## 5 Simulations Results and Analysis
### Results of Switch Control Strategy
#### 5.2.1 J-Turn Maneuver  
The random road input is shown in Figure 12(a), and the vehicle steering angle of J-turn maneuver is displayed in Figure 12(b). The dynamic responses of the HDSMC-controlled vehicle (blue lines), RCSMC-controlled vehicle (black lines), and the vehicle with the Switched SMC (red lines) are shown in Figure 14.  
It can be seen from Figure 12(b) that the vehicle is going straight in the time range of [0, 5] s, and the LTR value is much smaller than the threshold. During this period, the main task for the Switched SMC is to pursue the ride comfort. Therefore, the vehicle's vertical acceleration curves in Figure 13(a) during this period by the RCSMC and Switched SMC are basically identical, and the ride comfort of HDSMC is noticeably worse than that of the other two controllers. Moreover, the roll angle of the vehicle is small with different controllers during the time of [0, 5] s. The J-turn begins at the 5 th second; then the vehicle roll angle and the LTR increases rapidly. The sudden steering has an impact on the ride comfort of the vehicle (point I), which is can be seen in Figure 13(a). As a result, the switch of Switched SMC is not active until the LTR reaches the threshold at the 6.6 th s; then the main purpose of the Switched SMC changes from the ride comfort of the vehicle to the handling stability of the vehicle. As shown in Figure 13(b)-f, during [6.6, 10], the values of the roll angle are reduced significantly and the LTR is dragged towards to the set value with the control of the Switched SMC. However, the LTR of the vehicle with the RCSMC is increasing with the steering of the vehicle, which is likely to cause unsafe driving conditions that lead to accidents and delays. In addition, the switch action also can be confirmed by the switch value in Figure 13(e). When the switch value changes from 0 to positive, then the switch occurs. In addition, the switch action of the Switched SMC causes to a certain extent an impact on the ride comfort of the vehicle, which is point II shown in Figure 13(a). The frequency domain \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**J-turn/Fishhook**} \\ \hline
**Road Condition** & **Random Road** & **Bump Road** \\ \hline Vehicle speed & 70 km/h & 60 km/h \\ Road level (ISO/DIS8608) & C & F \\ \(G_{q}(n_{0})\) & \(256\times 10^{-6}\) m\({}^{-3}\) & 16,380 \(\times 10^{-6}\) m\({}^{-3}\) \\ Steering angle & 0.1 rad/\(\pm\)0.1 rad & 0.1 rad/\(\pm\)0.1 rad \\ \(\varphi_{\max}\) & 0.2 rad & 0.2 rad \\ \(\kappa_{1}\) & 0.1 & 0.1 \\ \(\kappa_{2}\) & 0.1 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The related parameter settings of different conditions. Figure 13: The input signals of vehicle: (**a**) the random road; (**b**) the steering angle under J-turn maneuver. response of the body acceleration and roll angle are shown in Figure 14c,d, which provide further obvious vindication of the Switched SMC. On the one hand, the curve in Figure 14c indicates that the Switched SMC performs better than the HDSMC with respect to ride comfort. On the other hand, curves in Figure 14d validate the superior stability of the vehicle with Switched SMC than the RCSMC. In other words, Switched SMC can take care of both sides of ride comfort and handling stability rather than one aspect. Figure 14: The rescue vehicle dynamic response based on the switch strategy under the random road and the J-turn maneuver: **(a)** the vehicle body vertical acceleration in time domain; **(b)** the roll angle acceleration in time domain; **(c)** the vehicle body vertical acceleration in time domain and in frequency domain; **(d)** the roll angle acceleration in frequency domain; **(e)** the switch value; **(f)** the load transfer ratio (LTR). In order to validate the robustness of the suspension system, simulations considering the uncertainty of system parameters and external disturbances were performed. In this paper, road disturbance was used as the external uncertain disturbance factor.