Abstract
”Fractional order lag” is a system that is popular in multiple applications. In this paper, authors consider a new method for approximation of this system based on its impulse response. Certain assumptions of the approximation method are verified and algorithm is presented. Also certain problems with this system analysis are discussed, especially its realisation in the form of non-integer order differential equations.
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Bania, P., Baranowski, J.: Laguerre polynomial approximation of fractional order linear systems. In: Mitkowski, W., Kacprzyk, J., Baranowski, J. (eds.) Theory & Appl. of Non-integer Order Syst. LNEE, vol. 257, pp. 171–182. Springer, Heidelberg (2013)
Baranowski, J.: Legendre polynomial approximations of time delay systems. In: Materiały XII Międzynarodowych Warsztatów Doktoranckich OWD, Wisła 23-26, pp. 15–20 (2010)
Djouambi, A., Charef, A., Besancon, A.V.: Approximation and synthesis of non integer order systems. In: 2nd IFAC Workshop on Fractional Differentiation and its Applications, FDA 2006, Portugal, Porto (July 2006)
Mitkowski, W.: Approximation of fractional diffusion-wave equation. Acta Mechanica et Automatica 5, 65–68 (2011)
Oldham, K., Spanier, J.: The fractional calculus. Academic Press, New York (1974)
Oustaloup, A.: La commande CRONE: commande robuste d’ordre non entier. Hermes (1991)
Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex noninteger differentiator: Characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47(1), 25–39 (2000)
Piątek, P., Zagórowska, M., Baranowski, J., Bauer, W., Dziwiński, T.: Discretisation of different non-integer order approximations. In: 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR (accepted 2014)
Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Mathematics in Science and Engineering. Elsevier Science (1998)
Podlubny, I., Chechkin, A., Skovranek, T., Chen, Y., Jara, B.M.V.: Matrix approach to discrete fractional calculus ii: Partial fractional differential equations. Journal of Computational Physics 228(8), 3137–3153 (2009)
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Zagórowska, M., Baranowski, J., Bania, P., Piątek, P., Bauer, W., Dziwiński, T. (2015). Impulse Response Approximation Method for “Fractional Order Lag”. In: Latawiec, K., Łukaniszyn, M., Stanisławski, R. (eds) Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering, vol 320. Springer, Cham. https://doi.org/10.1007/978-3-319-09900-2_11
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DOI: https://doi.org/10.1007/978-3-319-09900-2_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09899-9
Online ISBN: 978-3-319-09900-2
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