# American Institute of Mathematical Sciences

June  2009, 4(2): 359-380. doi: 10.3934/nhm.2009.4.359

## Distributed model predictive control of irrigation canals

 1 Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628CD Delft, Netherlands, Netherlands 2 Department of Water Management, Delft University of Technology, Stevinweg 1, 2628CN Delft, Netherlands 3 Delft Center for Systems and Control & Department of Marine and Transport Technology, Delft University of Technology, Mekelweg 2, 2628CD Delft, Netherlands

Received  September 2008 Revised  December 2008 Published  June 2009

Irrigation canals are large-scale systems, consisting of many interacting components, and spanning vast geographical areas. For safe and efficient operation of these canals, maintaining the levels of the water flows close to pre-specified reference values is crucial, both under normal operating conditions as well as in extreme situations.
Irrigation canals are equipped with local controllers, to control the flow of water by adjusting the settings of control structures such as gates and pumps. Traditionally, the local controllers operate in a decentralized way in the sense that they use local information only, that they are not explicitly aware of the presence of other controllers or subsystems, and that no communication among them takes place. Hence, an obvious drawback of such a decentralized control scheme is that adequate performance at a system-wide level may be jeopardized, due to the unexpected and unanticipated interactions among the subsystems and the actions of the local controllers.
In this paper we survey the state-of-the-art literature on distributed control of water systems in general, and irrigation canals in particular. We focus on the model predictive control (MPC) strategy, which is a model-based control strategy in which prediction models are used in an optimization to determine optimal control inputs over a given horizon. We discuss how communication among local MPC controllers can be included to improve the performance of the overall system. We present a distributed control scheme in which each controller employs MPC to determine those actions that maintain water levels after disturbances close to pre-specified reference values. Using the presented scheme the local controllers cooperatively strive for obtaining the best system-wide performance. A simulation study on an irrigation canal with seven reaches illustrates the potential of the approach.
Citation: Rudy R. Negenborn, Peter-Jules van Overloop, Tamás Keviczky, Bart De Schutter. Distributed model predictive control of irrigation canals. Networks & Heterogeneous Media, 2009, 4 (2) : 359-380. doi: 10.3934/nhm.2009.4.359
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