Robust tube MPC for suppressing stick-slip vibrations in drill string systems

Abstract

Addressing stick-slip vibrations in drill string systems is critical in drilling operations, as these vibrations can cause costly downtime and equipment damage. A four-degrees-of-freedom (4-DOF) model captures the dynamics of long vertical drilling systems, followed by a robust tube model predictive control (MPC) strategy to account for system uncertainties. The controller is designed to handle variations in key parameters, such as drill pipe inertia—affected by pipe length—and weight on bit—affected by axial vibrations—without relying on direct bit velocity measurements. Comparative analysis with sliding mode control (SMC) demonstrates that the proposed MPC achieves substantially faster settling times and lower mean squared error (MSE). Specifically, for the top driver, the settling time is reduced by 41% and MSE by 74% compared to SMC. Relative to proportional–integral–derivative (PID), the tube MPC improves MSE by 69% and reduces settling time by 40%. In addition, the linear quadratic tracking (LQT) and linear MPC controllers were compared with the proposed method. A sensitivity analysis further evaluates the influence of parameter uncertainties, with simulation results confirming the controller’s effectiveness in suppressing stick-slip oscillations and maintaining robust performance under uncertain conditions.