Mathematical Model with Feedback Loop in Company Control

Abstract

This article is devoted to the further development of feedback loop models. They are used in the management of a single-industry firm. The development of the studying consists in the mathematical modeling of transients and assessing their impact on economic indicators. To solve this problem, the following was done in the article. A structural model of the functioning of a single-industry firm (SIF) is presented. It is built in accordance with the theory of automatic control (TAC) and includes elements: a management unit, a production unit, a sales unit, information nodes, as well as a feedback loop (FL). Equations and relationships describing the logic of the functioning of the company as a production system are presented. They allowed us to derive dynamic relationships and differential equations that reflect feedback loops on revenue and production costs. The system of expressions in operator form is presented, which describes the contour of the FL SIF. It has the form of a system of differential equations. It forms the basis of the mathematical model of SIF in the control system. This model made it possible to obtain a graphical interpretation of transients with closed and open FL based on the use of the Mathcad editor. Transients are fluctuations in sales volumes and production costs in the presence of disturbing influences. This is the scientific result and determines the novelty of the article.