Objective It is challenging to control the borehole trajectories during directional drilling in complex strata in underground coal mines, resulting in significant deviations from the designed trajectories. Given this, this study proposed a method for tracking and controlling directional borehole trajectories based on model predictive control (MPC).

Methods Focusing on the directional drilling process conducted using a screw drill, this study investigated the movement patterns of the directional screw drill by analyzing the characteristics of directional drilling in complex strata in underground coal mines. Based on the kinematic theory, this study developed a borehole trajectory extension model for sliding directional drilling. Then, the model linearization was processed using Taylor series expansion, aiming to eliminate the coupling relationships between state variables such as dip angle and azimuth. Accordingly, this study constructed a borehole trajectory prediction model and an objective function with the minimum trajectory deviation as the control target. The steady-state errors of the prediction model were reduced using feedback correction. Furthermore, this study designed a model predictive controller with functions of predictive modeling, rolling optimization, and feedback correction. As a result, the optimal control variable for the borehole trajectory—toolface angle—was recommended. Accordingly, the optimized control for tracking directional borehole trajectories was achieved. Finally, the control algorithm was validated using the drilling data from a coal mine in Hancheng City, Shaanxi Province.

Results and Conclusions  The results indicate that the linearized borehole trajectory extension model simplifies the design process of the controller while effectively preserving the characteristics of the original model. The improved MPC method with the feedback correction mechanism for predicting directional borehole trajectories removes the impacts of model adaptation and steady-state errors. Compared to the human experience-controlled decision-making method based on the deflection rules of a screw drill, the improved MPC method reduces the average absolute errors of the dip angle and azimuth by 79.5% and 70.5%, respectively, providing a novel control algorithm for directional borehole trajectories in complex strata.