Nonlinear Control of Open-Channel Water Flow Based on Collocation Control Model
Publication: Journal of Hydraulic Engineering
Volume 130, Issue 3
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.
Get full access to this article
View all available purchase options and get full access to this article.
References
Alam, M. M., and Bhuiyan, M. A.(1995). “Collocation finite-element simulation of dambreak flows.” J. Hydraul. Eng., 121(2), 118–128.
Besançon, G. (2001). “A note on constrained stabilization for nonlinear systems in feedback form.” 5th IFAC Symp. on Nonlinear Control Systems.
Chen, M.-L. (2001). “Commandes optimale et robuste des équations aux dérivées partielles régissant le comportement des systèmes hydrauliques à surface libre.” PhD thesis, Laboratoire d’Automatique de Grenoble, Inst. National Polytechnique de Grenoble, Grenoble, France (in French).
Chen, M.-L., and Georges, D. (1999) “Nonlinear optimal control of an open-channel hydraulic system based on an infinite-dimensional system.” IEEE Conf. on Decision and Control, IEEE, New York, 4313–4318.
Cooley, R. L., and Moin, S. A.(1976). “Finite element solution of Saint-Venant equations.” J. Hydraul. Div., Am. Soc. Civ. Eng., 102(6), 759–775.
Coron, J. M., d’Andréa-Novel, B., and Bastin, G. (1999). “A Lyapunov approach to control irrigation canals modeled by Saint-Venant equations.” European Control Conf.
Dochain, D., Babary, J. P., and Tali-Maamar, N.(1992). “Modeling and adaptative control of nonlinear distributed parameter bioreactor via orthogonal collocation.” Automatica, 28(5), 873–883.
Dulhoste, J.-F. (2001). “Contribution à la commmande non linéaire de systèmes d’irrigation.” PhD thesis, Laboratoire d’Automatique de Grenoble, Inst. National Polytechnique de Grenoble, Grenoble, France (in French).
Dulhoste, J.-F., Besançon, G., and Georges, D. (2001). “Non-linear control of water flow dynamics by input–output linearization based on a collocation method model.” European Control Conf.
Fletcher, C. A. J. (1984). Computational Galerkin methods, Springer Series in Computational Physics, Springer, Berlin.
Georges, D., Dulhoste, J.-F., and Besançon, G. (2000). “Modelling and control of water flow dynamics via a collocation model.” Mathematical theory of network and systems, Perpignan, France.
Isidori, A. (1995). Nonlinear control systems, 3rd Ed., Springer, Berlin.
Litrico, X. and Georges, D. (1999). “Robust optimal control of a dam-river system with intermediate measurements.” European Control Conf.
Malaterre, P. O. (1994). “Modélisation, analyse et commande optimale LQR d’un canal d’irrigation.” PhD thesis, LAAS-CNRS-ENGREF-Cemagref (in French).
Molina, L. S., and Miles, J. P.(1996). “Control of an irrigation canal.” J. Hydraul. Eng., 122(7), 403–410.
Sawadogo, S., Faye, R., Malaterre, P. O., and Mora Camino, F. (1998). “Decentralized predictive controller for delivery canals.” IEEE Int. Conf. on Systems Man and Cybernetics (SMC’98), 11–14, 3880–3884.
Strelkoff, T.(1970). “Numerical solution of Saint-Venant equation.” J. Hydraul. Div., Am. Soc. Civ. Eng., 96(1), 223–252.
Stringam, B. L., and Merkley, G. P. (1997). “Fuzzy controller simulation for local downstream water level control in canals.” Int. Workshop on Regulation of Irrigation Canals: State of the Art of Research and Applications, 342–348.
Villadsen, J. V., and Michelsen, M. L. (1978). Solution of differential equations models by polynomial approximation, Prentice–Hall, Englewood Cliffs, N.J.
Voron, B., and Bouillot, A. P. (1997). “Application of the fuzzy set theory to the control of large canals.” Int. Workshop on Regulation of Irrigation Canals: State of the Art of Research and Applications, 317–331.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 130 • Issue 3 • March 2004
Pages: 254 - 266
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Feb 5, 2001
Accepted: Mar 12, 2003
Published online: Feb 19, 2004
Published in print: Mar 2004
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.