Nonlinear Control of Open-Channel Water Flow Based on Collocation Control Model

Abstract

This paper is devoted to the nonlinear control of open-channel water flow dynamics via a one-dimensional collocation control model for irrigation canals or dam-river systems. Open channel dynamics are based on the well-known Saint-Venant nonlinear partial differential equations. In order to obtain a finite-dimensional model an orthogonal collocation method is used, together with functional approximation of the solutions of Saint-Venant equations based on Lagrange polynomials. This method can give a more tractable model than those obtained from classical finite-difference or finite-element methods (from the viewpoint of both state dimension and structure), and is well suited for control purposes. In particular it is shown how such a model can be used to design a nonlinear controller by techniques of dynamic input–output linearization with the goal of controlling water levels along an open-channel reach. Controller performance and robustness are illustrated in simulations, with a simulated model for the canal chosen as more accurate than the one used for control design.