Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients

Abstract

The article considers the methods of calculating the transition matrix of a dynamic system, which is based on the transient matrix representation by the matrix exponent and on the use of the system signal graph. The advantages of the transition matrix calculating using a signal graph are shown. The application of these methods to find the transition matrix demonstrated on the simple electromechanical system example. It is shown that the expression for the transition matrix as a matrix exponent completely corresponds to the expression found by means of the inverse matrix and based on the use of the signal graph. The transient matrix of a dynamical system thus found as a matrix exponent can be used to analyze processes in a system that is described by differential equations with integer derivatives. The formation of a transient matrix for the analysis of system processes, which is described by equations with fractional derivatives, is also considered. It is shown that the description of processes in systems with fractional derivatives based on the transient matrix and the representation of the fractional derivative in the form of Caputo-Fabrizio makes it possible to study coordinate transients without approximations in the description of the fractional derivative.

Keywords

• control theory
• electromechanical system
• fractional derivative
• linear system
• state representation
• transient matrix