# Vehicle Control Strategy Evaluation Based on the Driving Stability Region
## 3 The Driving Stability Region for Control Strategy Evaluation
### Solving the Driving Stability Region of the Vehicle with 4 WS  
Using the same simulation conditions and solution process, the driving stability region of the 5 DOF vehicle system model (an all-wheel drive mode) with 4 WS was solved. The initial simulation conditions were as follows. The value range of the longitudinal velocity, \(v_{x}\), was from 10 m/s to 60 m/s and the value interval was 5 m/s; the value range of the front wheel angle, \(\delta_{f}\), was from \(-0.08\) rad/s to 0.08 rad/s and the value interval was 0.01 rad/s. The bifurcation points in the driving stability region obtained are shown in Table 4.  
Figure 4: The two\(-\)dimensional projection of the driving stability region of the five\(-\)degree\(-\)of\(-\)freedom (5 DOF) vehicle system model (an all\(-\)wheel drive mode) with DYC: (**a**) Driving stability region (\(\delta_{f}-v_{x}\)); (**b**) driving stability region (\(\delta_{f}-T_{d}\)).  
Figure 5: Driving stability regions with and without DYC.  
The region surrounded by the two-dimensional parameter bifurcation set, composed of the initial longitudinal velocity and driving torque, and the coordinate axis, is the driving stability region.  
Figure 6 shows the two-dimensional projection of the driving stability region of the 5 DOF vehicle system model in an all-wheel drive mode after the introduction of 4 WS (the equilibrium points are drawn in Table 4).  
Figure 7 shows the differences between the driving stability region of the vehicle system with and without 4 WS. Figure 7b is a partially enlarged view. From the results of the driving stability region with or without 4 WS, it can be seen that although the driving stability region with 4 WS is not as effective as DYC, the driving stability region is still larger than before. It is evident that by comparing the bifurcation point data in Table 4, when the initial longitudinal velocity is between 10 m/s and 30 m/s, the expansion of the driving stability region is the greatest. When the initial longitudinal velocity is greater than 30 m/s, the expansion of the driving stability velocity slows down. The simulation results show that the effect of 4 WS is still effective.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Initial Value of** \\ **Longitudinal** \\ **Velocity (m/s)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Driving** \\ **Torque (N-m)** \\ \end{tabular} } & \multicolumn{2}{c}{**Bifurcation**} & \multicolumn{2}{c}{**Bifurcation**} & \multicolumn{2}{c}{**Bifurcation**} \\  & & **Point 1** & **Point 1** & **Point 2** & **Point 2** \\  & & **(with 4 WS)** & **(without 4 WS)** & **(without 4 WS)** & **(with 4 WS)** \\ \hline
10 & 7.0018 & 0.0609 & 0.0603 & \(-\)0.0603 & \(-\)0.0609 \\
15 & 15.754 & 0.0276 & 0.0271 & \(-\)0.0271 & \(-\)0.0276 \\
20 &  
The above analysis results indicate that the DYC and 4 WS control strategies can expand the range of driving stability regions of vehicle systems, and the control effects of different control strategies can be evaluated through the analysis of driving stability regions.