A population dynamics approach for the water distribution problem

The water distribution system (WDS) is composed of several elements, where flow control is one of the most important components needed in order to provide a satisfactory level of service. In order to achieve an adequate level of water in the distribution tanks, we need to dynamically control the flo...

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Bibliographic Details
Published in:International journal of control 2010-09, Vol.83 (9), p.1947-1964
Main Authors: Ramírez-Llanos, Eduardo, Quijano, Nicanor
Format: Article
Language:English
Subjects:
Applied sciences
Buildings. Public works
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Distribution. Storage
dynamic resource allocation
Exact sciences and technology
passivity
population dynamics
replicator dynamics
Studies
water distribution system
Water supply. Pipings. Water treatment
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Summary:The water distribution system (WDS) is composed of several elements, where flow control is one of the most important components needed in order to provide a satisfactory level of service. In order to achieve an adequate level of water in the distribution tanks, we need to dynamically control the flow. Here, we propose a population dynamics approach in order to control tanks, by allocating in them the maximum uniform volume. The feedback interconnected systems reach a stable equilibrium point for both approaches presented (i.e. replicator and supply dynamics), and more specific an asymptotically stable equilibrium point for the replicator dynamics case. The stability analysis uses some passivity concepts and classic Lyapunov theory for a closed-loop system that combines the population dynamics (controller), and the WDS (process). We show via simulations the operation under different scenarios.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2010.501389