Trajectory Tracking for Directional Drilling in Underground Coal Mine Using Robust Model Predictive Control

This paper studies the problem of trajectory tracking control for directional drilling in underground coal mine by devising a robust model predictive control method. First, a directional drilling trajectory extension model is obtained by the linearization of a drilling tool kinematic model through the Taylor series expansion in the borehole depth domain. Then, in view of the influence of the uncertainty of the drilling tool slope and external interference, a robust model predictive control method is introduced in the form of an optimal control problem. A sufficient condition is obtained to calculate the corresponding controller gain matrix on the premise of satisfying the stability of the closedloop control system and the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance index. At last, the effectiveness of our method is illustrated through simulation analysis. Compared with model predictive control, robust model predictive control directly incorporates the uncertainty of the drilling tool slope and external interference into the control design, enabling it to better adapt to the complex and variable underground coal mine environment.