# Vehicle Control Strategy Evaluation Based on the Driving Stability Region
## 4 The Evaluation Based on the Driving Stability Region
### The Evaluation of the Driving Stability Region of the Vehicle with 4 WS  
A simulation model including a 4 WS controller is established in the MATLAB/Simulink (R2022b) simulation platform. The model includes an input module, a CarSim vehicle module, a 4 WS controller module, and a unit conversion module. The classic Runge-Kutta fourth-order single-step algorithm solver is used in the model. The input variables of the input module include the initial values of the front wheel steering angle and longitudinal velocity (driving torque). The fixed step size in the simulation is 0.005 s.  
Figure 8 shows the simulation results of the driving stability region of the vehicle with 4 WS. The input module transmits the initial values of the front wheel steering angle and longitudinal velocity to the CarSim vehicle model, and the vehicle model transmits the state variables (longitudinal velocity and yaw rate) to the 4 WS controller. The controller outputs the rear wheel angle to the vehicle model, achieving the goals of coordination and stability. This process forms a closed-loop feedback structure. Based on the time series changes of the longitudinal velocity, lateral velocity, and yaw rate, the stability of the vehicle with 4 WS is analyzed. To verify the correctness of the driving stability region with the 4 WS control strategy, driving input combinations with different front wheel steering angles and initial longitudinal velocity values (corresponding to different driving torques) are selected from the obtained driving stability region (as shown in Figure 9). The correctness of the obtained driving stability region is verified through single-point simulations. Figure 7: The driving stability region of the 5 DOF vehicle system model (an all–wheel drive mode) with 4 WS: (**a**) Global view; (**b**) partial enlarged view. Based on the physical significance and location of the selected test point, the specific values of the test points and the expected system stability properties at that point are shown in Table 5.  
Figure 8: The co-simulation structure scheme of the driving stability region of the vehicle with 4 WS. Figure 9: The simulation test points of the 4 WS: (**a**) Global view; and (**b**) enlarged view of test point 3. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Initial Value of** & **Driving Torque** & **Front Wheel** & **Expected Stability** \\
**Test Points** & **Longitudinal** & **(N-m)** & **Steering Angle** & **With 4 WS** & **Without 4 WS** \\  & **Velocity (m/s)** & **(rad)** & **(rad)** & **(rad)** & **(rad)** \\ \hline Test point 1 & 45 & 141.79 & \(-\)0.003 & stabilize & stabilize \\ Test point 2 & 25 & 43.76 & 0.02 & instability & instability \\ Test point 3 & 35 & 85.77 & 0.00785 & stabilize & instability \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Test point values and system stability properties. Figure 10 shows the simulation results within 15 s under the conditions of test point 1. During the moving process of the vehicle, the lateral velocity and yaw rate with 4 WS control are smaller than those without 4 WS control; the longitudinal velocity does not change significantly. The vehicle is in a stable state; this is consistent with the results discussed earlier. The 4 WS controller has a certain effect, which is in line with expectations. Test point 1 shows no significant fluctuations in lateral velocity or yaw rate of the model with or without 4 WS control, indicating a relatively stable state of the vehicle system. Figure 11 shows the simulation results within 15 s under the conditions of test point 2. At this time, the vehicle is both in an unstable state with and without 4 WS control. However, with 4 WS control, the fluctuation amplitude of the vehicle's yaw rate is smaller than that without 4 WS control, and the values of lateral velocity and yaw rate are much lower. The yaw rate of the system can be controlled within a small range, resulting in a lower degree of vehicle instability.