Article | Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015 | Fractional-Order Modelling in Modelica
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Title:
Fractional-Order Modelling in Modelica
Author:
Alexander Pollok: Institute of System Dynamics and Control, German Aerospace Center (DLR), Germany Dirk Zimmer: Institute of System Dynamics and Control, German Aerospace Center (DLR), Germany Francesco Casella: Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Italy
DOI:
10.3384/ecp15118109
Download:
Full text (pdf)
Year:
2015
Conference:
Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015
Issue:
118
Article no.:
011
Pages:
109-115
No. of pages:
7
Publication type:
Abstract and Fulltext
Published:
2015-09-18
ISBN:
978-91-7685-955-1
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press, Linköpings universitet


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Most dynamic systems with a basis in nature can be described using Differential-Algebraic Equations (DAE), and hence be modelled using the modelling language Modelica. However, the concept of DAEs can still be generalised, when differential operators of non-integer order are considered. These so called fractional order systems have counterparts in naturally occuring systems, for instance in electrochemistry and viscoelasticity. This paper presents an implementation of approximate fractional-order differential operators in Modelica, increasing the scope of systems that can be described in a meaningful way. Properties of fractional-order systems are discussed and some approximation methods are presented. An implementation in Modelica is proposed for the first time. Several testing procedures and their results are displayed. The work is then illustrated by the application of the model to several physically motivated examples. A possible usability-enhancement using the concept of "Calling Blocks as functions" is suggested.

Keywords: Fractional Order Systems; fractional calculus; Integer-Order Approximations

Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015

Author:
Alexander Pollok, Dirk Zimmer, Francesco Casella
Title:
Fractional-Order Modelling in Modelica
DOI:
http://dx.doi.org/10.3384/ecp15118109
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Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015

Author:
Alexander Pollok, Dirk Zimmer, Francesco Casella
Title:
Fractional-Order Modelling in Modelica
DOI:
http://dx.doi.org/10.3384/ecp15118109
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