Physical systems are constructed from a variety of components, some of which have relatively concentrated, pointwise features while others have spatially distributed characteristics. In contrast, models rarely reflect this structure, thereby avoiding the mathematical difficulties arising from the manipulation of sets of mixed algebraic, ordinary and partial differential equations which may generate irrational functions on transformation. In this paper general results are produced, enabling the response to systems comprising a series of distributed-lumped elements to be calculated. A simple example is included to illustrate the procedures outlined.
In this paper system models arising from process-plant installations are derived in the form of an interconnected series of mixed, distributed and lumped-parameter realisations. The terminal characteristics of these models is shown to be a rational, multidimensional function of a finite set of transformed discrete time-delay variables which may be used in feedback-control studies. By employing a linear mapping of the support of the model it is established that stability can be assessed using a corresponding algebraic function to that of the denominator of the system model. Simple worked examples are used to illustrate the procedure.
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