Discontinuities-induced phenomena in an industrial application: analysis and control solutions

Piecewise-smooth (PWS) systems are an interesting subclass of discontinuous dynamical systems. In these systems, trajectories evolve smoothly through the state space until some conditions are satisfied and an event is triggered inducing a change in the model characteristics. Due to the presence of discontinuous changes in system properties, PWS systems present a wide variety of complex dynamical behaviours. In this paper, an example of PWS system is presented: the model of a conventional vertical oilwell drillstring. Oilwell drillstrings exhibit a wide variety of complex phenomena and non-desired oscillations due to the presence of different types of friction. Special attention is paid to the effects of bitrock friction and torsional mechanical vibrations, mainly, stick-slip oscillations appearing at the bottom-hole assembly and other bit sticking phenomena which cause the bit to remain motionless. These phenomena are related to the existence of a sliding motion on the discontinuity surface when the bit velocity is zero. Some control solutions and system parameters selection are presented lest non-desired transitions appear