# Estimation of Intelligent Commercial Vehicle Sideslip Angle Based on Steering Torque
## 4 Results and Discussion  
### Simulation Results  
The proposed estimation method is tested based on TruckSim and Matlab/Simulink environment, which can simulate the driving conditions of the vehicle in the real environment and provide all the data needed for the vehicle model. The vehicle parameters required in the EKF algorithm simulation are shown in Table 3, which are available in TruckSim.  
The simulation results are shown in Figures 6-8. The simulation tests have been conducted at the adhesion coefficient of 0.85 and 0.75, which normally show a high-\(\mu\) value and a low-\(\mu\) value, respectively. When the vehicle speed is 50 km/h and the adhesion coefficient is high, the vehicle is considered to be in the linear region (the lateral acceleration is less than 0.4 g). The vehicle is considered to be in a nonlinear region when the speed is 65 km/h and the adhesion coefficient is low (the lateral acceleration is greater than 0.4 g).  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameters** & **Symbols** & **Values** \\ \hline Sprung mass & \(m_{s}\) & 4455 (kg) \\ Front axle unsprung mass & \(m_{f}\) & 607.3 (kg) \\ Rear axle unsprung mass & \(m_{r}\) & 1144 (kg) \\ Distance between the front axle and the vehicle gravity center & \(l_{f}\) & 1.25 (m) \\ Distance between the rear axle and the vehicle gravity center & \(l_{r}\) & 3.75 (m) \\ Yaw moment inertia of the whole vehicle & \(l_{z}\) & 34,802.6 (kg\(\cdot\)m\({}^{2}\)) \\ Front cornering stiffness & \(k_{1}\) & \(1.31\times 10^{4}\) (N/rad) \\ Rear cornering stiffness & \(k_{2}\) & \(5.11\times 10^{3}\) (N/rad) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The parameters used in TruckSim.  
Figure 6 shows the results carried out on the adhesion coefficient of 0.85 and the vehicle speed at 50 km/h.  
Figure 8: The simulation results at \(u=65\) km/h, \(\mu=0.75\): (**a**) Driving condition and lateral acceleration; (**b**) The estimation result of sideslip angle with double line change.  
Figure 6: The simulation results at \(u=50\) km/h, \(\mu=0.75\): (**a**) Driving condition and lateral acceleration; (**b**) The estimation result of sideslip angle with 90\({}^{\circ}\), 1 Hz.  
Figure 7: The simulation results at \(u=50\) km/h, \(\mu=0.85\): (**a**) Driving condition and lateral acceleration; (**b**) The estimation result of sideslip angle with double line change.  
Figure 5(a) shows the driving conditions, including steering wheel angle and lateral acceleration, where the steering angle amplitude is 90\({}^{\circ}\). According to Figure 5(b), the proposed sideslip angle observer based on steering torque shows better estimation performance compared with the results based on steering angle, which is generally consistent with the properties analyzed in Section 2.3. As can be seen from the double line change driving condition in Figure 7, when the adhesion coefficient increases, the estimation of sideslip angle based on torque is more consistent with the TruckSim output results, while the estimation based on steering angle has obvious phase advance. From Figure 8, we can see that when the steering angle reaches 300\({}^{\circ}\), the vehicle is put under a critical driving condition and is generally considered to be in a nonlinear region (the lateral acceleration is 0.46 g). According to Figure 5(b), in the nonlinear region, the accuracy of sideslip estimation based on steering torque is better than that based on steering angle.