Skip to main content

2017 | OriginalPaper | Buchkapitel

Accuracy Analysis for Fractional Order Transfer Function Models with Delay

verfasst von : Krzysztof Oprzędkiewicz, Wojciech Mitkowski

Erschienen in: Theory and Applications of Non-integer Order Systems

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In the paper a new accuracy estimation method for fractional order transfer functions with delay is presented. Oustaloup’s recursive approximation (ORA approximation) and Charef approximation allow us to describe fractional-order systems with the use of integer-order, proper transfer function, a delay is required to be modeled with the use of Pade approximant. Results are by simulations depicted.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Kaczorek, T.: Selected Problems in Fractional Systems Theory. Springer, New York (2011)CrossRefMATH Kaczorek, T.: Selected Problems in Fractional Systems Theory. Springer, New York (2011)CrossRefMATH
2.
Zurück zum Zitat Mitkowski, W., Obrączka, A.: Simple identification of fractional differential equation. Solid State Phenom. 180, 331–338 (2012)CrossRef Mitkowski, W., Obrączka, A.: Simple identification of fractional differential equation. Solid State Phenom. 180, 331–338 (2012)CrossRef
3.
Zurück zum Zitat Mitkowski, W., Skruch, P.: Fractional-order models of the supercapacitors in the form of RC ladder networks. Bull. Pol. Acad.: Tech. 61(3), 581–587 (2013) Mitkowski, W., Skruch, P.: Fractional-order models of the supercapacitors in the form of RC ladder networks. Bull. Pol. Acad.: Tech. 61(3), 581–587 (2013)
4.
Zurück zum Zitat Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)MATH Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)MATH
5.
Zurück zum Zitat Vinagre, B.M., Podlubny, I., Hernandez, A., Feliu, V.: Some approximations of fractional order operators used in control theory and applications. Fract. Calc. Appl. Anal. 3(3), 231–248 (2000)MathSciNetMATH Vinagre, B.M., Podlubny, I., Hernandez, A., Feliu, V.: Some approximations of fractional order operators used in control theory and applications. Fract. Calc. Appl. Anal. 3(3), 231–248 (2000)MathSciNetMATH
6.
Zurück zum Zitat Oprzędkiewicz, K.: A Strejc model-based, semi-fractional (SSF) transfer function model. Automatyka/Automatics; AGH UST 16(2), 145–154 (2012) Oprzędkiewicz, K.: A Strejc model-based, semi-fractional (SSF) transfer function model. Automatyka/Automatics; AGH UST 16(2), 145–154 (2012)
7.
Zurück zum Zitat Mitkowski, W.: Finite-dimensional approximations of distributed RC networks. Bull. Pol. Acad.: Tech. 62(2), 263–269 (2014) Mitkowski, W.: Finite-dimensional approximations of distributed RC networks. Bull. Pol. Acad.: Tech. 62(2), 263–269 (2014)
8.
Zurück zum Zitat Caponetto, R., Dongola, G., Fortuna, L., Petras, I.: Fractional Order Systems. Modeling and Control Applications. World Scientific Series on Nonlinear Science, Series A, vol. 72. World Scientific Publishing, Singapore (2010) Caponetto, R., Dongola, G., Fortuna, L., Petras, I.: Fractional Order Systems. Modeling and Control Applications. World Scientific Series on Nonlinear Science, Series A, vol. 72. World Scientific Publishing, Singapore (2010)
9.
Zurück zum Zitat Charef, A., Sun, H.H., Tsao, Y.Y., Onaral, B.: Fractal system as represented by singularity function. IEEE Trans. Autom. Control 37(9), 1465–1470 (1992)MathSciNetCrossRefMATH Charef, A., Sun, H.H., Tsao, Y.Y., Onaral, B.: Fractal system as represented by singularity function. IEEE Trans. Autom. Control 37(9), 1465–1470 (1992)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Oprzędkiewicz, K.: Approximation method for a fractional order transfer function with zero and pole. Arch. Control Sci. 24(4), 409–425 (2014)MathSciNet Oprzędkiewicz, K.: Approximation method for a fractional order transfer function with zero and pole. Arch. Control Sci. 24(4), 409–425 (2014)MathSciNet
11.
Zurück zum Zitat Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuits Syst. I. Fundam. Theory 47(1), 25–39 (2000)CrossRef Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuits Syst. I. Fundam. Theory 47(1), 25–39 (2000)CrossRef
12.
Zurück zum Zitat Mitkowski, W., Oprzędkiewicz, K.: An estimation of accuracy of Charef approximation. In: Domek, S., Dworak, P. (eds.) Theoretical Developments and Applications of Non-Integer Order Systems: 7th Conference on Non-Integer Order Calculus and Its Applications. Lecture Notes in Electrical Engineering, vol. 357, pp. 71–80. Springer, New York (2016) Mitkowski, W., Oprzędkiewicz, K.: An estimation of accuracy of Charef approximation. In: Domek, S., Dworak, P. (eds.) Theoretical Developments and Applications of Non-Integer Order Systems: 7th Conference on Non-Integer Order Calculus and Its Applications. Lecture Notes in Electrical Engineering, vol. 357, pp. 71–80. Springer, New York (2016)
13.
Zurück zum Zitat Oprzędkiewicz, K., Mitkowski, W., Gawin, E.: An estimation of accuracy of Oustaloup approximation. In: Szewczyk, R., et al. (eds.) Challenges in Automation, Robotics and Measurement Techniques. Advances in Intelligent Systems and Computing, vol. 440, pp. 299–307. Springer, New York (2016) Oprzędkiewicz, K., Mitkowski, W., Gawin, E.: An estimation of accuracy of Oustaloup approximation. In: Szewczyk, R., et al. (eds.) Challenges in Automation, Robotics and Measurement Techniques. Advances in Intelligent Systems and Computing, vol. 440, pp. 299–307. Springer, New York (2016)
14.
Zurück zum Zitat Vajta, M.: Some remarks on Pade-approximations. In: Proceedings of the 3rd TEMPUS-INTCOM Symposium (2000) Vajta, M.: Some remarks on Pade-approximations. In: Proceedings of the 3rd TEMPUS-INTCOM Symposium (2000)
15.
Zurück zum Zitat Isermann, R., Muenchhof, M.: Identification of Dynamic Systems. An Introduction with Applications. Springer, New York (2011)CrossRef Isermann, R., Muenchhof, M.: Identification of Dynamic Systems. An Introduction with Applications. Springer, New York (2011)CrossRef
Metadaten
Titel
Accuracy Analysis for Fractional Order Transfer Function Models with Delay
verfasst von
Krzysztof Oprzędkiewicz
Wojciech Mitkowski
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-45474-0_23

Neuer Inhalt