# Estimation of Intelligent Commercial Vehicle Sideslip Angle Based on Steering Torque
## 4 Results and Discussion
### Test Bench Results  
In order to verify the effectiveness of the proposed method, a hardware-in-the-loop (HIL) test bench is built, as shown in Figure 9. The test bench mainly consists of an electric-hydraulic power steering system (EHPS), an electro-hydraulic pump, a servo motor and reducer to provide steering resistance, a torque angle sensor, a control unit based on MPC5741, a host computer, and an NI/PXI real-time system to provide vehicle running environment. The signal between the EHPS controller unit and the host computer communicates through a CAN module. The sideslip angle estimation algorithm proposed in this paper is recorded into the controller for calculation, and the real sideslip angle is output through TruckSim. The estimated results and real results are obtained through the CAN bus.  
Hardware-in-the-loop test conditions adopt double line change conditions, which is a common working condition when the vehicle changes lanes. The vehicle speed is 50 km/h, and the road adhesion coefficient is 0.85; the test results are shown in Figure 10.  
From Figure 10a, we can see that the maximum value of lateral acceleration is 0.37 g when the time is 13 s. Here, we can assume that the vehicle is driving in the linear region. It can be seen from Figure 10b that the sideslip angle based on the steering angle estimation is slightly ahead in phase and overshoots in amplitude. However, the sideslip angle based on the torque estimation is more accurately matched to the real value.  
Figure 11 shows the estimated and measured sideslip angle under the condition that the vehicle speed is 65 km/h and the adhesion coefficient is 0.75. As shown in Figure 11a, the lateral acceleration reaches \(-\)0.4 g at 6.4 s and exceeds 0.5 g at 12 s. In general, we can assume that the vehicle has reached the nonlinear instability stage. Based on Figure 11b, we can see that the estimated sideslip angle based on the steering torque matches the real  
Figure 9: Structure of hardware-in-the-loop test bench.  
value more accurately than the ones based on the steering angle. Figure 12a shows the error between the two methods of sideslip angle estimation and the real angle. The maximum error of the sideslip angle based on the steering angle estimation and the steering torque estimation is 0.17\({}^{\circ}\) and 0.3\({}^{\circ}\), respectively. The average error values of the two estimation methods are 0.06\({}^{\circ}\) and 0.08\({}^{\circ}\), respectively. From Figure 12b, it can be seen that the error amplitude based on steering torque estimation is smaller than that based on steering angle estimation, and the average error values are 0.08\({}^{\circ}\) and 0.12\({}^{\circ}\), respectively.  
The mean absolute error (MSE) and root mean square error (RSME) results based on steering angle and steering torque methods are shown in Table 4. From Table 4, we can know that the maximum error value of the estimated sideslip angle based on steering torque is smaller than that based on the steering angle, whether on high- or low-adhesion roads. Under high-adhesion road conditions, the MSE indexes of estimated sideslip angle based on steering torque and steering angle are 0.0613 and 0.0805, and the estimation accuracy is improved by 23.9%. In addition, under low-adhesion road conditions, the MSE indexes of estimated sideslip angle based on steering torque and steering angle are 0.0822 and 0.1257, and the estimation accuracy is improved by 34.6%.