# Improved ADRC-Based Autonomous Vehicle Path-Tracking Control Study Considering Lateral Stability
## 5 Results and Discussion
### Validation of Controller Effectiveness without Disturbance
#### 5.1.2 DYC Controller Validation  
The experimental results given above verify the effectiveness of IADRC. To fully verify the performance of the control scheme proposed in this paper, the controller path-tracking accuracy after considering the yaw stability is compared and analyzed through double-lane change maneuver experiments; the performance of braking force distribution based on the CA concept is verified and analyzed.  
From Figure 12, it can be seen that the vehicle with and without DYC control both have better path-tracking accuracy; however, from Figure 13, it can be seen that the maximum value of the lateral deviation of the vehicle without DYC control is about 0.20 m, while the same value of the vehicle with DYC control is about 0.15 m; from Figure 14, it can be seen that the heading error of the vehicle is smaller after DYC control is applied. Moreover, Table 3 shows the maximum values and the RMS values of the tracking error for the cases of DYC control and no DYC control. It can be seen that after applying DYC control, the maximum value of lateral deviation is 0.1425 and the RMS value is 0.0456, both of which are smaller than the case without DYC control; similarly, the maximum value of heading angle is 2.6322 and the RMS value is 0.6601, both of which are also lower than the case without DYC control. Therefore, it can be seen that the path-tracking accuracy of the vehicle after applying DYC control is higher than that of the vehicle without DYC control.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Lateral Deviation**} & \multicolumn{2}{c}{**Heading Error**} \\ \cline{2-5}  & **Max** & **RMS** & **Max** & **RMS** \\ \hline LQR & 0.2052 & 0.0602 & 3.2727 & 0.9201 \\ \hline ADRC & 0.2027 & 0.0598 & 2.5001 & 0.7144 \\ \hline IADRC & 0.1840 & 0.0593 & 3.2043 & 0.8360 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Tracking error.  
Figure 11: Front-wheel steering angle.  
Figure 15 shows the vehicle yaw rate response, and Figure 16 shows the vehicle side-slip-angle response. It can be seen that the yaw rate of the vehicle can better track the desired value after DYC control is applied, and the deviation of the yaw rate is smaller; the vehicle side-slip angle is also smaller than that of the vehicle without DYC control. Thus, we can conclude that the vehicle has better lateral stability. From Figures 17 and 18, it can be seen that the braking force distributor based on the concept of CA proposed in this paper can fully and optimally coordinate the four wheels to achieve external yaw moment through the form of differential braking; thus, we can conclude that the braking force distributor proposed in this paper is effective.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Lateral Deviation**} & \multicolumn{2}{c}{**Heading Error**} \\ \cline{2-5}  & **Max** & **RMS** & **Max** & **RMS** \\ \hline IADRC (with DYC) & 0.1425 & 0.0456 & 2.6322 & 0.6601 \\ \hline IADRC(without DYC) & 0.1840 & 0.0539 & 3.2043 & 0.8360 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Tracking error.  
Figure 12: Path-following result.  
Figure 13: Lateral deviation.  
In summary, the IADRC control scheme proposed in this paper has a better path-tracking effect, while the new nonlinear function proposed in this paper instead of the classical piecewise function can solve the problem of variable control input jitter; in the braking force distribution, the braking force distribution scheme with CA method can  
Figure 16: Side-slip angle.  
Figure 17: External yaw moment.  
Figure 18: Individual wheel brake torque.  
Figure 15: Yaw rate.  
optimally coordinate the braking force of each wheel so as to realize direct yaw moment control output from IADRC. Application of DYC control not only improves the path-tracking accuracy, but also improves the yaw stability of the autonomous vehicle.