Linear dynamic system identification in the frequency domain using fractional derivatives

• Autorzy: Janiczek T. , Janiczek J.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a study of the Fourier transform method for parameter identification of a linear dynamic system in the frequency domain using fractional differential equations. Fundamental definitions of fractional differential equations are briefly outlined. The Fourier transform method of identification and their algorithms are generalized so that they include fractional derivatives and integrals.

Słowa kluczowe

EN

fractional differential equations; fractional differential systems; Fourier transform method; identification methods

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2010
• Tom: Vol. 17, nr 2
• Strony: 279--287
• Opis fizyczny: Bibliogr. 12 poz., rys., wykr., wzory

Twórcy

autor

Janiczek T.

autor

Janiczek J.

• Wroclaw University of Technology, Department of Electronics, The Institute of Computer Engineering, Control and Robotics, Z. Janiszewskiego 11/17, 50-372 Wroclaw, Poland,

Bibliografia

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• [3] P. Eykhoff: System identification. Parameter and Sate Estimation. John Wiley and Sons Ltd., London, 1974.
• [4] T. Janiczek: “Analysis of PVDF transducer signals stimulated by mechanical tension”. Journal of Electrostatics, vol. 51–52, 2001, pp. 167-172.
• [5] T. Janiczek: Models of systems described by fractional differential equations and basic algorithms of their identification. Preprint of Ph.D., Wroclaw University of Technology, 2003.
• [6] E.C. Levy: “Complex curve fitting”. IRE Trans. Aut. Contr., no. 4, 1959, pp. 37-43.
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• [8] K.S. Miller, B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley&Sons Inc. 1993.
• [9] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego, 1999.
• [10] Y. Sawaragi, T. Soeda, T. Nakamizo: Classical Methods and time series estimation. Trends And Progress In System Identification. Ed. by Pieter Eykhoff, Pergamon Press, Oxford, 1981.
• [11] T. Janiczek, D. Nowak-Woźny, W. Mielcarek, K. Prociow. “Equivalent model of modified bismuth oxides described by fractional derivatives”. The Fourth China International Conference on High-Performance Ceramics, Oct., 2005.
• [12] D. Nowak-Woźny, T. Janiczek, W. Mielcarek, J.B. Gajewski: Fractional electrical model for modified bismuth oxide. Journal of Electrostatics, no. 67, 2009, pp. 18-21.