# A Tuning Method for Speed Tracking Controller Parameters of Autonomous Vehicles
## 4 Simulation Results and Discussion
### Experimental Results Analysis  
These results indicate that as the road adhesion coefficient increases, the speed tracking accuracy of the autonomous vehicle improves. This improvement is a direct result of the optimized PID controller parameters, which allow the vehicle to maintain a closer match to the desired speed, even under varying road conditions. The reduction in both maximum and average errors, as well as lower standard deviations, demonstrates that the optimization has significantly enhanced the overall performance of the controller, leading to more precise and stable speed regulation. As shown in Figure 5a-c, under the condition where the road surface adhesion coefficient is 0.5, the desired speed range for the autonomous vehicle is 0-100 km/h, covering several common phases 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 wide speed range, the autonomous vehicle applied the PID controller before and after parameter optimization for different scenarios: a 6 s acceleration, a 3 s acceleration, and an 8 s emergency deceleration. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Road Adhesion** & **Maximum** & **Average** & **Standard** \\
**Coefficient** & **Value (m/s)** & **Value (m/s)** & **Deviation (m/s)** \\ \hline
0.5 & 0.222 & 0.063 & 0.124 \\
0.6 & 0.180 & 0.056 & 0.099 \\
0.8 & 0.179 & 0.056 & 0.098 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Speed errors of the autonomous vehicle after parameter optimization under different road surface adhesion coefficients. The simulation results indicate that, during each acceleration and deceleration phase, the actual speed of the autonomous vehicle with optimized PID controller parameters closely follows the target speed, compared to before the PID parameter optimization. The error consistently remains within a small range. Particularly during multiple acceleration phases, the vehicle responds quickly and smoothly to changes in the target speed, demonstrating high speed tracking accuracy. Even in emergency deceleration scenarios, despite the rapid speed drop, the actual speed continues to closely track the target speed without significant overshoot or lag, highlighting the stability and robustness of the control system. Moreover, as seen in Figure 5, the longitudinal dynamic response of the vehicle with optimized PID parameters during acceleration and deceleration is very smooth, with stable acceleration changes and no sudden fluctuations. This indicates that the PID controller parameter adjustment algorithm designed in this study not only 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 this series of simulation results, it can be concluded that the proposed controller parameter optimization algorithm enables the autonomous vehicle to maintain excellent speed tracking performance under complex driving conditions while exhibiting high 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 further development of intelligent transportation systems. As shown in Figure 6, under the condition where the road surface adhesion coefficient is 0.6, the desired speed range for the autonomous vehicle is 0-100 km/h, covering several common speed intervals 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 relatively wide speed range, the autonomous vehicle, both before and after PID controller parameter optimization, underwent two 6 s acceleration phases, one 3 s acceleration phase, and one 8 s emergency deceleration phase.