## 4 Simulation and Result Analysis
### Sine Wave Steer Input Test  
The sine wave steer input test is the most frequently used condition for verifying driver control stability. The basic parameters of the simulation analysis of the sine wave steer input test are shown in Table 7.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Vehicle Parameters** & **Value** \\ \hline P-yaw angle rate & 150 \\ I-yaw angle rate & 0.05 \\ D-yaw angle rate & 2 \\ P-sideslip angle & 10 \\ I-sideslip angle & 0.1 \\ D-sideslip angle & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Main parameters of PID control model of ESP.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Vehicle Parameters** & **Value** & **Unit** \\ \hline m\({}_{\text{t}}\) & 900 & kg \\ I\({}_{\text{z}}\) & 708 & Kg m\({}^{2}\) \\ L\({}_{1}\) & 970 & mm \\ L\({}_{2}\) & 903 & mm \\ g & 9.8 & m/s\({}^{2}\) \\ K\({}_{\text{\text{\text{\text{\text{\text{\text{\text{  
The results of simulation are shown in Figure 9.  
As shown in Figure 9, the longitudinal speed of NC decreases rapidly at 2 s, and the sideslip angle of the mass center and the yaw angle rate increase at the same time. Then, violent vibration occurs, and the frequency of the oscillation cycle increases. In terms of vehicle speed, the speed of the vehicle with P-ESP and MFCDC-ESP is only slightly reduced at the beginning due to the respective effects of lateral force and braking force; then the vehicle maintains a stable target speed. With regard to the sideslip angle of the mass center and yaw rate, the range of variations is relatively small. These comparisons show that the vehicle without control loses stability and that the vehicles with P-ESP and MFCDC-ESP present a good control effect on vehicle stability.  
In illustrating the control effect of MFCDC-ESP, this work shows the vertical force and damping force in Figure 10 and the simulation data results in Table 8.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Parameters** & **Value** & **Unit** \\ \hline Longitude target speed & 50 & km/h \\ Friction coefficient & 0.16 & - \\ Steer input angle peak value & 90 & deg \\ Simulation time & 20 & second \\ \hline \hline \end{tabular}
\end{table}
Table 7: Main parameters of sine wave steer input test.  
Figure 9: Steering angle, vehicle longitudinal speed, vehicle sideslip angle, and yaw angle rate of sine wave steer input test. The result of NC is expressed with a black dotted line; the result of P-ESP is expressed with a blue chain line; the result of MFCDC-ESP is expressed with a red solid line. (**a**) is the steer angle input of the simulation. (**b–d**) are the comparisons of the vehicle longitudinal speed, vehicle sideslip angle, and yaw angle rate, respectively.  
than that of P-ESP while the minimum value of the former is less than that of the latter; the difference for the rear axle wheels is even greater. These results show that MFCDC-ESP can maximize the rear axle, which lacks lateral force, for stability control. From the point of view of the damping force of each wheel, the damping forces of the front and rear axles on the right side of MFCDC-ESP increase suddenly at about 2 s. As shown in Figure 8, the moment at 2 s is the critical moment of lateral stability control (the vehicle with NC suddenly becomes unstable around this moment). The compensation effect of MFCDC-ESP also makes the vehicle establish good dynamic control. The standard deviation of the damping force of MFCDC-ESP is much smaller than that of P-ESP because of the sky-hook control effect after the vehicle enters the stationary period. This result also shows that the force on the vehicle body is reduced and that the passengers experience enhanced comfort. In practical application, MFCDC-ESP can automatically identify and switch the state between stability and comfort in real time due to its fuzzy control characteristics, so as to achieve the best driving effect.