Research of mathematical model of transitional process in electric drive by methods of operational calculus
DOI:
https://doi.org/10.31548/energiya2020.02.098Abstract
Abstract. Most often, the model of a process takes the form of a differential equation, so the next problem concerns the methods of its solution. Unlike classical methods, the operational calculus approach allows to effectively calculate any processes of oscillations of mechanical systems, automatic control systems, complex electrical circuits in the presence of arbitrary supply voltage.
From the standpoint of operational calculus, it is advisable to analyze the transient process in the electric drive, using different approaches depending on the type of roots of the corresponding parametric equation. In the case under study, the transient process in the electric drive occurs at the moment of static resistance of the working machine, which does not depend on the angular velocity, but which changes linearly over time.
The purpose of the study is to analyze the transient process in the electric drive from the standpoint of operational calculus.
The results of the analysis of the parametric model of the transient process in the electric drive of the belt conveyor from the standpoint of operational calculus are presented. The zero initial conditions for the corresponding Cauchy problem are considered. Depending on the type of roots of the operator equation, certain properties of the Laplace transform are applied. In this case, the differentiation operation is transformed into an algebraic one (multiplication by a number), and the original differential equation is transformed into a whole rational equation of the second order.
Key words: mathematical model, transient process, motor moment, parameters, Cauchy problem, Laplace transform, operator equation
References
Samoilenko A. M., Kryvosheia S. A., Perestiuk N. A. (1984). Differentsial’nyye uravneniya. Primery i zadachi [Differential equations. Examples and tasks]. Kyiv: Higher school, 408.
Harashchenko F. H., Pichkur V. V. (2014). Prykladni zadachi teorii stiikosti [Applied problems of stability theory]. Kyiv: Kyiv University, 125.
Hryshchenko O. Yu., Liashko S. I. (2008). Teoriia funktsii kompleksnoi zminnoi [Theory of functions of a complex variable]. Kyiv: Kyiv University, 460.
Martynenko M. A., Yuryk I. I. (2008). Teoriia funktsii kompleksnoi zminnoi. Operatsiine chyslennia. Navchalnyi posibnyk [Theory of functions of a complex variable. Operating calculus. Tutorial]. Kyiv: Publishing house "Slovo", 296.
Savchenko V. V., Sіnyavsky O. Yu. (2015). Peredposadkova obrobka kartopli v mahnitnomu poli [Pre-planting treatment of potatoes in a magnetic field]. Kyiv: "Comprint", 160.
Downloads
Published
Issue
Section
License
Relationship between right holders and users shall be governed by the terms of the license Creative Commons Attribution – non-commercial – Distribution On Same Conditions 4.0 international (CC BY-NC-SA 4.0):https://creativecommons.org/licenses/by-nc-sa/4.0/deed.uk
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
