Novel GPID: Grünwald–Letnikov Fractional PID for Enhanced Adaptive Cruise Control

This study demonstrates that the Grünwald–Letnikov fractional proportional–integral–derivative (GPID) controller outperforms traditional PID controllers in adaptive cruise control systems, while conventional PID controllers struggle with nonlinearities, dynamic uncertainties, and stability, the GPID enhances robustness and provides more precise control across various driving conditions. Simulation results show that the GPID improves the accuracy, reducing errors better than the PID controller. Additionally, the GPID maintains a more consistent speed and reaches the target speed faster, demonstrating superior speed control. The GPID’s performance across different fractional orders highlights its adaptability to changing road conditions, which is crucial for ensuring safety and comfort. By leveraging fractional calculus, the GPID also improves acceleration and deceleration profiles. These findings emphasize the GPID’s potential to revolutionize adaptive cruise control, significantly enhancing driving performance and comfort. Numerical results obtained in α=0.99 from the GPID controller have shown better accuracy and speed consistency, adapting to road conditions for improved safety and comfort. The GPID also demonstrated faster stabilization of speed at 60 km/h with smaller errors and reduced the error to 0.59 km/h at 50 s compared to 0.78 km/h for the PID.