Dynamical Behavior and Stability Analysis of Hydromechanical Gates
Publication: Journal of Irrigation and Drainage Engineering
Volume 143, Issue 9
Abstract
This study revisits the stability of hydromechanical gates for upstream water surface regulation, also known as AMIL gates. AMIL gates are used in irrigation canals, where they are often installed in series. From the regulation perspective, instabilities are undesired because they generate waves and fluctuations in the discharge. A mathematical model for an AMIL gate is described as a nonlinear dynamical system, which permits analyzing the dynamic interaction between the local water level and the gate position. The feedback effect of the gate on the water level is introduced by considering a storage volume of length . In the derived model, waves are simplified to fluctuations of the flat water surface of the storage volume. Although previous studies used the same model, none has clarified the sensitivity of the model to the parameter . The role of this parameter is investigated and it is calibrated with experimental measurements. The precision of the regulation is described by the decrement, the range of the water level around the target level. Based on the mathematical model, a relationship for calibration of the gate and precision of regulation is presented. The subsequent stability analysis of the dynamical system focuses on five control parameters and sheds light on their influence on the gate behavior. Hopf bifurcations are identified, which separate stable equilibrium solutions from stable periodic solutions. Further work might consider the implications of the periodic solutions on gates that work in series, as well as envision the innovative use of such gates outside of the domain of irrigation canals to obtain dynamic environmental flows in hydropower systems.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The Swiss National Science Foundation is greatly acknowledged for funding the projects REMEDY (Grant No. PP00P2153028/684 1). The Swiss Commission for Technology and Innovation (CTI) is greatly acknowledged for funding the Swiss Competence Center for Energy Research—Supply of Electricity (SCCER-SoE). Paolo Perona wishes to thank the Climatology Research Group at the Institute of Geography of the University of Bern for hosting him as academic guest.
References
AUTO-07p [Computer software]. Concordia Univ., Montreal.
Bernhard, F. (2015). “Dynamical behavior of automatic gates for upstream water surface regulation in irrigation canals.” Master thesis, École polytechnique fédérale de Lausanne (EPFL), Lausanne, Switzerland.
Cassan, L., Baume, J.-P., Belaud, G., Litrico, X., Malaterre, P.-O., and Ribot-Bruno, J. (2011). “Hydraulic modeling of a mixed water level control hydromechanical gate.” J. Irrig. Drain. Eng., 446–453.
Corriga, G., Patta, F., Tola, S., and Usai, G. (1977). “La dinamica delle paratoie autolivellanti nelle reti di distribuzione a pelo libero [reti di irrigazione].” Idrotecnica, 6, 249–255.
Corriga, G., Sanna, S., and Usai, G. (1980). “Frequency response and dynamic behaviour of canal networks with self-levelling gates.” Appl. Math. Modell., 4(2), 125–129.
Ermentrout, B (2002). Simulating, analyzing, and animating dynamical systems, Society for Industrial and Applied Mathematics, Philadelphia.
GEC Alsthom. (1992). “Amil gates—Constant upstream level control in reservoirs and canals.” ⟨http://www.canari.free.fr/papers/neyrpic_amil_fr.pdf⟩ (Nov. 14, 2015).
Gorla, L., and Perona, P. (2013). “On quantifying ecologically sustainable flow releases in a diverted river reach.” J. Hydrol., 489, 98–107.
Guckenheimer, J., and Holmes, P. (1993). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer, New York.
Higgins, B. G. (2013). “Stability analysis of periodic solutions.” ⟨https://sites.google.com/site/chemengwithmathematica/home/numerical-methods⟩ (Nov. 14, 2015).
Litrico, X., Belaud, G., and Fromion, V. (2007). “Stability analysis of automatic water level control gates in open-channels.” 46th IEEE Conf. on Decision and Control, 2007, IEEE, New York, 1591–1596.
Litrico, X., and Fromion, V. (2009). Modeling and control of hydrosystems, Springer, London.
Montañés, J. L. (2005). Hydraulic canals: Design, construction, regulation and maintenance, Taylor & Francis, London.
Munson, B. R., Young, D. F., Okiishi, T. H., and Huebsch, W. W. (2009). Fundamentals of fluid mechanics, Wiley, New York.
Perona, P., Dürrenmatt, D. J., and Characklis, G. W. (2013). “Obtaining natural-like flow releases in diverted river reaches from simple riparian benefit economic models.” J. Environ. Manage., 118, 161–169.
Ramirez-Luna, J. (1997). “Modélisation des ouvrages frontaux et latéraux dans les canaux d’irrigation.” Ph.D. thesis, Ecole Nationale du Génie Rural, des Eaux et des Fôrets (ENGREF), Ecole Nationale du Génie Rural, des Eaux et des Fôrets (ENGREF), Paris.
Ramirez-Luna, J., Baume, J., De León-Mojarro, B., Ruiz-Carmona, V., and Sau, J. (1998). “Wave motion stability for coupled canal pool-amil gate systems.” 1998 IEEE Int. Conf. on Systems, Man, and Cybernetics, Vol. 4, IEEE, San Diego, 3868–3873.
Razurel, P., Gorla, L., Crouzy, B., and Perona, P. (2015). “Non-proportional repartition rules optimize environmental flows and energy production.” Water Resour. Manage., 30(1), 1–17.
Rogers, D. C., and Goussard, J. (1998). “Canal control algorithms currently in use.” J. Irrig. Drain. Eng., 11–15.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Dec 21, 2016
Accepted: Mar 7, 2017
Published online: Jul 7, 2017
Published in print: Sep 1, 2017
Discussion open until: Dec 7, 2017
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.