Control of a String of Identical Pools Using Non-Identical Feedback Controllers


Within the distant-downstream management of irrigation channels, the interactions between pools and the internal time-delay for water to travel from upstream to downstream, impose limitations on global performance, i.e., there exists propagation of water-level errors and amplification of flows over gates in the upstream direction. This transient analyzes these coupling properties for a string of identical pools, each with identical feedback controllers and with non-identical feedback controllers. A definition of string stability in terms of bounded water-level errors and bounded flows is given. It's shown that for a string of an infinite range of pools, string stability can't be achieved by decentralized distant-downstream feedback management mainly because of the inner time-delay for water to travel from upstream to downstream. Applying the analysis results on string stability to a string of a finite number of pools, i.e., using non-identical feedback controllers in a very distant-downstream control structure such that the closed-loop bandwidths of the subsystems increase from downstream to upstream, a much higher international performance can be achieved than within the case of using identical feedback controllers.

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