Quantum mechanics

Control (management)

Engineering

Slip (aerodynamics)

Biology

Drill

Vibration

Computer science

Acoustics

Drill string

Controller (irrigation)

Mechanical engineering

Thermodynamics

Physics

Nonlinear system

Agronomy

Lyapunov function

Artificial intelligence

Control theory (sociology)

Mechanics

European Journal of Applied Mathematics

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.

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