Nonlinear Model Predictive Control for Directional Drilling Applications

Jiamin Xu

Abstract: In directional drilling, the nonlinear Delay Differential Equation (DDE) model is recognized for its high precision in predicting borehole trajectory but has rarely been integrated into Model Predictive Control (MPC) frameworks due to its inherent complexity. To address this challenge, this paper proposes a novel method to transform the nonlinear DDE model into discretized Ordinary Differential Equation (ODE) model. Following this transformation, a novel optimization framework is proposed to concurrently determine optimal control inputs and solve the linear complementarity problem (LCP). The validity of both the discretized model and the optimization strategy is verified through comparison with results from existing literature. Subsequent closed-loop simulations demonstrate the ability of the proposed MPC to maintain the drill string's alignment with the planned well trajectory, even in the presence of disturbances and noise. These results highlight the effectiveness and potential applicability of the proposed MPC strategy in real-world directional drilling operations.