Robust Control of Drillstring Vibrations: Modeling, Estimation, and Real-Time Considerations

This paper presents a comprehensive and hybrid control framework for the real-time regulation of drillstring systems that are subject to complex nonlinear dynamics, including torsional stick–slip oscillations, coupled axial vibrations, and intricate bit–rock interactions. The model also accounts for parametric uncertainties and external disturbances typically encountered during rotary drilling operations. A robust sliding mode controller (SMC) is designed for inner-loop regulation to ensure accurate state tracking and strong disturbance rejection. This is complemented by an outer-loop model predictive control (MPC) scheme, which optimizes control trajectories over a finite horizon while balancing performance objectives such as rate of penetration (ROP) and torque smoothness, and respecting actuator and operational constraints. To address the challenges of partial observability and noise-corrupted measurements, an Ensemble Kalman Filter (EnKF) is incorporated to provide real-time estimation of both internal states and external disturbances. Simulation studies conducted under realistic operating scenarios show that the hybrid MPC–SMC framework substantially enhances drilling performance. The controller effectively suppresses stick–slip oscillations, provides smoother and more stable bit-speed behavior, and improves the consistency of ROP compared with both open-loop operation and SMC alone. The integrated architecture maintains robust performance despite uncertainties in model parameters and downhole disturbances, demonstrating strong potential for deployment in intelligent and automated drilling systems operating under dynamic and uncertain conditions.