Robust output-feedback control to eliminate stick-slip oscillations in drill-string systems

The aim of this paper is to design a robust output-feedback controller to eliminate torsional stick-slip vibrations. A multi-modal model of the torsional dynamics with a nonlinear bit-rock interaction model is used. The controller design is based on skewed-¨ DK-iteration and the stability of the closed-loop nonlinear system is analyzed. The proposed controller design strategy offers significant advantages compared to existing strategies. First, it requires only surface measurements, second, it can effectively deal with multiple torsional flexibility modes, third, it provides robustness with respect to uncertainties in the bit-rock interaction and finally, control performance specifications can be taken into account. Simulation results confirm that stick-slip vibrations are indeed eliminated using the designed controller.