A nonlinear backstepping like controller for a three-point collocation model of water flow dynamics

This paper deals with the nonlinear control of irrigation canals or dam-river systems. Open-channel dynamics are based on the well-known Saint-Venant nonlinear partial differential equations. Here, the finite-dimensional model we (2001) previously developed, which is based on a collocation Galerkin method together with the functional approximation by Lagrange polynomials, is used as a basic model for the control. In our previous paper we showed 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 for control purposes. In this paper we show how this model can be used to design a nonlinear controller using the backstepping technique for controlling the water levels along an open-channel reach, and present some simulations of the system using the obtained controller.