The main objective of this paper is to suppress the stick–slip vibrations in the drilling system so that the drill bit can follow the desired nominal angular velocity of the Top Drive in an optimal time. Hence to protect drilling equipment from hazards and increase drilling performances by decreasing the non-productive time (NPT). Three control systems have been proposed to achieve this objective, a sliding controller is firstly designed and then a backstepping approach is discussed secondly. Furthermore, a hybridization of sliding mode control with a backstepping approach has been proposed on the so-called hybrid backstepping sliding mode controller. The latter has not been proposed before in the literature for rotary drilling systems. Moreover, two torsion models of the system have been discussed for different degrees of freedom. Based on the comparison between controllers’ responses, the effectiveness and the robustness of the hybrid controller have been demonstrated and highlighted, whose fast response can protect the drilling equipment from hazards that may be caused by the slip phase of the vibrations. Hence, it is recommended to implement the proposed controller in smart rotary drilling systems for petroleum industry.

本文的主要目的是抑制钻井系统中的粘滑振动，使钻头能够在最佳时间内跟随顶部驱动所需的标称角速度。因此，可以通过减少非生产时间 (NPT) 来保护钻井设备免受危险并提高钻井性能。为了实现这一目标，提出了三种控制系统，首先设计了滑动控制器，然后讨论了反步方法。此外，在所谓的混合反步滑模控制器上提出了滑模控制与反步方法的混合。后者之前在旋转钻井系统的文献中尚未提出。此外，还讨论了不同自由度的系统的两个扭转模型。基于控制器响应之间的比较，证明并强调了混合控制器的有效性和鲁棒性，其快速响应可以保护钻井设备免受振动滑移阶段可能造成的危害。因此，建议在石油工业智能旋转钻井系统中实施所提出的控制器。