A Numerical Implementation of Fractional-Order PID Controllers for Autonomous Vehicles

In the context of reaching the best way to control the movement of autonomous cars linearly and angularly, making them more stable and balanced on different roads and ensuring that they avoid road obstacles, this manuscript chiefly aims to reach the optimal approach for a fractional-order PID controller (or (Formula presented.) -controller) instead of the already classical one used to provide smooth automatic parking for electrical autonomous cars. The fractional-order (Formula presented.) -controller is based on the particle swarm optimization (PSO) algorithm for its design, with two different approximations: Oustaloup’s approximation and the continued fractional expansion (CFE) approximation. Our approaches to the fractional-order PID using the results of the PSO algorithm are compared with the classical PID that was designed using the results of the Cohen–Coon, Ziegler–Nichols and bacteria foraging algorithms. The scheme represented by the proposed (Formula presented.) -controller can provide the system of the autonomous vehicle with more stable results than that of the PID controller.