Fractional-Order Modelling in Modelica

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

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp15118109

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

Linköping Electronic Conference Proceedings 118:11, s. 109-115

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Publicerad: 2015-09-18

ISBN: 978-91-7685-955-1

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


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.


Fractional Order Systems; fractional calculus; Integer-Order Approximations


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