Torsional vibrations rejection in drilling systems: a combined observer-higher-order sliding mode control approach

One of the fundamental challenges in drilling systems is the phenomenon of torsional vibrations that can cause system destruction. This paper presents a new control approach to reject stick-slip vibrations in a drill-string. Firstly, a two-degree-of-freedom plant model with friction that represents the interaction between the rock formation and the drill bit is discussed. Secondly, a higher-order sliding mode control (HOSMC) is proposed in conjunction with a cascade structure to reject the vibrations. Thirdly, given the limitation of measuring only the surface top drive velocity, a state observer is designed to estimate system states, including bit-rock interaction torque. Realistic numerical simulations demonstrate the effectiveness of the proposed solution showcasing negligible residual oscillations on the order of 10 −3 and a better torque estimation, yet still to be improved, further demonstrating the effectiveness of the control strategy, highlighting its robustness, high precision, predefined convergence time, and ease of implementation.