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From Continuous to Discrete Models of Linear Repetitive Processes

Gramacki A., Gramacki J., Gałkowski K., Rogers E., Owens D. H.

Archives of Control Sciences

2002

Vol. 12, no. 1/2

151-185

Differential linear repetitive processes are a distinct class of 2D linear systems which pose problems which cannot (except in a few very restrictive special cases) be solved by application for computer aided annalysis and simulation. One such problem area is the construction of accurate numerically well conditioned discrete approximations of the dynamics of differential processes which could, as one example of number of immediate applications areas, from the basis for digital implementation of control laws. In this paper, we undertake a detailed investigation of the critical problems which arise when attempting to construct usefull discrete approximations of the dynamics of differential linear repetitive processes and develop solutions to them. Numerical examples to support the results obtained are also given using a specially developed MATLAB based toolbox.

On a New Method of Discretization of Differential Linear Repetitive Processes

Gramacki A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2000

Vol. 48, nr 4

539-560

A new method of discretization of linear repetitive processes is proposed. In comparison to the classical methods, it posses several important advantages. First, the assumption on input and pass profile vectors to be approximated by stepwise functions is not further needed. As result, this allows using greater sampling periods for achieving the accuracy level required, which is very important especially for repetitive processes analysis. The classical methods adopted to the repetitive processes may meet serious problems with obtaining correct discretization in the case when a linear differential repetitive process is very close to its stability margin. As it is shown the proposed method, comparing to classical ones, gives better results in such situations. In the paper, the theoretical investigations are illustrated by a rich computer simulation material.