The Problem of Aperture Delay in Digital Measurement Systems and its Analytic Solution by the Matrix Exponential Method

Abstract

A method of analytic solution of the problem of aperture delay in digital systems used for the measurement of the controlled state variables of linear deterministic systems is proposed. The mathematical apparatus for deriving an explicit form of the solution of linear differential equations, which is based on the matrix exponential operator and yields a low computer time, is used. It is shown that the proposed method may be effectively used to eliminate aperture delays if the measured parameters are dynamically related state variables of the controlled system. An algorithm and example of a solution that illustrates the efficiency of the proposed method are presented.