Non-desired transitions and sliding-mode control of a multi-DOF mechanical system with stick-slip oscillations

Systems with discontinuous elements exhibit a wide variety of complex phenomena which must be considered in the control design process. A dynamical sliding-mode control is used to avoid different bit sticking problems appearing in conventional vertical oilwell drillstrings. The aim of the control system is to drive the rotary velocities of drillstring components to specified values. A discontinuous lumped-parameter torsional model of four degrees of freedom is considered. This model is more generic than those so far reported in the literature. The closed-loop system dynamics have four discontinuity surfaces. One of these surfaces is introduced in order to accomplish the control goal despite variations of key drilling parameters, such as, the weight on the bit, the top-rotary velocity and friction characteristics. Self-excited bit stick-slip oscillations and sticking phenomena are avoided with the controller here proposed. Moreover, an alternative procedure to investigate the stick-slip motion is presented, it is based on the study of the stability characteristics of the different system equilibria and their relationships to different sliding motions.