Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain...

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Main Authors:	Raquel S. Rodríguez, Gilberto Gonzalez Avalos, Noe Barrera Gallegos, Gerardo Ayala-Jaimes, Aaron Padilla Garcia
Format:	Article
Language:	English
Published:	MDPI AG 2021-05-01
Series:	Symmetry
Subjects:	bond graph nonlinear systems linearization DC motor
Online Access:	https://www.mdpi.com/2073-8994/13/5/854

id	doaj-788105373145436fb59d9e5f4b5851da
record_format	Article
spelling	doaj-788105373145436fb59d9e5f4b5851da2021-05-31T23:41:51ZengMDPI AGSymmetry2073-89942021-05-011385485410.3390/sym13050854Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic LinearizationRaquel S. Rodríguez0Gilberto Gonzalez Avalos1Noe Barrera Gallegos2Gerardo Ayala-Jaimes3Aaron Padilla Garcia4Graduate Studies Division of the Faculty of Mechanical Engineering, University of Michoacán, Morelia 58000, MexicoGraduate Studies Division of the Faculty of Mechanical Engineering, University of Michoacán, Morelia 58000, MexicoFaculty of Mechanical Engineering, University of Michoacán, Morelia 58000, MexicoFaculty of Sciences of Engineering and Technology, Autonomous University of Baja California, Tijuana 22260, MexicoFaculty of Electrical Engineering, University of Michoacán, Morelia 58000, MexicoAn alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.https://www.mdpi.com/2073-8994/13/5/854bond graphnonlinear systemslinearizationDC motor
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Raquel S. Rodríguez Gilberto Gonzalez Avalos Noe Barrera Gallegos Gerardo Ayala-Jaimes Aaron Padilla Garcia
spellingShingle	Raquel S. Rodríguez Gilberto Gonzalez Avalos Noe Barrera Gallegos Gerardo Ayala-Jaimes Aaron Padilla Garcia Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization Symmetry bond graph nonlinear systems linearization DC motor
author_facet	Raquel S. Rodríguez Gilberto Gonzalez Avalos Noe Barrera Gallegos Gerardo Ayala-Jaimes Aaron Padilla Garcia
author_sort	Raquel S. Rodríguez
title	Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization
title_short	Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization
title_full	Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization
title_fullStr	Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization
title_full_unstemmed	Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization
title_sort	approximation of linearized systems to a class of nonlinear systems based on dynamic linearization
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2021-05-01
description	An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.
topic	bond graph nonlinear systems linearization DC motor
url	https://www.mdpi.com/2073-8994/13/5/854
work_keys_str_mv	AT raquelsrodriguez approximationoflinearizedsystemstoaclassofnonlinearsystemsbasedondynamiclinearization AT gilbertogonzalezavalos approximationoflinearizedsystemstoaclassofnonlinearsystemsbasedondynamiclinearization AT noebarreragallegos approximationoflinearizedsystemstoaclassofnonlinearsystemsbasedondynamiclinearization AT gerardoayalajaimes approximationoflinearizedsystemstoaclassofnonlinearsystemsbasedondynamiclinearization AT aaronpadillagarcia approximationoflinearizedsystemstoaclassofnonlinearsystemsbasedondynamiclinearization
_version_	1721416836009951232

Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

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