Real-Time Lexicographic MPC with Online Correction for Intelligent Drill-Bit Rotary Valves in Mud-Pulse Telemetry

Reliable front-end pressure-pulse generation is critical to mud-pulse telemetry because waveform distortion introduced at the rotary valve propagates through the telemetry chain and reduces downstream recoverability. This paper targets accurate and computationally tractable control of an intelligent drill-bit rotary valve under actuator limits, parameter drift, and downhole-like disturbances. A control-oriented electromechanical–hydraulic grey-box model is established, and a real-time lexicographic model predictive control (MPC) framework with candidate pre-screening, move blocking, and online correction/compensation is developed and compared with proportional–integral–derivative (PID) control and conventional MPC. Under a sampling period of $T_s=20\mathrm{ms}$, the proposed controller reduces the step-tracking rise time from $2.18\mathrm{s}$ to $1.76\mathrm{s}$ and the steady-state pressure error from $0.1208\mathrm{MPa}$ to $0.0292\mathrm{MPa}$ relative to conventional MPC. In the pulse-output and mismatch–disturbance scenarios, it further maintains lower steady-state pressure error while reducing the cumulative input variation from $51.0$ to $11.5$ and from $121.5$ to $19.5$, respectively. The observed 99th-percentile and worst-case MATLAB workstation execution times remain below one sampling period, while supplementary mismatch–disturbance sensitivity maps indicate a favorable accuracy–timing compromise within the tested numerical envelope. These results support the proposed method as a simulation-validated candidate for low-complexity rotary-valve control and motivate subsequent bench/hardware-in-the-loop (HIL) validation rather than field-qualified deployment claims.