Nonlinear Model Predictive Control of a Water Distribution Canal Pool

Abstract

Water distribution canals provide interesting examples of distributed parameter plants for which nonlinear model predictive control may be applied. Canals are formed by a sequence of pools separated by gates. Output variables are the pool level at certain points, manipulated variables are the position of the gates and disturbances are the outlet water flows for agricultural use. The operation of this system is subject to a number of constraints. These are the minimum and maximum positions of the gates, gate slew-rate and the minimum and maximum water level. The objective considered in this paper is to drive the canal level to track a reference in the presence of the disturbances. The pool level is a function of both time and space that satisfies the Saint-Venant equations. These are a set of hyperbolic partial differential equations that embody mass and momentum conservation. In order to develop a NMPC algorithm, the Saint-Venant equations are approximated by a set of ordinary differential equations corresponding to the variables at the so called collocation points. Together with the boundary conditions, this forms a nonlinear reduced predictive model. In this way, a nonlinear prediction of future canal levels is obtained. The paper details the control general formulation along with a computationally efficient algorithm as well as the results obtained from its application.