Control of a string of identical pools using non-identical feedback controllers

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 exist propagation of water level errors and amplification of flows over gates in the upstream direction. This paper analyses these coupling properties for a string of identical pools, both with identical feedback controllers and with non-identical feedback controllers. The definition of string stability in terms of bounded water level errors and bounded flows is given. It is shown that for a string of infinite number of pools, string stability cannot be achieved by decentralised distant-downstream feedback control. However, for a string of finite number of pools, a better global performance can be achieved by non-identical feedback controllers such that the closed-loop bandwidths of the subsystems increase from downstream to upstream.