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1 2001

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Manufacturing algebra and dynamics

Albrecht R.F., Canuto E.

Systems Science

2001

Vol. 27, nr 1

25-37

For system modeling we use two levels of abstraction: the logical structure (F, E(C), C) and algorithms on it in logical time, and the physical model structure (PROD, TRANS(ROUTE), ROUTE) for a model time T, being a subset of the set of intervals on R, the set of real numbers. PROD is a family of input-output objects modeling production modules, plants, processors of certain types. To PROD corresponds the family F of functions f, describing the functional behaviour of the PR < PROD. ROUTE is a set of transportation routes RT, connecting an output port of a PR with an input port of another PR. To RT corresponds an element c < C, C is the set of "connectors". TR transports a quantity z of items from the output port to the input port on route RT. This corresponds to a relation E(c) < E(C), c › z[c] in the logical structure. The set D of physical data on which the PR and TR operate is partitioned into a finite number of subsets, the "sorts", types, classes D(s). For our application, only the quantity q of elements of subsets U < D(s) is of interest, thus we consider q = card U, q < N0, the set of natural numbers with 0 included. The input- and output ports of a PR are physical storage objects ST < STORE, the set of storages under consideration. We assume, ST is dedicated to a sort s. A production module PR is located at a location l < L, input- and output storages of PR have locations (l, i) and (l, j). A storage content changes in the course of time. Thus, we have families of elements qslkt, k = i or j, t < T, to describe the states of all storages employed in a production process. The algebra of operations on such families is studied. In addition, variable structures and their control modules are considered.