Algorithm for Obtaining a Characteristic Polynom and Transfer Function of Dynamic Model of Drone “Swarm”

Abstract

In this paper receiving a characteristic polynom of dynamic model of "swarm" of drones is considered. The developed analysis algorithm of topological models allows to receive a characteristic polynom and a transfer function of the system in an alphabetic and numerical form by an accession method on one top. The algorithm differs from the existing ones by the use of more optimum mechanism of construction of trees and great trees of parts of the graph that allowed to reduce expenses of time and memory. The formalized information on the column including a set of the varied parameters also serves as the initial information at creation of a characteristic polynom and transfer function of the system. Basic elements of this information are internal and external tops. We lead up the description of parts of the graph for the purpose of identification of the closed contours by means of specially developed set of trains of a part which elements are the zero top and tops of a set. The process of formation of a set of trains made by the developed rules is described. Algorithms of receiving a characteristic polynom of a part of the count and characteristic polynom of the system are presented. Receiving the transfer function of the system is based on application of the considered algorithm of creation of a characteristic polynom for the graph of systems into which the additional (structural) arches specifying couples of input and output knots of the system are entered. Representation of scales of edges also in the form of the parametrical function of an edge allows to expand possibilities of methods of the topological analysis at the automated design of dynamic systems with the parameters changing in time. The algorithm gives the chance to receive a characteristic polynom of the system as the obvious function of various parameters, and not just those which directly are coefficients of the differential equations of the system. It greatly expands a scope for the designer in the choice of parameters of variation. The received model considers variability of the composition, structure and level of interaction of the "swarm". At the change of the "swarm" there is no need to recalculate all the graph but only its changed part.