Positive displacement motor (PDM) bottomhole assemblies (BHAs) are widely used in horizontal drilling due to their low cost and high rate of penetration (ROP) under rotary conditions. However, their limited-trajectory control ability often requires switching to sliding drilling for sharp corrections, which significantly reduces efficiency. Moreover, the quantitative relationship between build up rate (BUR) and controllable parameters such as revolutions per minute (RPM) and mud flow rate (MFR) remains unclear under rotary conditions.

To address these issues, we propose a machine learning (ML)–based model predictive control (MPC) framework that regulates trajectory solely through real-time optimization of drilling parameters. A hybrid prediction model, integrating mechanical principles and ML, is developed to map weight on bit (WOB), RPM, and MFR to BUR, with a Lipschitz continuity constraint enhancing stability and robustness. The MPC objective function is improved by incorporating adaptive weighting, which accelerates convergence, reduces overshoot, and improves control consistency. The proposed method is evaluated across five simulation scenarios, which are analysis of control behavior, objective function enhancement, piecewise setpoint tracking, comparison with classical controllers, and robustness testing.

The approach is validated using field data from a horizontal well in the Junggar Basin, northwest China. The results show that the ML-MPC strategy achieves accurate setpoint tracking under various conditions, maintains strong robustness to input noise, initialization variations, and measurement disturbances (with steady-state error < 0.2°/30  m), and meets real-time computation requirements (<20  seconds per control step). Analysis of the optimized control parameters provides data-driven insights into how WOB, RPM, and MFR influence BUR. Notably, a control inertia effect is observed: When the control objective aligns with the existing trend of variation, the system responds more efficiently; when it opposes the trend, the response becomes slower and more prone to overshoot. Overall, this work presents a practical framework for real-time trajectory control and contributes to the automation and intelligent drilling technologies in the oil and gas industry.