## 4 Yaw Stability Control Method for the Liquid Tank Semi-Trailer and Its Implementation
### Wheel Slip Rate Control in Yaw Stability Control Method for the Liquid Tank Semi-Trailer
It can be seen from Figure 14a,b that compared with no control, multi-object control reduces the maximum yaw rate of the tractor by 45.45% and the maximum yaw rate of the semi-trailer by 4.55%; for \(\omega_{1}+\omega_{2}\), the maximum yaw rate of the tractor is reduced by 50.15%, and the maximum yaw rate of the semi-trailer is reduced by 6.82%; for \(\omega_{1}+\theta\), the control reduces the maximum yaw rate of the tractor by 40.91%, and the maximum yaw rate of the semi-trailer by 2.27%. In conclusion, compared with the no control strategy, the multi-object control and \(\omega_{1}+\omega_{2}\) control can effectively reduce the maximum yaw rate of the tractor and semi-trailer. It can be seen from Figures 15 and 16 that compared with no control, the maximum lateral displacement deviation of the tractor under multi-object control is reduced by 3.71%, the maximum lateral displacement deviation of the semi-trailer is reduced by 5.45%, and the maximum articulation angle is reduced by 46.67%; for \(\omega_{1}+\omega_{2}\) control, the lateral displacement deviation of the tractor, semi-trailer, and the maximum articulation angle are reduced by 1.85%, 3.64%, and 33.33%, respectively; the \(\omega_{1}+\theta\) control reduced the lateral displacement deviation of the tractor by 5.56%, the lateral displacement deviation of the semi-trailer by 7.28%, and the maximum articulation angle by 58.33%. In conclusion, compared with the no control strategy, the multi-object control and \(\omega_{1}+\theta\) control can effectively reduce the maximum lateral displacement deviation and articulation angle of the tractor and semi-trailer. Verification of the Effectiveness of the Yaw Stability Control Method under the Step-Steering-Angle Input Working Condition  
In this section, the step-steering-angle input working condition simulation test is per-formed when the liquid tank semi-trailer is running on a low-adhesion coefficient road. The comparison diagrams of the yaw rate, the vehicle track, and the articulation angle of the tractor and semi-trailer are shown in Figures 17-19, respectively. It can be seen from Figure 17a,b that compared with no control, multi-object control reduces the maximum yaw rate of the tractor by 52.5% and the maximum yaw rate of the semi-trailer by 43.3%; for \(\omega_{1}+\omega_{2}\), the maximum yaw rate of the tractor is reduced by 57.5%, and the maximum yaw rate of the semi-trailer is reduced by 46.7%; for \(\omega_{1}+\theta\), the control reduces the maximum yaw rate of the tractor by 37.5%, and the maximum yaw rate of the semi-trailer by 36.7%. In conclusion, compared with the no control strategy, the multi-object control and \(\omega_{1}+\omega_{2}\) control can effectively reduce the maximum yaw rate of the tractor and semi-trailer. Figure 16: Comparison of articulation angle under the double-lane change working condition. It can be seen from Figures 18 and 19 that compared with no control, the maximum lateral displacement deviation of the tractor under multi-object control is reduced by 31.3%,  
Figure 19: Comparison of articulation angle under the step-steering-angle input working condition. Figure 17: Comparison of vehicle yaw rate under the step-steering-angle input working condition: (**a**) comparison of tractor yaw rate and (**b**) comparison of semi-trailer yaw rate. Figure 18: Comparison of vehicle track under the step-steering-angle input working condition: (**a**) comparison of tractor track and (**b**) comparison of semi-trailer track. the maximum lateral displacement deviation of the semi-trailer is reduced by 38.9%, and the maximum articulation angle is reduced by 81.5%; for \(\omega_{1}+\omega_{2}\) control, the lateral displacement deviation of the tractor, semi-trailer, and the maximum articulation angle are reduced by 25.3%, 33.3%, and 25.5% respectively; the \(\omega_{1}+\theta\) control reduced the lateral displacement deviation of the tractor by 37.5%, the lateral displacement deviation of the semi-trailer by 42.2%, and the maximum articulation angle by 88.2%.