Performance analysis of proportional-integral feedback control for the reduction of stick-slip-induced torsional vibrations in oil well drillstrings

The stick-slip phenomenon, in the process of drilling oil wells, can lead to large fluctuations in drill-bit angular velocity, due to the interaction between drill-bit and rock formation, and, thus, cause irreparable damage to the process. In this work, the performance of control laws applied to the rotary table (responsible for moving the drillstring) is analyzed, in order to reduce stick-slip and drill-bit angular velocity oscillations. The control laws implemented are based on a PI (Proportional-Integral) controller, for which the torque applied to the rotating table has components proportional and integral to the table angular velocity with constant or variable WOB (Weight-On-Bit). For the drillstring, a finite element model with a linear interpolation for the torsional motion was proposed. The torque at drill-bit was modeled considering a non-regularized dry friction model, with parameters that were adjusted using empirical data proposed in literature. Several performance criteria were analyzed and it was observed that a minimization of the mean deviation of the drill-bit angular velocity relative to the target one would provide the best operating condition. Parametric analyses of proportional and integral control gains were performed, yielding level curves for the mean deviation of drill-bit angular velocity. From these curves, stability regions were defined in which the deviation is acceptable. These regions were observed to be wider for smaller values of WOB and higher values of target angular velocity and vice-versa. In addition, the inclusion of a controlled dynamic WOB was proposed leading to reduced levels of mean deviation of angular velocity and, thus, improving stability regions for the drilling process.