-scale method and the perturbation method,the analytical solutions for stability boundary were obtained,and the equivalent linear stiffness and the equivalent linear damping expressions described by the time-delay feedback control parameters were obtained,which revealing the influence form of fractional-order time-delay feedback control on system stability.Then,the numerical method is used to verify analytical solutions for stability boundary,and the influence of time-delay feedback control parameters on stability boundary and resonance region was analyzed.It was found that the fractional-order time-delay feedback can control both displacement time-delay feedback and velocity time-delay feedback control roles.Finally,the main conclusions derived from this investigation were summarized and directions for future research were outlined. |
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