Graph Modeling of the Processes of Impulsive Time-Delay Systems

Abstract

Impulsive systems are widely used in metallurgy, chemical, and oil and gas industries, heat power engineering, irrigation and other industries. Periodic nature of the discrete control devices operation is the reason for the appearance of pure delay in the control channels. Methods for studying linear impulsive time-delay systems in synchronous-in-phase modes of operation of discrete devices are developed with sufficient completeness. At the same time, the methods of modeling and research of multiple-time-scale, multivariable, nonlinear impulsive time-delay systems require their further development. In this paper we propose a method for modeling impulsive time-delay systems based on dynamic graphs. The result of simulation of pulse systems with delay based on dynamic graphs is completely the same as the results obtained by the modified Z-transformation. In the case of one-dimensional systems, calculations are much easier to perform on the basis of the proposed method of dynamic graphs. The application of the modified Z-transformation for analytical studies is particularly problematic in the case of multi-dimensional pulse systems with delay, as it is accompanied by difficulties of a fundamental nature due to the structural complexity and the problem of formalized mathematical description of the processes using the traditional approach.