Application of local coordinates rectification in linearization of selected parameters of dynamic nonlinear systems. Issue 5 (19th August 2014)

• Record Type: Journal Article
• Authors: Zawadzki, Andrzej; Sykulski, Jan
• Is Part Of: Compel. Volume 33:Issue 5(2014)
• Publication Date: 2014-08-19
• Subjects: Electrical engineering -- Data Processing -- Periodicals; Electrical engineering -- Mathematics -- Periodicals; Electrical engineering -- Periodicals; Electronics -- Data Processing -- Periodicals; Electronics -- Mathematics -- Periodicals; 621.3
• DOI: 10.1108/COMPEL-11-2013-0358
• Languages: English
• ISSNs: 0332-1649

Abstract

<abstract> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <sec sec-type="purpose"> <title>Purpose</title> <p>This paper aims to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form.</p> </sec> <sec sec-type="design|methodology|approach"> <title>Design/methodology/approach</title> <p>It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system.</p> </sec> <sec sec-type="findings"> <title>Findings</title> <p>The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input - the state of the nonlinear system).</p> </sec> <sec sec-type="originality|value"> <title>Originality/value</title> <p>Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.</p> </sec> </abstract>