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Fractional-Order Modelling in Modelica

Pollok, Alexander and Zimmer, Dirk and Casella, Francesco (2015) Fractional-Order Modelling in Modelica. 11th International Modelica Conference 2015, 21. bis 23. September 2015, Versailles, Frankreich.

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Abstract

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.

Item URL in elib:https://elib.dlr.de/99401/
Document Type:Conference or Workshop Item (Speech)
Title:Fractional-Order Modelling in Modelica
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Pollok, Alexanderalexander.pollok (at) dlr.deUNSPECIFIED
Zimmer, DirkDirk.Zimmer (at) DLR.deUNSPECIFIED
Casella, FrancescoPolitecnico di MilanoUNSPECIFIED
Date:21 September 2015
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:Fractional Order Systems, fractional calculus, Integer-Order Approximations
Event Title:11th International Modelica Conference 2015
Event Location:Versailles, Frankreich
Event Type:international Conference
Event Dates:21. bis 23. September 2015
Organizer:Modelica Association
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Systems and Cabin
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of System Dynamics and Control > Aircraft System Dynamics
Deposited By: Pollok, Dipl.-Ing. Alexander
Deposited On:23 Nov 2015 16:25
Last Modified:31 Jul 2019 19:56

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