Fractional-order controllers for stick-slip vibration mitigation in oil well drill-strings

Abstract

Drillstring–borehole interaction can produce severely damaging vibrations. An example is stick–slip vibration, which negatively affects drilling performance, tool integrity and completion time, and costs. Attempts to mitigate stick–slip vibration typically use passive means and/or change the operation parameters, such as weight on bit and rotational speed. Automating the latter approach, by means of feedback control, holds the promise of quicker and more effective mitigation. The present work presents three separate fractional-order controllers for mitigating drillstring slip–stick vibrations. For the sake of illustration, the drillstring is represented by a torsional vibration lumped parameter model with four degrees of freedom, including parameter uncertainty. The robustness of these fractional-order controllers is compared with traditional proportional-integral-derivative controllers under variation of the weight on bit and the drill bit’s desired rotary speed. The results confirm the proposed controllers effectiveness and feasibility, with rapid time response and less overshoot than conventional proportional-integral-derivative controllers.