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 artikel
http://dx.doi.org/10.3384/ecp15118109Ingår i: Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015
Linköping Electronic Conference Proceedings 118:11, s. 109-115
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.
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