Modelling of Continuous-Time Dynamic Systems

Abstract

In this first chapter of the third part of this book, some fundamentals of conceptual model construction within the domain of continuous time dynamic systems (CTDS) are explored. This is carried out primarily in the context of several illustrative examples. These examples demonstrate, as well, the typical basis for the formulation of conceptual models in the CTDS domain, namely, the application of relevant relationships drawn from the physical laws governing the behaviour of the SUI. Nevertheless, it is true that conceptual models in the CTDS domain can also be formulated in the absence of established physical laws (i.e. deductively rather than inductively), and we provide an illustration of such a circumstance. The conceptual models that arise are often in the form of higher order ordinary differential equations that need to be reformulated in terms of an equivalent set of first-order equations in order to be compatible with requirements that are inherent in most differential equation solving tools. The transformation process is often straightforward, but there are simple cases where care must be taken in choosing the correct procedure. The potential difficulties in this regard are illustrated.