The dynamic behavior of cascade processes is examined. By a cascade process, we here refer to an interconnected system consisting of many similar subsystems placed after one another, in such a way that a subsystem is influenced only by its nabor subsystems. An example of such a process is a distillation column, which is essentially a cascade interconnection of its individual trays.
By using Laplace transform techniques, we first show how the poles of simple cascades may be determined from the knowledge of the subsystem transfer functions. Knowing these pole locations, it is then straightforward to obtain, for example, a time response of the cascade. We then proceed to show how positive feedback interconnections of such cascade sections may result in very long time constants. Such long time constants have been observed in high purity distillation columns; in fact, the magnitude of these time constants may increase exponentially with the number of stages in the column. Another way of understanding this, apart from the transfer function point of view, is by analogy to diffusion in plug flow. We present such an analogy and illustrate the behavior of a simple binary distillation column from this point of view.