Sliding mode controller design for torsional vibrations minimization under Rock-Bit interaction effects

Abstract

Torsional vibrations during drilling can have an adverse effect on drilling performance, as they generate Stick-slip phenomena, which reduces the quality of the drilling and the speed of penetration as well. The study of these vibrations can be done through the model of the torsion pendulum (mass-spring), because it is the model that responds to this type of systems. These models consist of several parallel discs, rotating around their common axis and connected to each other. Where, the drill pipes are represented by a torsion spring with a stiffness coefficient and the drill collars with a damping coefficient. The main objective of this study is to reduce the stick-slip vibrations in the drilling system so that the tool can follow the desired nominal angular velocity of the top drive in an optimal time. A simulation of a torsion model with two degrees of freedom has been tested in an open loop, and in order to analyze the severity of the vibrations, two rock-bit contact models with variable weight-on-bit has been studied. Moreover, a sliding mode controller is designed for each Rock-Bit model to achieve the goal of reducing torsional vibrations and to ensure that the Karnoop model global stability is guaranteed. The later implies that the stability is ensured for the other contact models. Furthermore, the obtained results demonstrated the effectiveness the designed controller in reducing the severe vibrations of the stick-slip phenomenon under the different rock-bit interaction effects, and also the robustness of the sliding mode control is verified for each rock-bit interaction