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Bond graph based frequency domain sensitivity analysis of multidisciplinary systems

  • Multidisciplinary systems are described most suitably by bond graphs. In order to determine unnormalized frequency domain sensitivities in symbolic form, this paper proposes to construct in a systematic manner a bond graph from another bond graph, which is called the associated incremental bond graph in this paper. Contrary to other approaches reported in the literature the variables at the bonds of the incremental bond graph are not sensitivities but variations (incremental changes) in the power variables from their nominal values due to parameter changes. Thus their product is power. For linear elements their corresponding model in the incremental bond graph also has a linear characteristic. By deriving the system equations in symbolic state space form from the incremental bond graph in the same way as they are derived from the initial bond graph, the sensitivity matrix of the system can be set up in symbolic form. Its entries are transfer functions depending on the nominal parameter values and on the nominal states and the inputs of the original model. The sensitivities can be determined automatically by the bond graph preprocessor CAMP-G and the widely used program MATLAB together with the Symbolic Toolbox for symbolic mathematical calculation. No particular program is needed for the approach proposed. The initial bond graph model may be non-linear and may contain controlled sources and multiport elements. In that case the sensitivity model is linear time variant and must be solved in the time domain. The rationale and the generality of the proposed approach are presented. For illustration purposes a mechatronic example system, a load positioned by a constant-excitation d.c. motor, is presented and sensitivities are determined in symbolic form by means of CAMP-G/MATLAB.

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Document Type:Article
Author:W. Borutzky, J. Granda
Parent Title (English):Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering
First Page:85
Last Page:99
Publishing Institution:Hochschule Bonn-Rhein-Sieg
Date of first publication:2002/02/01
Embargo Date:2003/02/01
Copyright:© IMechE 2002. This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Keyword:First-order frequency domain sensitivities; Incremental bond graph; Sensitivity matrix in symbolic form
Departments, institutes and facilities:Fachbereich Informatik
Dewey Decimal Classification (DDC):0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Open access funding:Deutsche Forschungsgemeinschaft / Allianz- und Nationallizenzen: Diese Beiträge sind mit Zustimmung der Rechteinhaber aufgrund einer DFG-geförderten National- bzw. Allianzlizenz frei zugänglich.
Entry in this database:2015/04/02
Licence (Multiple languages):License LogoIn Copyright (Urheberrechtsschutz)