Sliding-mode control of an underactuated oilwell drill-string with parametric uncertainty

The stick-slip oscillations of a multibody oilwell drill-string are studied in this paper from the point of view of control of underactuated system. The model has one control input acting on the rotary table from the land surface and multi-degree-of-freedom downhole parts comprising a series of hollow drill pipes, a number of much stiffer drill collars, and a drill bit suffering highly nonlinear friction to be controlled. The control objective of the drill-string is to avoid the undesired bit sticking and stick-slip oscillation while tracking a desired angular velocity. Two sliding-mode controllers are studied for the drill-string with estimated physical parameters. The proposed controllers can guarantee that any trajectory of the system can reach and stays thereafter on the pre-designed sliding surface where the desired equilibrium is asymptotically stable. Simulation results are given to demonstrate their efficacy and robustness to parametric uncertainty.