Vibration Control For Pantograph-Catenary System Based On Fractional-Order Model

With the continuous improvement of running speed,the high-speed trains require better current-receiving quality,and the pantograph-catenary system,as the power supply equipment for electrified railways,directly affects the safety and stability of railway operations.Modeling the pantograph-catenary system using fractional calculus theory can accurately reflect its dynamic characteristics.Studying the vibration control of the pantograph-catenary system is of great significance for improving the quality of current collection and ensuring the safe operation of high-speed trains.The main research focuses on the following aspects:(1)Establishing a fractional-order pantograph-catenary system model.Firstly,the fractional-order air spring model is established,and the accuracy of the model is verified by experiments.Then,the fractional-order air spring model is applied to modeling of the pantograph,and the fractional-order pantograph-catenary system model is established.(2)Studying LQR active control of the fractional-order pantograph-catenary system based on feedback linearization.The fractional-order derivative term in the pantograph-catenary model is approximately calculated using the Oustaloup filter algorithm.The extended variable method is used to deal with the time-varying stiffness of the catenary,the differential geometry method is used to feedback linearize the augmented model of the pantograph-catenary,and the LQR active controller is designed.Simulation results show that the feedback linearized LQR active control has a better control effect than PID control,and it can also performs well under different pantograph parameters and different train speeds,which fully proves the effectiveness of the feedback linearized LQR active control for the pantograph-catenary system with fractional-order terms.(3)Studying the vibration control analysis of the fractional-order pantographcatenary system with a dynamic vibration absorber.The pantograph-catenary model with dynamic vibration absorber is established,which is solved by the harmonic balance method and verified by the numerical solution.The influence of constant excitation,dynamic vibration absorber parameters and suspension position on the vibration characteristics of the pantograph head are studied,and the parameters of the dynamic vibration absorber are optimized by the grey wolf algorithm.The vibration reduction effect of dynamic vibration absorber is discussed when the pantograph is excited periodically with the excitation frequency being an integer multiple of the parameter excitation frequency.The results show that the dynamic vibration absorber can effectively reduce the peak amplitude-frequency response of the pantograph head and the vibration reduction effect is obvious.(4)Studying the vibration control analysis of the fractional-order pantographcatenary system with a nonlinear energy sink.The pantograph-catenary model with the nonlinear energy sink is established,which is solved by the incremental harmonic balance method and verified by the numerical solution.The influence of constant excitation,nonlinear energy sink parameters and suspension position on the amplitudefrequency response of the pantograph head is analyzed,and the parameters of the nonlinear energy sink are optimized.When the pantograph is excited periodically with the excitation frequency being an integer multiple of the parameter excitation frequency,the influence of nonlinear energy sink on the vibration control of the pantographcatenary system is studied.Finally,the vibration reduction effects of nonlinear energy sink and dynamic vibration absorber under different working conditions are compared.In summary,this article investigates the vibration control problems of the pantograph-catenary system in high-speed trains based on the theory of fractional calculus.A fractional-order model of the pantograph-catenary system is established.On one hand,a feedback linearization-based LQR active control strategy is proposed.On the other hand,the application and analysis of two different vibration dampers,namely the dynamic vibration absorber and the nonlinear energy sink,in the vibration control of the pantograph-catenary system are investigated.Finally,the main results are summarized in the last Section,and the existing problems and the research in the future are also pointed out in this section.