Robust Model Predictive Control for the Beam-Pumping Unit Dynamic Liquid Level Stabilization

As reservoir development enters the middle and late stages, variations in formation pressure and water cut lead to significant changes in liquid supply capacity. Under conventional fixed stroke-per-minute (SPM) operation, the production capacity of beam pumping wells often fails to match the dynamically varying inflow, resulting in severe dynamic fluid level fluctuations and subsequent pump-off, gas locking, and abnormal rod string loading. To address these issues, this paper develops a dynamic fluid level model based on the operating mechanism of beam pumping wells, explicitly incorporating system uncertainties and reservoir disturbances. On this basis, a tube-based robust model predictive control (Tube-RMPC) strategy is proposed, in which nominal predictions are combined with local feedback compensation to effectively mitigate model uncertainties and external disturbances. Simulation results demonstrate that, compared with conventional PID control and traditional MPC methods, the proposed approach achieves superior performance in dynamic fluid level tracking accuracy, disturbance rejection, and closed-loop stability.