To improve the tracking accuracy and stable operation of the train control system,an improved multiple-input multiple-output(MIMO)model-free adaptive control(MFAC)method was proposed.Based on the dynamic linearization technology,the input-output data of each power unit of the system were equivalently transformed into a full form dynamic linearization(FFDL)data model that better fitted the actual operation characteristics of high-speed electric multiple units(EMUs).By incorporating the output error rates into the objective criterion function and weighting the fusion of output errors and output error rates,a new model-free adaptive control scheme with output error rates(MFAC-OER)was derived.The control performance of the algorithm and the equivalent description degree of the system were further improved by delayed estimation of uncertainty factors,such as external disturbances and parameter errors in the FFDL data model.The proposed method was simulated and tested on a CRH380A high-speed EMUs semi-physical test platform equipped in the laboratory to track the actual speed-displacement curve from Jinan to Xuzhou and compare it with some traditional algorithms.Simulation results show that the speed errors of each power unit of EMUs obtained by the MFAC-OER method are within[-0.151,0.136]km·h-1,with the control force and acceleration smoothly varying in the ranges of[-48,42]kN and[-0.785,0.687]m·s-2,respectively.The proposed method outperforms the proportional-integral-derivative(PID)and traditional MFAC methods in the control performance.The overall simulation results show that the MFAC-OER method can not only quickly reach the steady state of the system but also possesses good resistance to external disturbances,meeting the tracking accuracy and safety requirements of the EMUs.3 tabs,12 figs,30 refs.