# 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 DYC  
Similarly, a simulation model containing a DYC controller was established using the MATLAB/Simulink (R2022b). The model included an input module, a CarSim vehicle module, a DYC controller module, and a unit conversion module. The model adopted the classic Runge-Kutta fourth-order single-step algorithm solver. The simulation solution step was 0.005 s. Figure 13 shows the simulation program diagram of the driving stability region of the vehicle with DYC. The simulation test points composed of different front wheel steering angles and initial longitudinal velocities are shown in Figure 14. The test points include steering angles in different directions (left and right turns) and different vehicle velocities. The specific values of the test points and the expected system stability properties of the points are shown in Table 6.  
Figure 12: The simulation results under the conditions of test point 3: (**a**) Lateral velocity; (**b**) yaw rate; (**c**) longitudinal velocity; (**d**) partial enlargement of the longitudinal velocity; and (**e**) rear wheel steering angle. Figure 13: The co-simulation structure scheme of the driving stability region of the vehicle with DYC. Figure 15 shows the simulation results of test point 1 within 15 s. Although each state variable fluctuates more within 0-10 s, at 10-15 s they gradually converge to a constant. The state variables of lateral velocity and yaw rate under DYC control are smaller than those without DYC control, and the longitudinal velocity decreases more significantly. The DYC controller has a certain effect, which is in line with expectations. Although the lateral velocity of test point 1 fluctuated significantly in the early stage of simulation, the vehicle's dynamic states were ultimately stable. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Points** & \begin{tabular}{c} **Initial Value of** \\ **Longitudinal** \\ **Velocity (m/s)** \\ \end{tabular} & \begin{tabular}{c} **Driving Torque** \\ **(N-m)** \\ \end{tabular} & \
\begin{tabular}{c} **Front Wheel Steering** \\ **Angle (rad)** \\ \end{tabular} &
\begin{tabular}{c} **Expected Stability** \\ **With DYC** \\ \end{tabular} \\ \hline Test point 1 & 20 & 28.01 & \(-\)0.012 & stabilize & stabilize \\ Test point 2 & 35 & 85.77 & 0.0106 & stabilize & instability \\ Test point 3 & 50 & 175.04 & 0.02 & instability & instability \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The test point values and system stability properties. Figure 14: The simulation test points of DYC. Figure 15: _Cont._  
Using the same control condition parameters, Figure 16 shows the simulation results of test point 2. In the vehicle system without DYC control, the longitudinal velocity and lateral velocity oscillate between positive and negative ranges, and the yaw rate increases sharply. The vehicle experiences a series of unstable behaviors, such as rapid acceleration, deceleration, jerking, and even reverse. When the DYC control works, the lateral velocity and yaw rate can be approximately maintained at a stable value in a short period of time. The results also demonstrate the effectiveness of DYC's controller and the correctness of the driving stability region. Figure 16: _Cont._  
Figure 15: The dynamic characteristics of the vehicle with and without DYC control under test point 1 conditions: (**a**) Lateral velocity; (**b**) yaw rate; (**c**) longitudinal velocity; and (**d**) system additional yawing moment. Figure 17 shows the simulation results of the conditions of test point 3. The severe fluctuations in lateral velocity, longitudinal velocity, and yaw rate indicate that the vehicle system without DYC control is in an unstable state. When DYC control works, the yaw rate varies within a small range. However, it makes the driver or passenger uncomfortable during driving, and the lateral velocity also gradually increases. Therefore, the vehicle system with DYC control can still be judged as unstable.