On the study of control effectiveness and computational efficiency of reduced Saint-Venant model in model predictive control of open channel flow

Model predictive control (MPC) of open channel flow is becoming an important tool in water management. The complexity of the prediction model has a large influence on the MPC application in terms of control effectiveness and computational efficiency. The Saint-Venant equations, called SV model in this paper, and the Integrator Delay (ID) model are either accurate but computationally costly, or simple but restricted to allowed flow changes. In this paper, a reduced Saint-Venant (RSV) model is developed through a model reduction technique, Proper Orthogonal Decomposition (POD), on the SV equations. The RSV model keeps the main flow dynamics and functions over a large flow range but is easier to implement in MPC. In the test case of a modeled canal reach, the number of states and disturbances in the RSV model is about 45 and 16 times less than the SV model, respectively. The computational time of MPC with the RSV model is significantly reduced, while the controller remains effective. Thus, the RSV model is a promising means to balance the control effectiveness and computational efficiency.