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Summary This paper considers the design of a nonlinear observer‐based output‐feedback controller for oil‐field drill‐string systems aiming to eliminate (torsional) stick–slip oscillations. Such vibrations decrease the performance and reliability of drilling systems and can ultimately lead to system failure. Current industrial controllers regularly fail to eliminate stick–slip vibrations under increasingly challenging operating conditions caused by the tendency towards drilling deeper and inclined wells, where multiple vibrational modes play a role in the occurrence of stick–slip vibrations. As a basis for controller synthesis, a multi‐modal model of the torsional drill‐string dynamics for a real rig is employed, and a bit–rock interaction model with severe velocity‐weakening effect is used. The proposed model‐based controller design methodology consists of a state‐feedback controller and a (nonlinear) observer. Conditions, guaranteeing asymptotic stability of the desired equilibrium, corresponding to nominal drilling operation, are presented. The proposed control strategy has a significant advantage over existing vibration control systems as it can effectively cope with multiple modes of torsional vibration. Case study results using the proposed control strategy show that stick–slip oscillations can indeed be eliminated in realistic drilling scenarios in which industrial controllers fail to do so. Moreover, key robustness aspects of the control system involving the robustness against uncertainties in the bit–rock interaction and changing operational conditions are evidenced. Copyright © 2017 John Wiley & Sons, Ltd.

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Summary This paper considers the effect of an antistall tool on the dynamics of deep drilling systems. Field results show that the antistall tool increased the rate of penetration (ROP) of drilling systems when compared with ROP in offset wells drilled without this tool. We developed a model–based approach to investigate the effect of this downhole tool on the ROP and on the mechanical specific energy. Toward this, a drillstring model including the antistall tool was constructed; it describes the coupled axial/torsional dynamics in the form of delay differential equations. Simulation results and a dynamic analysis based on averaging the obtained steady–state response show that an increased drilling efficiency was obtained using the antistall tool, resulting in a higher ROP.