Saint-Venant Reduced Order Model for Water Level Control in Open Channels

Water level control in open channels used for hydroelectric production is addressed in this paper. In order to use classical methods of controller design, a new reduced order model based on Saint-Venant equations is proposed. It is derived from irrational transfer functions developed with the WKB method for any non-uniform subcritical flow regime. The reduced model captures the first two modes. A comparison of open-loop simulations with the proposed 5th order plus delay transfer functions and with numerical non linear model is performed. The inputs of the simulations are given by on-site measurements to show the accuracy of the model in realistic conditions. Based on the resulting model, a robust tuning of controller is developed. It consists of a two-degree-of-freedom proportional integral controller. Time domain scenarii are shown to illustrate the closed-loop performance.