Abstract Torsional vibrations in lumped drill strings pose a significant challenge in oil and natural gas exploration drilling, often leading to detrimental phenomena such as stick-slip. These torsional dynamics directly affect equipment performance, operational efficiency, costs, and safety. To address this issue, a two-degree-of-freedom torsional vibration model is developed, incorporating the complex nonlinear friction interactions between the drill bit and the rock formation. The adopted methodology first establishes a nonlinear two-degree-of-freedom drill-string model, upon which a composite backstepping adaptive sliding mode controller with a time-varying barrier function is designed and its stability ensured through Lyapunov analysis, before being validated in MATLAB/Simulink under parameter uncertainties. The proposed approach combines the strengths of backstepping control and adaptive sliding mode control, utilizing a barrier function with time-varying characteristics to effectively handle nonlinear dynamics, parameter variations, and external disturbances in drill-string systems. Furthermore, the design ensures torque transmission through the shaft while maintaining values within safe operational limits. Simulation results demonstrate that the backstepping sliding mode control with time-varying methods effectively suppresses stick-slip vibrations and enables precise monitoring and regulation of angular velocity for both the rotary motor and the Bottom Hole Assembly (BHA) within predefined parameters. Additionally, the controller successfully maintains torque transmission within permissible thresholds by appropriately selecting the decay factor. This study contributes to the advancement of sophisticated control methodologies for drill-string systems.
Tuama et al. (Thu,) studied this question.