New algorithm based active method to eliminate stick-slip vibrations in drill string systems

The drill string is always exposed to various types of vibrations among which, stick slip is one of the most important types. It is a severe state of torsional vibrations. This phenomenon can decrease the rate of penetration of drilling, wear of expensive equipment prematurely and cause catastrophic failures. In this paper, a novel adaptive sliding mode (SM) controller is proposed to eliminate stick slip in drill string systems. This proposed algorithm has a more robust capacity than existing 1st-order SM schemes in the literature regarding the robustness to parametric uncertainties, variations in weight on bit (WOB), variations in reference velocity and measurement noise. Moreover, the proposed controller does not require a priori knowledge of the upper bounds of parametric uncertainties, external disturbances and can be easily applied for any operating mode of the drill rig. A proof of stability based on the Lyapunov criterion of the system is given. Simulation results show that the proposed algorithm suppresses the stick-slip while keeping good performances compared to other SM controllers. A comparative study between the proposed controller and classic SM controllers and other adaptive SM scheme is performed in order to assess the advantages of the proposed algorithm and illustrate the overall performance improvements. The obtained results show that the proposed controller succeeded to eliminate the stick-slip phenomenon with the best performance compared to the classic SM controllers. In fact, the proposed controller presented a reduction of nearly 26 in terms of overshoot and 1.6 times better settling time values while having the smoother input signal.