Suppressing stick-slip oscillations in underactuated multibody drill-strings with parametric uncertainties using sliding-mode control

Stabilisation of multibody drill-strings which exhibit stick-slip oscillations is studied in this paper from the point of view of underactuated system. The model has one control torque input acting on the rotary table from the land surface and multi-degree-of-freedom downhole parts to be controlled. Three motion regimes of the model including bit sticking, stick-slip oscillation and rotating at a constant speed are identified and their equilibria are analysed accordingly. The control objective of the system is to avoid the undesired bit sticking and stick-slip oscillation while tracking a desired angular velocity. Three sliding-mode controllers are studied for the drill-string with estimated physical parameters. The stabilities of the proposed controllers are proved by using the Lyapunov direct method ensuring that any trajectory of the system can reach and stays thereafter on the pre-designed sliding surface where the desired equilibrium is asymptotically stable. Extensive simulation results are given to demonstrate the effectiveness of the proposed controllers and their robustness to parametric uncertainties.