The Simulation of Variable Delay

Abstract

A dual classification of variable delays 1) by their explicit dependence on time or through a state variable and 2) through their origins as ``pipe'' or ``nonpipe'' problems is presented. Techniques of simulation through standard analog components and, more particularly, transport devices are analyzed and further classification made of the latter to distinguish those suitable for state-variable delay systems from those that are not. The construction and testing of a simple variable delay are described. An application to a system in which the delay is a sinusoidal function of time is discussed in detail. A theory is presented that predicts what frequencies will be present in the output of such a device when excited by a sinusoid of commensurate frequency; experimental results corroborating this are presented. A scheme for converting a problem with variable delay to one with fixed delay is further analyzed and its range of application delimited. Conclusions include a discussion of the best type of simulator to be used for variable delay problems.