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During the drilling process, the drilling system devices can be exposed to several types of phenomena incited by lateral, axial, and torsional vibrations. The latter can lead to severe damages if they are not efficiently controlled and quickly mitigated. This research work is focused on the torsional vibrations, which are stimulated by the nonlinear dynamical interaction between the geological rocks and the drill bit. Wherein, a model with three degrees of freedom was designed to demonstrate the severity of the stick-slip phenomenon as consequence of torsional vibrations. The main objective of this study was to design a robust controller based on hybridizing a conventional PID controller with sliding mode approach in order to mitigate rapidly the torsional vibrations. Moreover, a comparative study between PI, PID and sliding mode controllers allowed us to emphasize the effectiveness of the new hybrid controller and improve the drilling system performances. Furthermore, the chattering phenomenon in the sliding surface was overcome by using the saturation function rather than the sign function. The obtained results proved the usefulness of the proposed controller in suppressing the stick-slip phenomenon for smart industrial drilling systems.

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