Control of a downhole drilling system using an integral Barrier Lyapunov Function based method

Abstract

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 the 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 constrained by a delay differential equation. To eliminate damaging oscillations such as stick-slip, the Barrier Lyapunov Function 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 system states are proved, and validated by a series of simulation results.

Keywords:

• Vertical drilling system
• vibration mitigation
• Barrier Lyapunov Function

Acknowledgments

A preliminary version of the work was presented at the 2019 American Control Conference (Tian & Song, 2019). This submission features a much detailed modelling, control-oriented model transformation, new theorem for control design and the proofs, and new simulation results for different operating conditions and robustness analysis.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was partially supported by the National Academies of Sciences, Engineering and Medicine GRP Early Career Research Fellow Award.