Wider application of multipass systems theory. Part 2: Controlled distributed processes

Multipass-systems theory is applied to the stability analysis of distributed processes subject to nonlocal feedback control and involving counterflow phenomena resulting from mixed boundary conditions. This is achieved by discretising the process in space and time to produce a model (such as might be used for elementary numerical solution) involving a sequence of bidirectional spatial sweeps of the process and from which is derived a multiple delay representation to which frequency-response analysis is applied. It is shown that criteria for not only system stability, but also for achieving noninteracting control, can be readily derived by inspection of the delay network, the exercise being particularly straightforward if attention is restricted to process outputs occurring at the locations of the feedback controller sensors. The examples of a binary distillation column and a liquid/liquid heat exchanger are used to illustrate the method, the latter demonstrating also how the multipass approach can determine the numerical stability of a discrete approximation to a continuous system.