Fractional Vector-Order h-Realisation of the Impulse Response Function

Ewa Pawłuszewicz

doi:10.2478/ama-2020-0016

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Fractional Vector-Order h-Realisation of the Impulse Response Function

Acta Mechanica et Automatica

Volume 14 (2020): Issue 2 (June 2020)

By: Ewa Pawłuszewicz

Open Access

|Jul 2020

Abstract

The problem of realisation of linear control systems with the h–difference of Caputo-, Riemann–Liouville- and Grünwald–Letnikov-type fractional vector-order operators is studied. The problem of existing minimal realisation is discussed.

References

1. Ambroziak L., Lewon D., Pawluszewicz E. (2016), The use of fractional order operators in modeling of RC-electrical systems, Control & Cybernetics, 45(3), 275-288
Search in Google Scholar Back to article
2. Bartosiewicz Z., Pawluszewicz E. (2006), Realizations of linear control systems on time scales, Control and Cybernetics, 35(4), 769-786.
Search in Google Scholar Back to article
3. Bastos, N.R.O., Ferreira, R.A.C., Torres, D.F.M. (2011), Necessary optimality conditions for fractional difference problems of the calculus of variations, Discrete and Continuous Dynamical Systems, Vol.29(2), 417-437.
Search in Google Scholar Back to article
4. Bettayeb M., Djennoune S., Guermah S., Ghanes M. (2008), Structural properties of linear discrete-time fractional order systems, Proc. of the 17th World Congres The Federation of Automatic Control, Seoul, Korea, 15262—15266.
Search in Google Scholar Back to article
5. Das S. (2008), Functonal Fractional Calculus for System Identyfication and Controls, Springer.
Search in Google Scholar Back to article
6. Ferreira, R.A.C., Torres, D.F.M. (2011) Fractional h–difference equations arising from the calculus of variations, Applicable Analysis and Discrete Mathematics, 5(1), 110-121.10.2298/AADM110131002F
Search in Google Scholar Back to article
7. Gantmacher F.R. (1959), The Theory of Matrices, Chelsea Pub. Comp., London.
Search in Google Scholar Back to article
8. Kaczorek T. (1998), Vectors and Matrices in Automation and Electrotechnics, WNT Warsaw 1998 (in Polish).
Search in Google Scholar Back to article
9. Kaczorek T. (2017), Cayley-Hamilton theorem for fractional linear systems, Theory and Applications of Non-integer Order Systems, LNEE 407, 45-55, Springer.10.1007/978-3-319-45474-0_5
Search in Google Scholar Back to article
10. Koszewnik A., Nartowicz t., Pawluszewicz E. (2016), Fractional order controller to control pump in FESTO MPS® PA Compact Workstation, Proc. of the Int.Carpathian Control Conference, 364-367.
Search in Google Scholar Back to article
11. Mozyrska D., Girejko E. (2013), Overview of the fractional h–differences operator, in: Almeida A., Castro L., Speck FO. (eds) Advances in Harmonic Analysis and Operator Theory, Operator Theory: Advances and Applications, 229, Birkhäuser, Basel.10.1007/978-3-0348-0516-2_14
Search in Google Scholar Back to article
12. Mozyrska D., Girejko E., Wyrwas M. (2013), Comparision of h –difference fractional operatots, Theory and Appication of Non-integer Order systems, LNEE 257, 191-197, Springer.10.1007/978-3-319-00933-9_17
Search in Google Scholar Back to article
13. Mozyrska D., Wyrwas M., Pawluszewicz E. (2017), Local observability and controllability of nonlinear discrete-time fractional order systems based on their linearisation, International Journal of Systems Science, 48(4), 788-79410.1080/00207721.2016.1216197
Search in Google Scholar Back to article
14. Mozyrska, D., Wyrwas, M. (2015), The Z-Transform Method and Delta Type Fractional Difference Operators, Discrete Dynamics in Nature and Society, Article ID 852734, 12 pages10.1155/2015/852734
Search in Google Scholar Back to article
15. Oprzędkiewicz K., Gawin E. (2016), A non integer order, state space model for one dimensional heat transfer process, Archives of Control Sciences, 26(2), 261-27510.1515/acsc-2016-0015
Search in Google Scholar Back to article
16. Pawluszewicz E., Koszewnik A. (2019), Markov parameters of the input-output map for discrete-time fractional order systems, Proc. of the 24th Int.Conf. on Methods and Models in Automation and Robotics MMAR’2019, Miedzyzdroje, Poland10.1109/MMAR.2019.8864668
Search in Google Scholar Back to article
17. Podlubny I. (1999), Fractional differential systems, Academic Press, San Diego
Search in Google Scholar Back to article
18. Sierociuk D., Dzieliński A., Sarwas G., Petras I., Podlubny I., Skovranek T. (2013), Modelling heat transfer in heterogenous media using fractional calculus, Phylosophical Transaction of the Royal Society A-Mathematical, Physical and Engineering Sciences, Soc A 371: 20120146, 10 pages10.1098/rsta.2012.014623547224
Search in Google Scholar Back to article
19. Sontag E. (1998), Mathematical Control Theory, Springer – Verlag10.1007/978-1-4612-0577-7
Search in Google Scholar Back to article
20. Wu G.Ch., Baleanu D., Zeng S.D., Luo W.H. (2016), Mittag-Leffler function for discrete fractional modelling, Journal of King Saud University - Science, 28, 99—10210.1016/j.jksus.2015.06.004
Search in Google Scholar Back to article
21. Wu, D.Baleanu, Zeng S.D., Deng Z.G. (2015), Discrete fractional diffusion equation, Nonlinear Dynamics, 80, 281–28610.1007/s11071-014-1867-2
Search in Google Scholar Back to article
22. Zabczyk J. (2008), Mathematical Control Theory, Birkhaüser.10.1007/978-0-8176-4733-9
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/ama-2020-0016 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088

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Language: English

Page range: 108 - 113

Submitted on: Mar 12, 2020

Accepted on: Jul 3, 2020

Published on: Jul 24, 2020

Published by: Bialystok University of Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Realisation,

Linear system,

Fractional vector-order system,

h – Markov parameters

Related subjects:

Engineering,

Electrical engineering,

Electronics,

Mechanical engineering,

Mechanics,

Bioengineering and biomedical engineering,

Biomechanics,

Civil engineering,

Environmental engineering

© 2020 Ewa Pawłuszewicz, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 14 (2020): Issue 2 (June 2020)