Use of Differential Equations With Variable Coefficients to Describe the Motions of Nonlinear Electromechanical Systems

TL;DR

This paper discusses modeling nonlinear electromechanical systems using differential equations with variable coefficients to better capture their complex dynamics, addressing limitations of traditional linear models.

Contribution

It introduces a mathematical modeling approach employing differential equations with variable coefficients to describe nonlinear EMS motions more accurately.

Findings

Differential equations with variable coefficients effectively model nonlinear EMS dynamics.

Traditional linear models are insufficient for complex nonlinear system analysis.

The proposed approach enhances stability analysis and trajectory synthesis for EMS.

Abstract

Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such systems is completely determined by external influences acting on the EMS, their parameters, and initial operating conditions. The above-mentioned factors complicate the study of electromechanical systems and, in the general case, make it impossible to use classical methods of analyzing the dynamics of the EMS since the latter neglect the features of nonlinear systems and describe their dynamics using ordinary linear differential equations with constant coefficients. At the same time, many methods and approaches have been developed in control theory for analyzing stability and synthesizing motion trajectories based on linear differential equations. Therefore, an important task arises to create mathematical models of nonlinear EMS that consider the peculiarities of their motion but have a form similar to linear models.