Fractional-order PID controller design for strongly coupled high-frequency axial–torsional vibrations in drill string system

A rotary drilling rig is a critical system in the oil and gas industry; nevertheless, vibrations during drilling, particularly coupled axial and torsional vibrations, can significantly reduce the rate of penetration and pose challenges to safety, drilling performance, and borehole quality. The nowadays developed control systems are mainly designed for individual vibration types while neglecting the coupling effects of these vibrations. Therefore, the main objective of this paper is to fill this gap by designing and implementing a fractional-order PID (FOPID) controller to mitigate the impact of the coupled axial–torsional vibrations. A ‘Measurement While Drilling’ tool has been logged in three wells in an Algerian petroleum field to collect the coupled axial–torsional vibrations; then, simulation scenarios have been conducted to mimic the dynamic of the rotary drilling system in these three wells. The obtained results demonstrated the ability of the designed FOPID controller to mitigate both axial and torsional vibration even with the presence of high-frequency strongly coupled mode. Moreover, comparative studies were conducted between the FOPID and conventional PID controllers, as well as between FOPID controllers tuned with particle swarm optimization (PSO) and trial-and-error methods. The results demonstrate that the FOPID controller provided improved performance than the conventional PID controller, especially in terms of closed-loop stability under high-frequency vibration scenarios. Furthermore, the PSO-tuned FOPID controller also showed superior vibration reduction and better robustness when compared to the trial–error tuning FOPID controller. Thus, it is highly recommended to consider this proposed controller as a reliable solution for improving drilling performance and safety in rotary drilling systems.