Y. Li and B. De Schutter, "Control of a string of identical pools using non-identical feedback controllers," IEEE Transactions on Control Systems Technology, vol. 20, no. 6, pp. 1638-1646, Nov. 2012.
In the distant-downstream control 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 paper analyzes these coupling properties for a string of identical pools, both 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 is shown that for a string of an infinite number of pools, string stability cannot be achieved by decentralized distant-downstream feedback control mainly due to the internal 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 distant-downstream control structure such that the closed-loop bandwidths of the subsystems increase from downstream to upstream, a much better global performance can be achieved than in the case of using identical feedback controllers.