DECOMPOSITION METHOD FOR MODELING AND ANALYSIS OF THE MULTIVARIABLE PULSE-FREQUENCY SYSTEM DYNAMICS

An analysis of the complexity factors, accompanying analytical methods of modelling and researching nonlinear impulse, relay and logic-dynamic systems indicates the following fundamental methodological reasons for the emergence of difficulties when using classical methods of analysis and synthesis of complex automatic control systems. The first main reason for the emergence of fundamental difficulties is the consideration of pulse elements, discrete devices and computers in systems, only as sources of signal discretization. That is when trying to use classical approaches to study structurally and parametrically complex control systems, the fundamental property of discreteness of system structures is not used. The second main reason for the difficulties is that the classical approaches consider the systems initial structures from the standpoint of a single whole. That is, the simplest single-variable linear impulse systems, and multivariable systems, and multi-rate systems, and nonlinear single-variable and multivariable impulse systems in the mathematical description, analysis and synthesis are considered from the standpoint of a single whole [1-14]. A similar situation is typical for pulse-frequency automatic control systems, which are the essentially nonlinear systems. The approach from the standpoint of a single whole was justified, so far we were talking about simple single-variable linear control systems.

This article researches the features of the decomposition method for modeling multivariable pulse-frequency systems. As a mathematical modeling apparatus, we use state variables graphs, which are one types of dynamic graphs and take into account the physical features of pulse-frequency systems most fully.  An algorithm for constructing graph models and analyzing the dynamics of multivariable pulse-frequency systems is proposed. The article provides an example of the algorithm application.