Conversion from Discharge to Gate Opening for the Control of Irrigation Canals

The paper reviews several methods to convert discharge into gate opening. A control algorithm for one or several reaches of an irrigation canal sometimes uses a discharge as the control action variable even though the device to be manipulated is a gate or a weir. In this case a slave controller has to convert the discharge into a gate opening or a sill elevation in case of a weir. This is usually done by inverting the static relation between discharge and gate opening. An improved method can be based on the characteristics theory to estimate the water levels deviations. However, both methods underestimate the gate opening deviations required to deliver a desired discharge deviation, because water levels vary continuously along time when the gate is operated. The paper proposes a method to take account of this dynamic behavior of the pool-gate interaction by using a simple linear model for the pools dynamics, the IDZ model. The proposed method enables to better estimate the gate opening necessary to get a desired average discharge. The method is evaluated in simulation and on a gate of the Gignac Canal, located in the South of France. A dimensionless analysis of the problem is finally performed to evaluate the methods’ applicability. Introduction In the design of controllers for irrigation canals, it is well-known that using the discharge as the control variable enables to partially decouple the pools (Malaterre, 1995; Schuurmans, 1997; Malaterre et al., 1998; Malaterre and Baume, 1999). With such a choice as control variable, one needs to use a master-slave structure, where the master controller computes a discharge that is delivered by a local slave controller operating the gate. The functioning of this local slave controller is rarely mentioned in scientific publications, because it appears at first sight as a simple problem. Indeed, if the water levels upstream and downstream of the gate are measured, it seems sufficient to invert the gate discharge equation in order to compute the required gate opening to let a desired discharge flow through the gate. However, this is only Researcher, Unité Mixte de Recherche, Gestion de l’Eau, Acteurs, Usages, Cemagref, B.P. 5095, 34196 Montpellier Cedex 5, France. e-mail: xavier.litrico@cemagref.fr Researcher, Unité Mixte de Recherche, Gestion de l’Eau, Acteurs, Usages, Cemagref, B.P. 5095, 34196 Montpellier Cedex 5, France. e-mail: pierre-olivier.malaterre@cemagref.fr Hydraulic Engineer, Unité Mixte de Recherche, Gestion de l’Eau, Acteurs, Usages, Cemagref, B.P. 5095, 34196 Montpellier Cedex 5, France. e-mail: jean-pierre.baume@cemagref.fr Assistant Engineer, Unité Mixte de Recherche, Gestion de l’Eau, Acteurs, Usages, Cemagref, B.P. 5095, 34196 Montpellier Cedex 5, France. e-mail: jose.ribot-bruno@cemagref.fr 1 Journal of Irrigation and Drainage Engineering, 2008, 134(3):305-314 author-produced version of the final draft post-refeering the original publication is available at http://scitation.aip.org doi: 10.1061/(ASCE)0733-9437(2008)134:3(305) true if it is possible to measure the water levels and to operate the gate continuously along time. For computer controlled system, i.e. in the vast majority of cases, this is not possible, because the controller only operates at given sampling time steps. It may be objected that the local slave controller used to manipulate the gate is usually designed to operate at a smaller time step than the master controller which controls the discharge. However, even if this is the case, the gates motors have mechanical constraints which limit the possible number of operations per hour. As an example, some large gates may not be operated more than a few times an hour, which directly limits the operation of a local slave controller. A limited number of operations of the slave local controller is also advisable to limit the power consumption of the control system. Therefore, the ‘natural’ solution to the discharge-gate opening conversion (i.e. invert the gate equation continuously along time or with a very small time step, say a few seconds) is usually not applicable in this case. The slave controller is a priori not able to provide the required discharge as specified by the master controller. Indeed, when the gate is operated, the water levels immediately upstream and downstream of the gate change instantaneously, and therefore modify the discharge, which is then no longer equal to the desired one. Then a static inversion may not be an efficient method. To our knowledge, despite its poor performance as demonstrated in this paper, the static method is the only one used for the moment in the field for controllers with a master-slave structure. To overcome this limitation, De Leon Mojarro (1986) proposed to use the characteristics approximation to predict the water levels variations due to a discharge change at a gate. This solution improves the static inversion method by taking into account the initial deviations in water levels due to the gate operation as calculated using the characteristics theory. But the model remains quasi-static, because the water levels and the discharge are supposed to stay constant after the gate movement, which is not true. Because it is not possible to ensure a constant discharge through the gate during the whole sampling period Ts, we suggest to calculate the gate opening deviation so as to ensure that the average discharge flowing through the gate during Ts corresponds to the desired one. We propose in this paper a way to take account of the full dynamic behavior of a canal when a gate is operated. The proposed method uses a simplified linear dynamic model for each pool, the IDZ model presented by Litrico and Fromion (2004b), which enables to compute a closed-form linear approximation of the discharge flowing through the gate along time. This gives us a way to better approximate the gate opening necessary to get a desired average discharge during the sampling time period Ts. A nonlinear version of this dynamic method is also proposed to cover for the gate nonlinearities. The paper is structured as follows: • The dynamic behavior of gate-channel interaction is first examined, and three approximations are compared for estimating the discharge flowing through a gate after a step gate opening or closing: the static approximation, the one based on the characteristics, and the dynamic one, based on the IDZ model. Both a linear and a nonlinear version of each method are presented. • The problem of the conversion from discharge to gate opening is then considered, and the three methods are compared in simulation. • A field experiment is reported where the three methods are compared on a gate of the Gignac Canal, located in the South of France, near Montpellier.