Sampling errors in closed-loop hybrid computer programs

Abstract

This paper applies a previously derived equation for sampling error in hybrid systems to the case of hybrid computer systems which use first-order analog hold de vices. Explicit expressions for sampling error are ob tained for a general hybrid computer program and for several classes of programs corresponding to particular cases. The equations apply for most types of hybrid com puter operation including the case for which the digital computer is used to integrate one or more of the prob lem equations.

The error equations are used to examine the effect of various allocations of computing operations, both in general terms and through use of a particular example. The results, while providing no new insight into gross effects, give quantitative relations which sharpen intui tive guidelines for programming a hybrid computer.

The equations place in evidence the following facts which are not apparent from a qualitative study: (1) The major components of sampling error depend on the first power of the sampling period, making the hybrid computer a first-order numerical method. (2) Digital execution time has an effect on error which is similar to that of the sampling period, but is weighted twice as heavily. (3) A numerical integration method in the digi tal computer produces negligible error in relation to other error sources if it is of order 2 or higher.