Prediction-Based Control for Mitigation of Axial–Torsional Vibrations in a Distributed Drill-String System

Abstract

This article proposes a control strategy to stabilize the axial–torsional dynamics of a distributed drill-string system. An infinite-dimensional model for the vibrational dynamics of the drill string is used as a basis for controller design. In this article, both the cutting process and frictional contact effects are considered in the bit–rock interaction model. Moreover, models for the top-side boundary conditions regarding axial and torsional actuation are considered. The resulting model is formulated in terms of neutral-type delay differential equations that involve constant state delays, state-dependent state delays, and constant input delays arising from the distributed nature of the drill-string dynamics and the cutting process at the bit. Using a spectral approach, the stability and stabilizability of the associated linearized dynamics are analyzed to support controller design. An optimization-based continuous pole-placement technique has been employed to design a stabilizing controller. Since the designed state-feedback control law needs state prediction, a predictor with observer structure is proposed. Both the controller and the predictor only employ top-side measurements. The effectiveness of the control strategy, in the presence of measurement noise, is shown in a representative case study. It is also shown that the controller is robust to parametric uncertainty in the bit–rock interaction.