Stick–Slip Prevention of Drill Strings Using Model Predictive Control Based on a Nonlinear Finite Element Reduced-Order Model

During the drilling process, stick–slip vibrations are one of the critical causes of bottom-hole assembly (BHA) failure and reduced drilling efficiency. To address this, this study first proposes a drill-string model based on a three-dimensional nonlinear finite beam element, combined with Hamilton’s principle of virtual work, to comprehensively describe the nonlinear behavior of the drill-string system. Next, to improve computational efficiency, the model is reduced using the modal truncation method, which retains the key modes of drill-string vibrations. Based on this, a model predictive control (MPC) method is designed to eliminate stick–slip vibrations. Furthermore, the robustness of the MPC method under parameter uncertainties is also investigated. In particular, the impact of the weight on bit (WOB) on the drill bit’s torsional velocity is further considered, and an MPC angular velocity comprehensive control scheme based on the dynamic WOB (DWOB-MPC) is proposed. This scheme stabilizes the velocity of the drill bit by dynamically adjusting the WOB, thereby eliminating stick–slip vibrations. Simulation results demonstrate that both the proposed MPC and DWOB-MPC methods effectively suppress stick–slip vibrations. Notably, the DWOB-MPC method further reduces the settling time and overshoot, exhibiting superior dynamic performance.