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

Vahid Vaziri*, Marcin Kapitaniak, Marian Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)
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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.

Original languageEnglish
Pages (from-to)805-825
Number of pages21
JournalEuropean Journal of Applied Mathematics
Issue number5
Early online date18 May 2018
Publication statusPublished - Oct 2018


  • Drill-string dynamics
  • experimental studies
  • mathematical modelling
  • nonlinear behaviour
  • sliding mode control
  • stick–slip
  • torsional vibration


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