# Stability Analysis of Lane-Keeping Assistance System for Trucks under Crosswind Conditions
## 3 Results  
The lateral stability performance of the vehicle was judged by comparing the sideslip angle, yaw rate, and lateral acceleration during driving, because they are important parameters to characterize the lateral stability of the vehicle, and whether the vehicle is in a stable state during driving can be seen through these parameters. In the first condition, without crosswind, that was under normal driving conditions without any lateral interference, the LKAS strategy could control the vehicle to track the target path on the test road, so that the vehicle was kept in the middle of the road line, where the vehicle was driven at a speed of 80 km/h. As shown in Figure 7, from 4 s to 20 s, the vehicle was on the curved part of the test road and was constantly adjusting its position, so the lateral position deviation was also increased with the continuous changes. However, the LKAS control strategy can maintain the accuracy of the lateral position deviation at the millimeter level, and the vehicle was smoothly kept in the middle of the road line. Therefore, the designed LKAS control strategy exhibited high precision. In the other conditions, when the crosswind interference was considered, the LKAS strategy controlled the vehicle to track the target path on the test road, so that the vehicle remained in the middle of the road line, the maximum crosswind speed was 40 km/h, and the vehicle was traveling at 80 km/h. As shown in Figure 8, The vehicle began to enter the curve at 4 s after being affected by the crosswind. However, the steering angle quickly adjusted after 0.1 s, enabling the vehicle to continue tracking the path with high precision. The maximum steering angle with LQR control was 30\({}^{\circ}\) during the crosswind  
Figure 6: Hardware-in-the-loop flowchart. Figure 7: Vehicle lateral position deviation. disturbance, while the maximum steering angle without LQR control reached 40\({}^{\circ}\). After leaving the crosswind zone, the vehicle with LQR control quickly stabilized to 19\({}^{\circ}\) after 1 s, while the vehicle without LQR control continued to oscillate. The sideslip angle, yaw rate, and lateral acceleration of the vehicle are shown in Figures 9-11, respectively. As shown in Figure 9, the sideslip angle of the vehicle using the LQR control strategy had a significant adjustment and changed quickly, and the amplitude change of the lateral acceleration was smaller than that of the vehicle without the use of LQR control. Then, starting from the 6 th second, the interference of crosswind disappeared, and the vehicle without the LQR control strategy had a large fluctuation, so the vehicle was in an unstable state. As show in Figure 10, when the crosswind disappeared from the 6 th second, the rapidly rising lateral acceleration was quickly pulled back to 0.1 m/s\({}^{2}\) and became stable. As shown in Figure 11, the yaw rate of the LQR-controlled vehicle responded quickly after encountering the crosswind in the 4 th second, and after leaving the crosswind zone, the yaw rate rapidly became stable. Meanwhile, the compared parameters of the vehicle without LQR control were slow to respond when it encountered crosswind interference at 4 s, and the amplitude of the adjustment was higher. After leaving the crosswind area, the vehicle did not quickly enter a stable state but kept oscillating, so the vehicle was in an unstable state. Therefore, by comparing the differences in the sideslip angle, lateral acceleration, and yaw rate of the vehicle when driving on a curved road while being disturbed by crosswinds, it can be seen that the LQR control strategy can ensure that the vehicle can drive smoothly on the test road when disturbed by crosswinds, without instability, which further proves the effectiveness of the designed LKAS control strategy. Figure 12 presents the experimental results of the desired and actual steering angles.