Spatial Adaptive Iterative Learning Tracking Control For High-speed Trains Considering Passing Through Neutral Sections

High-speed railway is an important developing industry related to the economy,society and national security.With the rapid development of high-speed railway in China,the requirements for high-efficiency,punctuality and comfort of the high-speed trains are increasing constantly.The precise tracking control has become a research hotspot in the field of train automatic driving control.In addition,in order to avoid causing the adverse negative sequence current in the power supply system,neutral sections are usually set in railway catenary.The non-electricity property of neutral sections will cause the loss of train speed.In the serious case,the train will stop in the neutral section and fail to get out without the traction force,causing a safety accident.How to make full use of the repetitive characteristics of high-speed trains to realize the precise tracking control considering passing through neutral sections is of great theoretical value and practical application.Firstly,the development of automatic train operation control is briefly introduced,as well as the iterative learning control(ILC)strategy used in this paper,including its control basis and research situation.Compared with the model-based control theory,ILC can learn the historical information and prior knowledge of the system based on the repetitive characteristics.This part is the control basis and theoretical basis for the controller design.Secondly,the force analysis of the high-speed train is carried out.Combining with the Newton’s second law,the train is regarded as a single particle model and a motion dynamic model of high-speed trains in time domain is established.In order to resolve the contradiction caused by the neutral section,it is considered as the input saturation constraint in the space domain.Since the train is affected by random external disturbances and parameter uncertainties during operation,adaptive control strategy is introduced to reduce the impact and achieve higher precision tracking.Via the spatial differential operator,the model in time domain is transformed into the spatial dynamics model under the framework of ILC.An adaptive iterative learning controller is designed,which is composed of two parts:control law and parameter update law.The control law includes a nonlinear feedback term that can continuously learn and improve the speed tracking performance.The parameter update law can repeatedly learn the nonlinear structure characteristics and unknown parameter information of train system.Based on the Composite Energy Function(CEF)theory,a composite energy function containing a Lyapunov function term is constructed,of which non-increasing and boundedness are analyzed.In addition,the stability of the control system and the error convergence is proved.The factors that affect the convergence speed is discussed.Finally,the proposed ILC scheme is verified by simulation experiments on the MATLAB platform.Numerical simulation is performed based on a CRH2-type train.The simulation trial considered two cases where the neutral section is located on a gentle slope and a long steep grade.The results show that the speed tracking performance improves along the iterative domain.The stability of the closed-loop system and the control scheme effectiveness are confirmed.