مرکز منطقه ای اطلاع رساني علوم و فناوري - A new method of analysis of sampled-data systems

Abstract :

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.