Conference article

Recording of Model Frequency Responses and Describing Functions in Modelica

Tilman Bünte
German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Germany

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Published in: Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany

Linköping Electronic Conference Proceedings 63:76, p. 686-696

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Published: 2011-06-30

ISBN: 978-91-7393-096-3

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


An assistant Modelica package is introduced which supports the determination of model frequency responses or describing functions of Modelica models; as the case may be. The result is frequency response data which can be used for further analysis such as stability properties of the system in closed loop control or the derivation of linear time invariant (LTI) model approximations. The paper addresses inter alia proper scheduling of excitation frequency and amplitude; a brief theory of describing functions (harmonic linearization); the Modelica classes implemented in the package; and some application examples.


Frequency response; describing function; system identification


[1] Baur; M.; Otter; M.; Thiele; B.: Modelica Libraries for Linear Control Systems. Proc. 7th Modelica Conference; Como; Italy; 2009.

[2] Abel; A.; Nähring; T.: Frequency-Domain Analysis Methods for Modelica Models. Proc. 6th Int. Modelica Conference; Bielefeld; Germany; 2008

[3] Heckmann; A. et. al: The DLR FlexibleBodies library to model large motions of beams and of flexible bodies exported from finite element programs. Proc. 5th Int. Modelica Conference; Vienna; Austria; 2006.

[4] Edrén; J. et. al.: Modelica and Dymola for education in vehicle dynamics at KTH. Proc. 7th Int. Modelica Conference; Como; Italy; 2009.

[5] Ackermann; J.; Bünte; T.: Robust prevention of limit cycles for robustly decoupled car steering dynamics. Kybernetika; 35(1):105-116; 1999.

[6] Ackermann; J. et. al.: Robust Control: The Parameter Space Approach. Springer; Lon-don; 2002.

[7] EUROSYSLIB Project Profile;; 2007.

[8] FAIR Project profile; 2009.

[9] Gelb; A.; Vander Velde W.: Multiple-Input Describing Functions and Nonlinear System Design. New York: MacGraw-Hill; 1968.

[10] Siljak; D.: Nonlinear systems: the parameter analysis and design. New York: Wiley; 1969

[11] Duda; H.: Fliegbarkeitskriterien bei begrenzter Stellgeschwindigkeit. Ph.D. thesis; Technische Universität Braunschweig; April 1997. Forschungsbericht 97-15; Deutsche Forschungsanstalt für Luft- und Raumfahrt e.V.; Köln.

[12] Pintelon; R.; Schoukens; J.: System identification: a frequency domain approach. IEEE Press; New York; 2001.

[13] Mitschke; M.; Wallentowitz; H.: Dynamik der Kraftfahrzeuge. 4. Auflage; Springer-Verlag; 2004.

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