# Robust Control with Uncertain Disturbances for Vehicle Drift Motions
## 4 Simulation and Discussion
### Motion Mechanism Analysis Result  
The vehicle main parameters are shown as Table 1.  
The steady-state motion mechanism of the vehicle is analyzed as Section 2.2, and the transient-state motion mechanism is directly used as a target in the controller. Considering the maximum steering angle is 0.7 rad in practice, variation trends of the sideslip angle and \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline \(m\) (vehicle mass) & kg & 1126.7 \\ \(m_{b}\) (vehicle body mass) & kg & 1111.0 \\ \(l_{f}\) (distance from gravity center to front axle) & m & 1.265 \\ \(l_{r}\) (distance from gravity center to rear axle) & m & 1.335 \\ \(h_{g}\) (height of gravity center) & m & 0.518 \\ \(\mu\) (friction coefficient) & & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The vehicle main parameters. yaw rate and the velocity limitation in drift conditions are shown in Figure 4 by analyzing counterclockwise circle motions with radiuses from 2 m to 18 m.  
Because circle motions are counterclockwise, according the equation of \(\gamma\) in Section 2.2, values of yaw rates are greater than zero. Radiuses in Figures 4-6 all are obtained based on the equation of \(R\) in Section 2.3. According to Figure 4a, it suggests that the yaw rate is basically smaller with the larger radius, which means the relationship substantially conforms the negative correlation; the minimum yaw rate consists in the maximum circle with the 18 m radius and equals 0.5 rad/s, which is larger than the circle motion in non-limit conditions. According to Figure 4b, it suggests that the sideslip angle is basically larger with the larger steering angle, which means the relationship substantially conforms the positive correlation; combined with Figure 4a, the sideslip angle is not associated with the radius. According to Figure 4c, it suggests that the yaw rate is basically smaller with the larger velocity, which means the relationship substantially conforms the negative correlation; and the steering angle is not associated with the velocity. According to Figure 4d, it suggests that the velocity is positively associated with the radius, and the maximum and minimum permissible limit of the vehicle velocity \(v\) in drift motions are obtained. Figure 4: The motion mechanism analysis result in drift conditions: (**a**) The relation between the sideslip angle, the yaw rate and the radius; (**b**) the relation between the sideslip angle, the steering angle and the radius; (**c**) the relation between the steering angle, the yaw rate and the velocity; and (**d**) the velocity limitation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(R\) **(m)** & \(v\) **(m/s)** & \(\beta\) **(rad)** & \(\gamma\) **(rad/s)** & \(\delta_{f}\) **(rad)** & \(\kappa_{r}\) \\ \hline (a) & 16 & 9.5 & \(-\)0.56 & 0.7 & \(-\)0.29 & 0.72 \\ (b) \({}^{1}\) & 9.6 & 8 & \(-\)0.08 & 0.84 & 0.13 & 0.07 \\ \hline \end{tabular} \({}^{1}\) Group (b) is one part of Figure 4d with the maximum velocity at the radius 9.6 m.  
\end{table} 
Table 2: The vehicle main status parameters in drift motions based on the steady-state analysis. Figure 5: The simulation result of group (a) in Table 2 with the origin uniform linear: (**a**) The variation curve of the velocity; (**b**) the variation cure of the sideslip angle; (**c**) the variation curve of the yaw rate; (**d**) the variation cure of the steering angle; (**e**) the variation curve of the TYDEX longitudinal slip ratio of the rear tire; and (**f**) the variation cure of the radius.