## 5 Simulation Experiment
Figure 4: Position tracking performance ATSM-FTC-RBFNN. Figure 5: Speed tracking performance of ATSM-FTC-RBFNN. Figure 6: Position error of ATSM-FTC-RBFNN. As shown in Figure 7, the overall speed error of ATSM-FTC-RBFNN is \(-0.04\)-\(0\) m/s, which does not exceed the desired speed, ensuring the safety of train operation. When the train operates to 1148 s, the control accuracy of the ATSM-FTC-RBFNN controller is reduced due to the sudden change of desired speed, the uncertainty of Davis equation coefficient of basic resistance, and the interference of route additional resistance, and the speed error is \(-0.06\) mm. In order to overcome the mutation, uncertainty, and disturbance of the outside condition, the controller enhances the discontinuous nonlinear switching control in this period to maintain the control accuracy, as shown in Figure 8, which not only ensures the stable operation of the train on the route under the influence of various factors and disturbances, but also the final  
As shown in Figure 11, the position tracking error of ATSM-FTC is \(-0.4\)\(-0.42\) m. In the process of train operation, the position tracking error and speed tracking error have fluctuations due to the influence of train performance and external interference. The speed tracking error of ATSM-FTC is shown in Figure 12, which is between \(-0.11\) and \(0.02\) m/s. When the train just starts, it exceeds the expected speed by \(0.02\) m/s. After the train operates normally, its speed does not exceed the given desired speed. However, when the train operates between \(846\) and \(1148\) s, the control accuracy of the ATSM-FTC controller decreases due to the sudden change of desired speed and the influence of the operation environment. In order to overcome the mutation and influence of the outside environment, the controller enhances the nonlinear switching control in this period to maintain the control accuracy, as shown in Figure 13.  
Figure 10: Speed tracking performance of ATSM-FTC. Figure 9: Position tracking performance of ATSM-FTC. In order to further explore the performance of the controller, ATSM-FTC-RBFNN controller, ATSM-FTC controller, MFAC, and MFA-FTC controller in reference [17] are used for comparison. The actuator fault coefficient in reference [17] is shown in Table 2. In  
Figure 11: Position error of ATSM-FTC. Figure 12: Speed error of ATSM-FTC. Figure 4:0 Control input of ATSM-FTC. addition, in [17], the parameter settings of RBFNN remain unchanged, and the remaining parameters of the controller are set as \(u_{s}(1)=0.001\), \(u_{s}(2)=0.414\), \(v_{s}(1)=0.001\), \(v_{s}(2)=0.001\), \(\varphi_{1}(1)=0.001\), \(\rho_{1}=0.874\), \(\rho_{2}=0.001\), \(\lambda_{1}=0.002\), and \(\lambda_{2}=0.0015\). Figures 14-16 show the simulation comparison results of four controllers. Figure 14 is the position tracking error of the four controllers; Figure 15 is the speed tracking error of the four controllers; and Figure 16 is the control input of the four controllers. It can be seen from Figures 14 and 15 that when facing external interference, the ATSM-FTC-RBFNN controller has fast adjustment speed, fast convergence of the whole process state, strong anti-disturbance ability, good control performance, and strong fault tolerance, and can ensure the safe and reliable operation of the train. When the ATSM-FTC control is faced with external interference, its state error converges slowly. That is to say, in the whole process of train operation, the position error and speed error of the train are large. The position tracking error and speed tracking error of the MFAC controller in reference [17] gradually diverge with the increase of fault degree, and the tracking performance is significantly reduced. Compared with MFAC, the position tracking error and speed tracking error of the MFA-FTC control algorithm in [17] are significantly improved. But when the degree  
Figure 4:1 Control input comparison. Figure 4:2 Position error comparison. Figure 4:3 Speed error comparison.