Active control of stick-slip torsional vibrations in drill-strings

This paper presents active vibration control to reduce the stick-slip oscillations in drill-strings. A simplified two degrees-of-freedom drill-string torsional model is considered. The nonlinear interaction between the rock and the bit is included in the model, where its parameters are fitted with field data from a 5 km drill-string system. Different proportional-derivative (PD)-control strategies are employed and compared, including the one that takes into account the weight-on-bit (axial force) and the bit speed. Optimization problems are proposed to obtain the values of the gain coefficients, and a torsional stability map is constructed for different weight-on-bit values and top-drive speeds. It is noted that the information of the dynamics at the bottom increases the performance of the PD-controller significantly in terms of the torsional vibration suppression, for the system analyzed.