Information support to solve direct dynamic problem for the previously disturbed electromechanical systems

Abstract

The article is devoted to the creation of methodological foundations for solving a direct problem of dynamics for linear dynamic systems, the motion of which is described by ordinary differential equations with nonzero initial conditions. Consideration of the motions of linear dynamic systems allows to simplify the mathematical apparatus used and to solve motion determination problems by using a known approach based on transfer functions. However, due to the fact that the classical definition of transfer functions does not involve taking into account non-zero initial conditions, which are caused by the presence of initial deviations of the coordinates of the control object from their desired values, in our work we use the Laplace-Carson transformation to find the corresponding images and write the equations of motion in operator form. This approach, in contrast to the generally accepted one, led to the introduction of information about the initial conditions of motion in the right-hand side of the corresponding operator differential equations and necessitated the generalization of the vector of control signals by including in it components that take into account the initial conditions of motion of the system under consideration. Such transformations made it possible to generalize the concept of a matrix transfer function as a matrix linear dynamic operator, which consists of two components that define disturbed free and controlled forced movements. The use of such an operator makes it possible to study the dynamics of the considered linear system both separately for each of the components of the generalized vector of controlling influences, and in the complex, thus solving the direct problem of the dynamics of linear systems.

As an example, we show the use of the proposed approach for motion analysis of a DC motor with nonlinear fan friction based on its piecewise linearized model.