# Research on Tracking Control of Urban Rail Trains Based on Improved Disturbance Observer
## 4 Simulation Verification and Results Analysis  
In order to verify the effectiveness of the IDOBC strategy proposed in this paper, simulation experiments are conducted for the URTs subjected to lumped disturbances and actuator faults. In the simulation experiment, we selected the type B URTs of Nanchang Metro containing six carariages as the study object. The Nanchang Metro adopts the formation mode of four motor carariages and two trailers, and the carriage at both ends does not provide power. The entire traction/braking system of the URTs consists of three relatively independent power units so that it can be divided into three power units, and the train formation structure is shown in Figure 4.  
In the actual URTs operation, the fastest speed of the type B train can reach 80 km/h, and its primary parameter data are shown in Table 2.  
Here, this paper takes one interval in a subway line in Nanchang Metro as a simulation case, and the travel time is the 150 s, \(t\in[0,150]\), and the distance between two stations is 2265.3 m. In this interval, the track curve length is \(l_{r}=10^{3}\) m, the curve center angle size is \(\alpha=(2\pi/3)\), the slope angle is \(\theta=(0.5\pi/180)\), and the tunnel length is \(l_{s}=5\times 10^{3}\) m. Since the two carriages are considered as one power unit, \(S\) is taken as 46.6 m in the simulation experiment. The target curves are the desired curves obtained using the optimization algorithm in previous research, as shown in Figure 5.  
Considering the external disturbances experienced during the operation of the URTs, select a large uncertainty [23]: \(O(\centerdot)=5\times 10^{3}\sin(5+(0.1\centerdot\centerdot rand)t)\), \(t\in[60,70]\), which means that the external disturbance is introduced at the 60 s during the operation of the URTs and maintained for 10 s, the size is about 60% of the additional resistance. _rand_ denotes an arbitrary constant in the interval \([0,1]\). The observ \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Symbols (\(i=1,2,3\))** & **Parameter Value** \\ \hline \(m_{1}\) & \(9.58\times 10^{4}\) kg \\ \(m_{2}\) & \(9.56\times 10^{4}\) kg \\ \(m_{3}\) & \(9.58\times 10^{4}\) kg \\ \(a_{i}\) & 2.031 N/kg \\ \(b_{i}\) & 0.0622 Ns/mkg \\ \(c_{i}\) & 0.00187 Ns\({}^{2}\)/m\({}^{2}\)kg \\ \(\kappa\) & \(8\times 10^{4}\) N/m \\ \(21\) & 23 m \\ \(\theta_{i}+\theta_{i+1}\) & 0.6 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The URTs parameters. Figure 4: The type B URTs formation structure diagram  
Figure 5: Desired position curve and desired velocity curve. as \(L=3\times 10^{4}[zero(3,3),diag([1,1,1])]\). The controller gain matrix can be solved by Equation (23) through the MATLAB toolbox, and the value obtained from the solution is  
\[K=2.5\times 10^{5} \begin{bmatrix}-1&0&-1&-4.4&-1&0\\ -1&-2000&0&-3&-4.45&-2\\ -20&-10&-2000&0&-50\end{bmatrix} \]  
Assuming the actuator failure parameter \(\rho=diag\{1,0.8,0.6\}\), this means that the actuators of the second and third power units have partially failed, and the first actuator is working properly. Define the initial value of the state \(X(0)=zeros(6,1)\) and \(g=9.8\) N/kg. The simulation curves of the proposed IDOBC strategy are shown in Figures 6-9. The position error \(\tilde{x}_{i}(t)\) variation curves and speed error \(\tilde{v}_{i}(t)\) variation curves are given in Figures 6 and 7. As illustrated in Figure 6, the tracking error of the first power unit has large fluctuations in magnitude at the beginning due to the aerodynamic resistance. Due to the influence of external disturbance, the tracking error of the first power unit has a short fluctuation at the 60 s. Still, the accuracy of the tracking error is within the allowed \(\pm 0.3\) m range during the whole running process [29]. From Figure 7, it can be get that the external disturbance has some effect on the speed track, but it converges to zero within a very short time of less than 1s after the appearance of the disturbance. The speed tracking error satisfies the operating conditions of the URTs.