Nonlinear Control of Open-Channel Water Flow Based on Collocation Control Model |
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Authors: | Jean-Fran?ois Dulhoste Didier Georges Gildas Besan?on |
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Affiliation: | 1Dept. de Ciencias Térmicas, Escuela de Ingeniería Mecánica, Univ. de Los Andes, Mérida, Venezuela. 2Laboratoire d’Automatique de Grenoble, Inst. National Polytechnique de Grenoble–CNRS, B.P. 46, 38402 Saint Martin d’Hères, France.
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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. |
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Keywords: | Open channel flow Control systems Canals River systems Water distribution Hydraulic models |
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