Nonlinear model predictive control for directional drilling applications

Abstract

In directional drilling, a nonlinear Delay Differential Equation (DDE) model may be used for its high precision in predicting how a borehole may be drilled according to a well plan. To address challenges associated with real-time control of a drill drilling wellbore, techniques of generalized feedback linearization, finite element concept, and zero-order hold discretization may be used to transform a nonlinear DDE model into discretized domain with a linear Ordinary Differential Equation (ODE) form. Following this transformation, a novel optimization framework may be used to concurrently determine optimal control inputs and solve a linear complementarity problem (LCP). The validity of both the discretized model and the optimization strategy may be verified by comparing modeled results with real-world results. Subsequent closed-loop simulations demonstrate the ability of the proposed model predictive control to maintain alignment of a drill string with a planned well trajectory, even in the presence of disturbances and noise.