# Study on the Multi-Mode Optimal Control of Four-Wheel Steering Vehicle
## 3 Design of Multi-Mode Optimal Decision Control System
### Design of Self-Tuning Double Yaw Rate Feedback Controller
#### 3.1.2 Comparison of Simulation Analysis  
To analyze the characteristics of the self-tuning dual yaw rate feedback controller, the front wheel angle step simulation experiment is carried out and compared with other controllers. The input vehicle speed is 72 km/h, the front wheel angle is 8.5\({}^{\circ}\), and the simulation is 8 s. The results are shown in Figures 6 and 7. The input vehicle speed is 72 km/h and 80 km/h, the front wheel angle is 6\({}^{\circ}\) and 15\({}^{\circ}\), and the simulation is 8 s. The results are shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**U**} & \multicolumn{8}{c}{**E**} \\ \cline{2-10}  & & **NL** & **NM** & **NS** & **ZE** & **PS** & **PM** & **PL** \\ \hline \multirow{6}{*}{EC} & NL & PL & PL & PL & PM & PM & PS & ZE \\  & NM & PL & PL & PL & PS & PS & ZE & NS \\  & NS & PL & PL & PM & PS & ZE & NS & NS \\  & ZE & PL & PM & PS & ZE & NS & NS & NL \\  & PS & PS & PS & ZE & NS & NM & NM & NL \\  & PM & PS & ZE & NS & NM & NL & NL & NL \\  & PL & ZE & NS & NM & NL & NL & NL & NL \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fuzzy rules of main fuzzy controller. Figure 4: Membership function of input variable E, EC and output variable U. As shown in Figure 6, the overall performance of the four-wheel steering vehicle with self-adjusting control is better than that without self-adjusting control. The steady-state response value of the sideslip angle is 0.29 rad, and the steady-state value without self-adjusting is 0.41 rad, which is reduced by 29%, the yaw rate is reduced by 21%, and the lateral acceleration is reduced by 21%. When the four-wheel steering vehicle with self-adjusting double yaw rate control is used, the sideslip angle, yaw rate, and lateral acceleration are reduced by 29.3%, 69%, and 69% compared with the self-adjusting control, and the handling stability is better. Figure 5: Membership function of input variable E, EC and output variable T.  
Figure 6: Response comparison. (**a**) Sideslip angle. (**b**) Yaw rate. (**c**) Lateral acceleration. Figure 7: Comparison of different controllers. (**a**) Sideslip angle. (**b**) Yaw rate. (**c**) Lateral acceleration. Figure 7a shows that the response speed of sideslip angle of the four-wheel steering vehicle with the yaw rate feedback controller is the same as that of the front-wheel steering vehicle, but the amplitude is large. However, the response speed of sideslip angle of the four-wheel steering vehicle under the self-tuning feedback control strategy is fast and the amplitude is small, the steady-state is 0, and the time to reach the steady-state is 0.1 s, which is greatly reduced compared with the yaw rate feedback and the 3 s under the steady-state condition of 2 WS. It can be seen from Figure 7b that the yaw rate amplitude of the four-wheel steering vehicle with yaw rate control is large and the response speed is slow. After the self-tuning control is added, the response speed is further reduced, and the amplitude is smaller than that of the front wheel steering and yaw rate feedback control. It can be seen from Figure 7c that the lateral acceleration amplitude of the four-wheel steering vehicle with the self-adjusting double yaw rate control strategy is smaller and the response is faster. It can be seen from Figure 8 that under the conditions of the same speed and different rotation angles of the vehicle, the amplitude of the sideslip angle of the four-wheel steering vehicle with the self-adjusting double yaw rate feedback controller increases, and the response speed decreases slightly with the increase of the rotation angle. Under the conditions of the same rotation angle and different speeds, with the increase of the speed, the amplitude of the sideslip angle of the four-wheel steering vehicle with the self-adjusting double yaw rate feedback controller further increases and the stability decreases slightly. The performance of yaw rate and lateral acceleration decreases with the increase of vehicle speed.