13. Sliding Mode Control for Suppression of Stick-Slip Vibrations in Oilwell Drillstrings

In drill strings, stick-slip vibrations are a particular case of torsional vibrations, which cause large fluctuations in the angular velocity at the bottom of the well, resulting in premature wear of the bit and other components of the drilling system. This work introduces a sliding mode controller designed to regulate the torque applied to the top of the column in order to mitigate or eliminate stick-slip vibrations in the dynamic behavior of the drillstring. The drillstring is modeled as a two-degree-of-freedom lumped parameter model, representing its torsional behavior at both the top of the column and the bottom hole. The controller stability analysis is performed from the Lyapunov stability theory, in order to guarantee the system convergence to the desired state. Initially, the behavior of the system without the action of the controller is investigated and later, its influence on the dynamic behavior of the system is analyzed. For the studied cases, the controller was able to eliminate stick-slip vibrations, keeping the column angular velocity at the desired value, presenting results in agreement with experimental and field data. The chattering behavior is also verified and its elimination through a signal saturation function, guaranteeing an adequate behavior to the developed controller.