# A Tuning Method for Speed Tracking Controller Parameters of Autonomous Vehicles
## 4 Simulation Results and Discussion
### Experimental Results Analysis
The simulation results indicate that, during each acceleration and deceleration phase, the actual speed of the autonomous vehicle with optimized PID controller parameters is able to more closely follow the target speed compared to the vehicle without PID parameter optimization. The error consistently remains within a small range. Particularly during multiple acceleration phases, the optimized vehicle responds to changes in the target speed quickly and smoothly, demonstrating high speed tracking accuracy. Even in emergency deceleration phases, despite the rapid drop in speed, the actual speed still closely tracks the target speed without significant overshoot or lag, highlighting the stability and robustness of the control system. Figure 5: Simulation results for road adhesion coefficient 0.5. (**a**) Longitudinal speed. (**b**) Longitudinal speed error. (**c**) Longitudinal acceleration. Furthermore, as seen in Figure 6a, the longitudinal dynamic response of the vehicle controlled by the optimized PID controller is smoother during acceleration and deceleration. Figure 6b,c show that the vehicle's acceleration changes are stable without sudden fluctuations when using the optimized PID controller. This demonstrates that the PID controller parameter optimization algorithm designed in this study not only effectively improves the speed tracking accuracy of the PID controller but also significantly enhances the system's dynamic response capability, enabling the autonomous vehicle to maintain stable and precise speed control across different speed ranges. Therefore, based on these simulation results, it can be concluded that the proposed controller parameter optimization algorithm enables the autonomous vehicle to achieve excellent speed tracking performance under complex driving conditions, while also demonstrating a high level of longitudinal control stability. This provides strong technical support for the practical application of autonomous vehicles in handling complex road conditions and dynamic changes, and lays a solid foundation for the future development of intelligent transportation systems. As shown in Figure 7a-c, under the condition where the road surface adhesion coefficient is 0.8, the desired speed range for the autonomous vehicle is 0-100 km/h, covering multiple speed phases typical in daily driving, including low speed (0-30 km/h), medium speed (30-60 km/h), and high speed (above 60 km/h). Within this broad speed range, the vehicle used the PID controller both before and after parameter optimization, undergoing two 6 s acceleration phases, one 3 s acceleration phase, and one 8 s emergency deceleration phase. The simulation results show that during each acceleration and deceleration phase, the actual speed of the autonomous vehicle with optimized PID controller parameters follows the target speed more effectively compared to the unoptimized controller. The error remains consistently small. Particularly during multiple acceleration phases, the optimized controller enables the vehicle to respond to changes in the target speed quickly  
Figure 6: Simulation results for road adhesion coefficient 0.6. (**a**) Longitudinal speed. (**b**) Longitudinal speed error. (**c**) Longitudinal acceleration. Figure 7: Simulation results for road adhesion coefficient 0.8. (**a**) Longitudinal speed. (**b**) Longitudinal speed error. (**c**) Longitudinal acceleration. and smoothly, demonstrating high speed tracking accuracy. Even during the emergency deceleration phase, despite the rapid drop in speed, the actual speed closely follows the target speed without significant overshoot or lag, highlighting the stability and robustness of the control system. Additionally, from Figure 7, it can be seen that the PID controller with optimized parameters results in a very smooth longitudinal dynamic response throughout the acceleration and deceleration phases, with no sudden fluctuations in acceleration changes.