Stabilization of multibody drill-strings which exhibit stick-slip oscillations is studied inthis paper from the point of view of underactuated system. The model has one controltorque input acting on the rotary table from the land surface and multi-degree-of-freedomdownhole 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 equilibriaare analyzed accordingly. The control objective of the system is to avoid the undesired bitsticking and stick-slip oscillation while tracking a desired angular velocity. Three slidingmodecontrollers are studied for the drill-string with estimated physical parameters. Thestabilities of the proposed controllers are proved by using the Lyapunov direct methodensuring that any trajectory of the system can reach and stays thereafter on the predesignedsliding surface where the desired equilibrium is asymptotically stable. Extensivesimulation results are given to demonstrate the effectiveness of the proposed controllersand their robustness to parametric uncertainties.
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