Control of Axial–Torsional Dynamics of a Distributed Drilling System

Self-excited vibrations in drill-string systems are one of the main causes of failure and efficiency reduction in drilling operations. To suppress these vibrations, an active control strategy is proposed in this article based on a distributed drill-string model. Herein, the coupled axial–torsional dynamics of the drill string are taken into account. This coupling takes place through the bit–rock interaction, consisting of the cutting and the frictional components. The drill-string model is expressed as a neutral-type delay differential equation (NDDE) with constant and state-dependent state delays and constant input delays. As a first step in the novel controller design, a compensator is designed to mitigate the reflective waves at the top side of the string, which, in turn, results in the elimination of the neutral terms and some of the constant time delays in the delay system model. This supports a simplified next step of stabilizing controller design. Second, a new method is proposed to provide sufficient conditions for exponential stability with a prescribed minimal transient decay rate. Based on these conditions, a parametric feedback control law is designed. Finally, to make the controller causal, a predictor is designed which predicts the future state by only employing top-side measurements, available in practice. A simulation-based case study reflecting real-life scenarios is presented to illustrate the effectiveness of the proposed controller. It is also illustrated that the controller is robust against parametric uncertainties and measurement noise.