Practical Considerations in the Use of Distributed Parameter Systems in Modeling: A Control Point of View

This paper is a condensed version of recent work [17] wherein several fundamental practical concerns pertaining to the use of linear, time-invariant, distributed parameter systems as models of physical processes are investigated. In particular, it is argued here that certain common distributed parameter systems exhibit properties which make them unsuitable for use as plant models in the design of feedback compensation. Classes of distributed parameter systems exhibiting these properties are defined and are said to be ill-posed for use in feedback compensator design. The structure of these classes is investigated within an extremely general mathematical framework which imposes no a priori restrictions on the class of distributed parameter systems under consideration. Within this framework necessary and sufficient conditions are given which completely characterise the classes of ill-posed models and establish their equivalence. These conditions are concretely illustrated by way of applications to several well-known flexible structure models. Surprisingly, several of these models are determined to be ill-posed for use in feedback compensator design.