## 5 Hardware-in-the-Loop Test
### Sine with Dwell Condition  
The setting of vehicle speed and road adhesion coefficient in the sine with dwell condition in the loop test is consistent with the software co-simulation. The vehicle speed is set to 80 km/h, the road adhesion coefficient is 0.5 and 0.8, and the peak steering angle is 1.5 A, 2 A, 2.5 A, \(\ldots\), 6.5 A and 270 deg respectively.  
Compared with the software co-simulation, as shown in Figures 21-26, firstly, the overshoot caused by the fluctuation of the yaw rate during the steering hysteresis phase of the test of the controller designed in this paper is smaller than that of the vehicle model with PID controller under the low adhesion coefficient condition. Secondly, the fluctuation of the yaw rate for the controller based on tire force observation during the steering hysteresis phase is larger for the vehicle model with PID control. Thirdly, at high pavement adhesion coefficients, the yaw rate response of the vehicle model with both controllers is improved at lower pavement adhesion coefficients, and the nominal yaw rate response of the vehicle model with the PID controller is also improved at lower pavement adhesion coefficients, both controller-controlled vehicle models have improved yaw rate response to low pavement adhesion coefficients, and also improved the follow-through of nominal yaw rate for low pavement adhesion coefficients conditions. Among them, the improvement in the yaw rate response of the vehicle model based on tire force observations is more pronounced.  
Figure 20: Test results based on the conventional PID-based controller at \(u=100\) km/h and \(\mu=0.8\). (**a**) is a comparison of the nominal and actual values of the yaw rate, and (**b**) is the wheel cylinder pressure value collected from the wheel cylinder pressure sensor.  
Figure 21: The yaw rate graphs of the vehicle model based on tire force observation when \(\mu=0.5\). (a,b) are graphs of nominal yaw rate and actual yaw rate when the road adhesion coefficient is 0.5, using the vehicle model based on tire force observation.  
Figure 22: The yaw rate graphs of the vehicle model based on tire force observation when \(\mu=0.8\). (a,b) are graphs of nominal yaw rate and actual yaw rate when the road adhesion coefficient is 0.8, using the vehicle model based on tire force observation control.  
Figure 23: Based on the observation of tire force, the brake wheel cylinder pressure value under the test condition of the maximum steering angle. (a,b) are the brake wheel cylinder pressure values of the vehicle model using tire force observation when the maximum steering angle of the test conditions is 270 deg and the road adhesion coefficient is 0.5 and 0.8 respectively.  
Figure 26: Based on the traditional PID control, the brake wheel cylinder pressure value under the test condition of the maximum steering angle is shown. (**a**,**b**) are the brake wheel cylinder pressure values of the vehicle model using traditional PID control when the maximum steering angle is 270 deg and the road adhesion coefficient is 0.5 and 0.8.  
Figure 24: The yaw rate graphs of the vehicle model based on traditional PID control when \(\mu=0.5\). (**a**,**b**) are the nominal yaw rate and actual yaw rate of the vehicle model using traditional PID control when the road adhesion coefficient is 0.5.  
Figure 25: The yaw rate graphs of the vehicle model based on traditional PID control when \(\mu=0.8\). (**a**,**b**) are the nominal yaw rate and actual yaw rate of the vehicle model using traditional PID control when the road adhesion coefficient is 0.8.  
According to the images of brake cylinder pressure shown in Figures 23 and 26, it can be concluded that there is a certain discrepancy between the yaw rate of actual value and nominal value after the controller control as well as a small range of fluctuation, this is caused by a delay in the brake hydraulic circuit for a certain period of time, insufficient response to high frequency braking signals, and inconsistent response of the front and rear wheels to braking pressure.