# Research on Tracking Control of Urban Rail Trains Based on Improved Disturbance Observer
## 4 Simulation Verification and Results Analysis
Figure 8 provides the variation curves of the coupler position. The variation curves show that the proposed method can ensure that  
Figure 6: Position tracking error curves under IDOBC. Figure 7: Speed tracking error curves under IDOBC. the coupler position of the URTs remains within the safety range of \([-0.01,0.01]\) m during the whole operation, which satisfies the important index of security [30]. As shown in Figure 9, the estimation error converges to near the zero region at \(t=0.8\) s and can quickly compensate for the effect of unknown disturbances on the URTs within 1 s. It is evident that the proposed improved disturbance observer demonstrates outstanding capacity for compensating for disturbances. To validate the advantages of the proposed method in terms of control precision and disturbance rejection capability, we conduct comparison experiments with the traditional disturbance observer-based control (TDOBC) method under the same experimental conditions. The design of the TDOBC law is the same as (20). The plots of position tracking error, speed tracking error, coupler position, and disturbance estimation error under the TDOBC method are shown in Figures 10-13, respectively. Comparing Figures 6 and 10, the convergence effect of the position tracking under the IDOBC strategy is better than that of the TDOBC method, and the error fluctuations are smaller, especially on the first power unit. In Figures 7 and 11, both control methods have good speed tracking effects. However, the time for power unit 1 to converge to near the zero region after suffering from external perturbations under the IDOBC strategy is reduced by nearly 50% compared to the TDOBC approach. From Figures 8 and 12, the IDOBC strategy can make the coupler displacement fluctuate in a smaller range, extending the coupler  
Figure 8: Coupler position variation curves under IDOBC. Figure 9: Disturbance estimation error under IDOBC. In order to analyze the control performance of the two methods more clearly, we have calculated the maximum positive error (MPE), maximum negative error (MNE), and mean absolute error (MAE) under the two different methods in Tables 3 and 4, respectively. The MAE metrics for speed are shown as (29). \[MAE=\frac{1}{n}\sum_{i=1}^{n}|v_{i}-v_{r}| \tag{29}\]  
The data obtained from the statistics for each indicator are shown in Tables 3 and 4. According to the position tracking data of the URTs in Table 3, it is apparent that the maximum positive and negative tracking errors for each carriage under the same conditions with the IDOBC method are \([-7.8091\times 10^{-4},2.7326\times 10^{-4}]\) m. The range is smaller compared to the IDOBC method, which indicates that the method in this paper can better cope with the situation where the operating conditions change. Although Table 4 shows that the maximum positive and negative speed tracking errors of IDOBC \([-0.0035,0.0018]\) m/s and IDOBC \([-0.006,0.0042]\) m/s are very similar, the MAE of the IDOBC method is an order of magnitude smaller than that of IDOBC. MAE is the deviation of the actual value from the expected value and is very sensitive to outliers. The smaller the MAE, which means that the error fluctuation more minor in the whole operation process, to a certain extent, improving the stability of the driving process. In conclusion, the proposed control strategy can enable the URTs to track the target curves better than the IDOBC method and has a more robust attenuation capability in dealing with complex road conditions and unknown external disturbances, which improves the safety and stability of the train. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Strategy (m/s)** & **MPE (m/s)** & **MNE (m/s)** & **MAE (m/s)** \\ \hline IDOBC & 0.0018 & \(-0.0035\) & \(6.8497\times 10^{-6}\) \\ IDOBC & 0.0042 & \(-0.006\) & \(8.9933\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Speed error statistical analysis  
Figure 13: Disturbance estimation error under TDOBC.