Sliding-mode control of a multi-DOF oilwell drillstring with stick-slip oscillations

A dynamical sliding-mode control is used to avoid different bit sticking problems present in a conventional vertical oilwell drillstring. The control goal of driving the rotary velocities of drillstring components to a constant positive value is achieved by means of this control. A discontinuous lumped- parameter torsional model of four degrees of freedom is considered. This model allows to describe drill pipes and drill collars behavior. The closed-loop system has two discontinuity surfaces. One of them gives rise to self-excited bit stick-slip oscillations and bit sticking phenomena. The other surface is introduced to accomplish the control goal despite variations in the weight on the bit (key to the dynamics) and other system parameters.