Fractional vector-order h-realisation of the impulse response function

• Autorzy: Pawłuszewicz Ewa

Identyfikatory

DOI

10.2478/ama-2020-0016

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

realisation; linear system; fractional vector-order system; Markov parameters

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2020
• Tom: Vol. 14, no. 2
• Strony: 108--113
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Pawłuszewicz Ewa

• Faculty of Mechanical Engineering, Department of Mechatronics Systems and Robotics, Bialystok University of Technology, Wiejska 45c, 15-351 Białystok, Poland

Bibliografia

• 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
• 2. Bartosiewicz Z., Pawluszewicz E. (2006), Realizations of linear control systems on time scales, Control and Cybernetics, 35(4), 769-786.
• 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.
• 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.
• 5. Das S. (2008), Functonal Fractional Calculus for System Identyfication and Controls, Springer.
• 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.
• 7. Gantmacher F.R. (1959), The Theory of Matrices, Chelsea Pub. Comp., London.
• 8. Kaczorek T. (1998), Vectors and Matrices in Automation and Electrotechnics, WNT Warsaw 1998 (in Polish).
• 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. 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.
• 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.
• 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.
• 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--794
• 14. Mozyrska, D., Wyrwas, M. (2015), The Z-Transform Method and Delta Type Fractional Difference Operators, Discrete Dynamics in Nature and Society,
• 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), 261-275
• 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, Poland
• 17. Podlubny I. (1999), Fractional differential systems, Academic Press, San Diego
• 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 pages
• 19. Sontag E. (1998), Mathematical Control Theory, Springer – Verlag
• 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—102
• 21. Wu, D.Baleanu, Zeng S.D., Deng Z.G. (2015), Discrete fractional diffusion equation, Nonlinear Dynamics, 80, 281–286
• 22. Zabczyk J. (2008), Mathematical Control Theory, Birkhaüser.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).