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A new method of analysis of sampled-data systems

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1 Author(s)
Papoulis, A. ; Polytechnic Institute of Brooklyn, Brooklyn, NY, USA

In many sampled-data systems the sampling interval T is "small" and the response r_{s}(t) closely approximates the response r(t) of the continuous system; one is then interested in evaluating the difference r_{s}(t) - r(t) for various values of T . In this paper this difference will be given as a power series in T whose coefficients can easily be determined in terms of the continuous response; if one wants to estimate the size of T for r_{s}(t) to equal r(t) within a specified error, the first term of this expansion will give an adequate measure of the error and hence of the maximum permissible T . Furthermore, since the resulting series converges rapidly, the expansion provides a simple method of evaluating r_{s}(t) for a given T . The method is applied to a feedback system with a sampler; the singularities of the p-rational system function that gives the actual response at the sampling points, are obtained by a displacement of the singularities of the continuous system function.

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Automatic Control, IRE Transactions on  (Volume:4 ,  Issue: 2 )