Nonlinear model predictive controller for gate control in open canal irrigation systems with flexible water demands

Abstract

Model Predictive Control (MPC) stands a real-time water level control method employed in large-scale irrigation water canals. The efficacy of MPC relies, to a certain extent, on the predictive accuracy of its internal model. Current MPC implementations in open canal water level control predominantly utilize an Integrator Delay (ID) model as the internal model (ID-MPC) due to its simplicity and compatibility with feedback mechanisms. However, the limitations of ID-MPC become apparent when facing significant and dynamic downstream water demand changes, stemming from the inherent linear assumption in the ID model. To address this issue, this study proposes a Numerical Model-based MPC (NM-MPC) that integrates numerical models capable of accurately simulating nonlinear processes during flow adjustments as the internal model. NM-MPC integrates the ensemble Kalman filter (EnKF) with measured data to assimilate numerical model calculation results. Additionally, by incorporating corrections for changes in water demand during assimilation, NM-MPC provides estimates for potential alterations in water demand, thus enhancing the predictive accuracy of the internal model. The application of this approach to Test Canal 2 proposed by the American Society of Civil Engineers (ASCE), demonstrates that NM-MPC outperforms ID-MPC, especially during significant nonlinear changes in observed water levels, irrespective of the predictability of offtake water demand alterations. Specifically, when the canal’s nonlinearity intensifies due to substantial relative flow changes in water demand, NM-MPC achieves a substantial reduction in integrated absolute gate movement and gate control times by 99.4% and 77.4% (for predictable disturbances), and 32.4% and 36.8% (for unpredictable disturbances), respectively, compared to ID-MPC. The proposed NM-MPC demonstrates a notable advantage in water level control when dealing with flexible water demand disturbances.