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Suppression of drill-string stick–slip vibration by sliding mode control: Numerical and experimental studies

Published online by Cambridge University Press:  18 May 2018

VAHID VAZIRI ,
MARCIN KAPITANIAK  and
MARIAN WIERCIGROCH
VAHID VAZIRI
Affiliation:
Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK emails: [email protected], [email protected], [email protected]
MARCIN KAPITANIAK
Affiliation:
Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK emails: [email protected], [email protected], [email protected]
MARIAN WIERCIGROCH
Affiliation:
Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK emails: [email protected], [email protected], [email protected]
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Abstract

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We investigate experimentally and numerically suppression of drill-string torsional vibration while drilling by using a sliding mode control. The experiments are conducted on the novel experimental drill-string dynamics rig developed at the University of Aberdeen (Wiercigroch, M., 2010, Modelling and Analysis of BHA and Drill-string Vibrations) and using commercial Polycrystalline Diamond Compact (PDC) drill-bits and rock-samples. A mathematical model of the experimental setup, which takes into account the dynamics of the drill-string and the driving motor, is constructed. Physical parameters of the experimental rig are identified in order to calibrate the mathematical model and consequently to ensure robust predictions and a close agreement between experimental and numerical results for stick–slip vibration is shown. Then, a sliding mode control method is employed to suppress stick–slip vibration. A special attention is paid to prove the Lyapunov stability of the controller in presence of model parameter uncertainties by defining a robust Lyapunov function. Again experimental and numerical results for the control cases are in a close agreement. Stick–slip vibration is eliminated and a significant reduction in vibration amplitude has been observed when using the sliding controller.

Keywords

Drill-string dynamicsstick–sliptorsional vibrationnonlinear behaviourexperimental studiesmathematical modellingsliding mode control
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 5: Theory and applications of nonsmooth dynamical systems , October 2018 , pp. 805 - 825
Copyright
Copyright © Cambridge University Press 2018 

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