Non-linear control of water flow dynamics by input-output linearization based on a collocation method model

This paper is devoted to the non-linear control of irrigation canals or dam-river systems. Open-channel dynamics are based on the well-known Saint-Venant non-linear partial differential equations [9]. Here, a finite-dimensional model previously developed in [7], and based on a collocation Galerkin method together with a functional approximation by Lagrange polynomials, is used as a basic model for the control. In [7] it has indeed been shown how such a model is much more tractable than those obtained from classical finite-difference or finite-element methods (from the viewpoint of both state dimension and structure) and well suited to control purposes. In this paper we show in more details how this model can be used to design a non-linear controller using techniques of dynamic input-output linearization for the goal of controlling water levels along an open-channel reach.