Mitigation of negative damping effects in deep drilling operations through active control

Abstract

Rotary drilling systems face harmful interactions between the drill-bit and rock formation, resulting in torsional stick–slip vibrations that reduce efficacy and damage drilling components. To mitigate these issues, designing an active controller that effectively reduces vibrations using the limited real-time data available during field operations is crucial. In this context, this paper examines the apparent negative damping effects leading to instability in the drilling system and introduces a novel control technique, based on the concept of a negative damping coefficient developed within this study, to counterbalance them. Given the critical importance of measured signals for the proposed technique’s efficiency, this paper also identifies relevant feedback signals to ensure asymptotic stability. To evaluate the effectiveness of the proposed controller, representative models of bit-rock interaction and drill-string torsional dynamics are developed, employing non-regularized dry friction and the finite element method. The model also addresses specific aspects required by the controller, including the addition of the error integral as a state variable and the reformulation of the equations of motion as a stabilization problem. The performance and stability of the proposed controller are compared with proportional–integral (PI) and optimal static output feedback (OSOF) controllers. Simulations show that it outperforms the PI controller, both for the nominal model and under parameter uncertainties. Robustness analyses further confirm its superiority over PI and OSOF, in addition to indicating a seeming global stability of the closed-loop system equipped with the proposed controller. Results encourage further investigations into the apparent global stability provided by the proposed controller and its implementation in laboratory setups or full-scale drilling rigs.