## 6 Discussion  
One of the most important functions of ATO is to control the train to accurately track the speed curve according to different train models and operating conditions (such as tunnels, curves, and steep slopes) so that the train can run safely and smoothly. The most widely used control method in ATO is PID controller (such as Beijing Metro Yizhuang Line, Changing Line, etc.) and the combination of PID and other intelligent control, such as fuzzy PID [35], sliding mode PID [36], RBF neural network PID [37], etc. Although the controller based on PID can obtain better tracking performance in the practical application of ATO, the ride comfort based on PID controller is poor due to the frequent switching of PID control commands. In addition to the mainstream PID control, other research on ATO control algorithms can be divided into two categories. One is the ATO controller designed by using train dynamics model information to ensure the accuracy of curve tracking, which is called model-based control method in this paper. The second category is to use the input and output data generated during train operation to estimate the system parameters online so as to realize the model-free adaptive control of the train, which is called the model-free adaptive control method in this article. The model-free adaptive control method only establishes the connection between the input and output data of the system, and does not have a clear physical meaning. It cannot predict and analyze the train dynamic behavior based on the dynamic input and output data model. For the straight routes, this method can track the position and speed curve with less error, but for the train operation environment with large external interference, the current model-free adaptive control method is difficult to ensure a consistent train operation control performance index for a long time, which needs to be further improved. Model-based control methods include single-particle dynamics models and multi-particle dynamics models. Since train dynamics is related to multiple factors, it is too complicated to establish a multi-particle dynamics model that can describe many factors, such as describing seven cars dynamics requires 84 differential equations [38]. The overly complex models are not conducive to the design of ATO controllers. Therefore, the mainstream research on the ATO control algorithm is based on the single-particle dynamics model. The research on the ATO control method in this paper is based on the single-particle train dynamics model. The establishment of the train dynamics model is an important part of ATO controller design. The accuracy of the model is directly related to the controller design and control effect. The dynamic behavior of train motion is related to many factors. It is very difficult to establish an accurate model. Besides its own traction and braking force, it is also affected by a variety of external and internal forces, including bearing friction resistance, wheel rolling and sliding resistance, impact and vibration resistance, air resistance, ramp resistance, curve resistance, tunnel resistance, etc. However, for different models, routes, and even different weather conditions, the model parameters will change, resulting in the uncertainty of the system model parameters. Therefore, it is necessary to design an adaptive control strategy that can identify unknown parameters and ensure good convergence. It is the first step to study the ATO control algorithm. The automatic train operating process also needs to consider multiple performance goals, namely energy consumption, punctuality, and ride comfort. In addition, under the long-term high-speed operation of urban rail trains, the traction or braking mechanism of the train is prone to failure due to factors such as high-temperature friction and severe vibration. Therefore, the fault-tolerant ability should also be considered in the design of the ATO system to ensure the operation safety of urban rail trains.