Fixed-Time Tracking Control of Two-Dimensional Trajectories for Directional Boreholes Based on Rotary Steerable System

Rotary steering technology, with the advantages of controllable inclination building, high borehole quality, and strong adaptability to complex formations, has been applied in complex environments such as coal mines, engineering geology, and oil-gas exploration. This paper focuses on tasks like advanced working face exploration and geological anomaly identification in the aforementioned fields. To address the issues of target point deviation and trajectory deviation accumulation caused by the lag in inclination adjustment response, a fixed-time tracking control method for the two-dimensional trajectory of directional drilling holes oriented to rotary steering systems is proposed. Firstly, based on the time-delay differential equation describing borehole extension, a state-space representation of the directional drilling trajectory model is established. Then, a nonlinear controller with a power feedback term is designed to achieve rapid convergence of trajectory errors. Furthermore, a Lyapunov function is constructed to derive the upper bound of the convergence time, proving that the closed-loop system has fixed-time convergence characteristics. Finally, simulation experiments demonstrate that the proposed method features fast convergence speed, high trajectory control accuracy, and strong robustness, and has good application value in enhancing exploration efficiency and reducing operational risks.