Nonlinear output‐feedback control of torsional vibrations in drilling systems

Abstract

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.

Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

“…When masses are non zero, they belong to the class of so-called "juggling systems" whose structure is particular [140,131]. It is noteworthy that so-called play operators of hysteresis (as in Figure 2.3 (b) [440,149,85], and naturally yields Lur'e set-valued systems [20,561]. Two-dimensional Coulomb's friction is represented in the tangent direction, by the mapping…”

Mitigation of Torsional Vibrations in Drilling Systems: A Robust Control Approach

“…The same objective is set in [5], where a PI controller to damp the first resonance mode based on feedback of the top drive velocity only is used. Other control methods, including torsional rectification [25], observer-based output feedback [7], [28], [29], feedback linearization [30], impedance matching [31], adaptive output-feedback for infinite dimensional drill-string models [23], backstepping control [32], sliding mode control [33], model predictive control [34], weight-on-bit (WOB) control [35], and robust control [6], [14], have been developed. A nonlinear observer-based approach for stick-slip mitigation is presented in [29], which uses a similar approach to model the drilling dynamics as employed in this paper.…”

“…Other control methods, including torsional rectification [25], observer-based output feedback [7], [28], [29], feedback linearization [30], impedance matching [31], adaptive output-feedback for infinite dimensional drill-string models [23], backstepping control [32], sliding mode control [33], model predictive control [34], weight-on-bit (WOB) control [35], and robust control [6], [14], have been developed. A nonlinear observer-based approach for stick-slip mitigation is presented in [29], which uses a similar approach to model the drilling dynamics as employed in this paper. Such an observer-based state-feedback approach requires information about the bit-rock interaction in the observer, which is typically not available in practice.…”

Nonlinear Torsional Vibration Analysis and Control of Semidirect Electromechanical Coupling Transmission System in Shearer

“…erefore, the torsional vibrations of the system cannot be interpreted rationally, neither from electrical nor from mechanical aspect. It is important to establish an accurate model of the electromechanical coupling system to further analyze the torsional vibration dynamic characteristics in the semidirect transmission system of the shearer and control the torsional vibration from the aspect of motor [21]. Gustavsson and Aidanpää [22] established the model of electromagnetic excitation produced by the uniform magnetic field, and the influence of nonlinear magnetic pull on rotor vibration of the hydrogenerator unit was discussed.…”

“…21 is coefficient vector corresponding to u 2 u.F 21 � F 21,1 F 21,2 0 F 21,4 0 , F 21,1 � c φ 2 H 11,4 + φ 2 H 20,4 + φ 4 H 11,2 + φ 4 H 20,2 � 0.0022 + 0.0015i, F 21,2 � f φ 1 H 11,4 + φ 1 H 20,4 + φ 4 H 11,1 + φ 4 H 20,1…”