Control of a Downhole Drilling System Using Integral Barrier Lyapunov Functionals

Emergence of shale oil & gas and the unconventional wellbore condition motivate an increasing number of studies on analysis and control of the downhole drilling system. Due to complex downhole environments and underactuated, nonlinear, and nonsmooth features of the drilling dynamics, control synthesis of the drilling system is a challenging task. In this study, we propose a novel nonlinear control design for set-point tracking of torsional velocity and axial rate of penetration, for a vertical drilling system with coupled axial and torsional dynamics and a velocity-independent bit-rock interaction model. To eliminate damaging oscillations such as stick-slip, the Barrier Lyapunov Function (BLF) approach is introduced to ensure smooth motion of the drill bit, and to avoid having drilling operate in undesired working conditions. Meanwhile, the stability, boundedness and convergence properties with respect to different system states are proved. To this end, simulation results of two case studies are given to evaluate efficacy and robustness of the proposed control approach.