# Vehicle Rollover Warning and Control Based on Attitude Detection and Fuzzy PID
## 4 Co-Simulation Analysis and Result Verification
### Fish Hook Steering Test  
The fishhook steering test is a kind of difficult test that is very effective in evaluating the lateral stability of the car. By inputting two consecutive 720\({}^{\circ}\) opposite direction steering wheel turns, the car is made to drive continuously at the limit to test the stability of the car, and the forward trajectory of the car in the test is very similar to that of a fishhook.  
CarSim and Simulink joint simulation of the fishhook steering test was performed on the model, and the response curves of the system parameters under no control, PID control and fuzzy-PID control were obtained as shown in Figure 15. These parameters such as LTR value, lateral tilt angle, lateral acceleration, etc. can reflect the motion trend of the car during the driving process, and especially can be used to assess whether the car has side tilt or the three control states of the car under the same driving conditions can be compared, which can effectively evaluate whether the control effect of the control strategy is good.  
The speed of the test vehicle is set to 80 km/h, the simulation run time is 8 s and the corresponding results of the simulation control are shown in Figure 15, When the forest fire truck does not receive instructions, the LTR value reaches the rollover threshold of \(-\)0.8 at 1.4 s, and the value of LTR reaches the limit value of 1 at 2.4 s, and the vehicle has already rolled over. After applying PID control to the braking system, it can be seen from the graph that the PID control only starts to work when the value of LTR reaches 1. In contrast, the fuzzy PID control already starts to work at 1.4 s. As the time increases, the value of LTR stabilizes at about 0.7, which is within the safety range of rollover. Eventually, the value of LTR was controlled at around 0.4 after fuzzy-PID control and below 0.2 after PID control. Although the PID control can minimize the \(|\) LTR\(|\), but the fast braking is difficult to ensure the safety and driving stability of the vehicle in the actual driving process. In contrast, the output curve oscillation of the fuzzy PID control is smoother and more responsive. Comparing Figure 15b with Figure 15c, both the lateral swing angular velocity and the lateral acceleration can converge to a value of 0 to reach a stable state after control, while the fuzzy PID control has stabilized at 5.3 s, and the PID control only converges to a stable state at 5.9 s, which proves that the response of the fuzzy PID is faster. Figure 15d shows that the maximum value of mass-side eccentricity in fuzzy PID control is 40\({}^{\circ}\), and the maximum value of mass-side eccentricity in PID control is 55\({}^{\circ}\). T In contrast, fuzzy PID control range improved by 27.27%, and the time of fuzzy PID control is short, the oscillation is small, and the control process is smoother. From Figure 15e, it can be seen that both PID control and fuzzy PID control can smooth the vehicle (the vehicle side deflection angle is close to 0\({}^{\circ}\)), and the fuzzy PID response time is earlier.  
In other words, both control effects of the auxiliary braking system are confirmed, and they effectively minimize the rollover tendency of the vehicle. The fuzzy-PID control has a smaller overshoot, faster response and adjustment, better sensitivity, and better comprehensive control effect compared with PID control. The braking torque curve is depicted in Figure 15f. When the braking torque is positive or negative, the left or right front wheel achieves braking, respectively. The maximum value of the braking torque is 650 N\(\cdot\)m.