PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

On Grünwlad-Letinkov fractional operator with measurable order on continuous-discrete time scale

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Considering experimental implementation control laws on digital tools that measurement cards are discharged every time unit one can see that time of simulations is partially continuous and partially discrete. This observation provides the motivation for defining the Grünvald-Letnikov fractional operator with measurable order defined on continuous-discrete time scale. Some properties of this operator are discussed. The simulation analysis of the proposed approach to the Grünwald-Letnikov operator with the measurement functional order is presented.
Rocznik
Strony
161--165
Opis fizyczny
Bibliogr. 30 poz., rys., wykr.
Twórcy
  • Faculty of Mechanical Engineering, Department of Mechatronics Systems and Robotics, Bialystok University of Technology, Wiejska 45c, 15-351 Białystok, Poland
  • Faculty of Mechanical Engineering, Department of Mechatronics Systems and Robotics, Bialystok University of Technology, Wiejska 45c, 15-351 Białystok, Poland
  • Faculty of Mechanical Engineering, Department of Mechatronics Systems and Robotics, Bialystok University of Technology, Wiejska 45c, 15-351 Białystok, Poland
Bibliografia
  • 1. Alagoz B.B., Tepljakov A., Ates A. (2019) Time-domain identifica-tion of one noninteger order plus time delay models from step re-sponse measurements, International Journal of Modeling, Simulation and Scientific Computing, Vol. 10, No. 1, 1941011-1–1941011-22.
  • 2. Alagz B.B., Alisoy H. (2018) Estimation of reduced order equivalent circuit model parametres of batteries from noisy current and voltage measurements, Balkan Journal of Electrical & Computer Engineer-ing, Vol. 6, No. 4, 224–231.
  • 3. Balaska H., Ladaci S., Djouambi A., Schulte H., Bourouba B. (2020) Fractional order tube model reference adaptive control for a class of fractional order linear systems International Journal of Ap-plied Mathematics and Computer Science,, Vol. 30, No. 3, 501–515
  • 4. Bohner M., Petrson A. (2002) Dynamic Equations on Time Scales: A survey, Journal of Computational and Applied Mathematics, Vol. 141, No. 1–2, 1–26.
  • 5. Buslowicz M. Nartowicz T. (2009) Design of fractional order control-ler for a class of plants with delay, Measurement Automation and Robotics, Vol. 2, 398–405.
  • 6. Coimbra C.,(2003), Mechanics with variable-order differential opera-tors, Annual Physics, Vol. 12, 692-703.
  • 7. Djennoune S., Bettayeb M., Al-Saggaf U.M. (2019) Synchroniza-tion of fractional order discrete-time chaotic systems by exact state reconstructor: application to secure communication, International Journal of Applied Mathematics and Computer Science, Vol. 29, No. 1, 179–194.
  • 8. Janczak J., Kondratiuk M., Pawluszewicz E. (2016) Testing of adaptive non-uniform sampling switch algorithm with real-time simu-lation-in-the-loop, Control and Cybernetics, Vol. 45, No. 3, 317–328.
  • 9. Kavuran G., Yeroğlu C., Ates A. Alagoz B.B. (2017) Effects of fractional order integration on ASDM signals, Int. J. Dynam. Control Vol. 5, 10–17
  • 10. Kondratiuk M., Ambroziak L., Pawluszewicz E, Janczak J. (2018) Discrete PID algorithm with non-uniform sampling Practical imple-mentation in control system, AIP Conference Proceedings 2029, 020029, doi: 10.1063/1.5066491.
  • 11. Koszewnik A., Ostaszewski M., Pawłuszewicz E., Radgowski P. (2018) Performance Assessment of the Tilt Fractional Order Integral Derivative Regulator for Control Flow Rate in Festo MPSR©PA Compact Workstation, Proceedings of 23rd International Conference on Methods and Models in Automation and Robotics, Poland.
  • 12. Koszewnik A., Pawluszewicz E., Nartowicz T., (2016), Fractional order controller to control pomp in Festo MPS® PA Compact Work-station, Proceedings of the 17th International Carpathian Control Con-ference (ICCC 2016), 364–367.
  • 13. Lorenzo C.F., Hartley T.T. (2002) Variable order and distributed order fractional operators, Nonlinear Dynamics, Vol. 29, 57–98.
  • 14. Ortigueira M., Torres D.M.F., Trujillo J. (2016) Exponents and Laplace transforms on non-uniform time scale, Communications in Nonlinear Science and Numerical Simulations, Vol. 39, 252–270.
  • 15. Ortigueira M.D. (1997) Fractional discrete-time linear systems, Proceedings of the EEICASSP, Munich, Germany, IEEE New York, Vol. 3, 2241–2244.
  • 16. Ostalczyk P. (2012) Variable- fractional-order discrete PID control-ler, IEEE Proceedings of the 17th International Conference on Meth-ods and Models in Automation and Robotics, MMAR 2012, Miedzyzdroje, Poland, 534–539.
  • 17. Ostalczyk P., Duch P. Brzezinski D.W., Sankowski D. (2015) Order functions selection in the variable-, fractional-order PID con-troller in: Advances in modelling and control of non-integer-order sys-tems, Eds. Latawiec K.J., Lukaniszyn M., Stanislawski R., 159–170.
  • 18. Patniak S., Hollkamp J.P., Semperlotti A. (2002) Applications of variable-order fractional operators: a review, Proceedings of the Royal Society A, 476, 1–32.
  • 19. Pawluszewicz E., Koszewnik A., (2019), Markov parameters of the input-output map for discrete-time order systems with Grünwlad-Letnikov h-difference operator, Proceedings of the 24th International Conference on Methods and Models in Automation and Robotics (MMAR), 456–459.
  • 20. Podlubny , I., Dorcak, L., Misanek, J. (1995) Application of frac-tional order derivatives to calculation of heat load intensity change in blast furnace walls, Transactions of Technical University of Kosice, Vol. 5, 137–144.
  • 21. Samko S.G., Ross B. (1993) Integration and differentiation to a variable fractional order, Journal Integral Transforms and Special Functions, Vol. 1, No. 4, 277–300.
  • 22. Sierociuk D., Macias M. (2013) Comparison of variable fractional order PID controller for different types of variable order derivatives, Proceedings of the 14th International Carpathian Control Conference ICCC 2013, Rytro, Poland, 334–339.
  • 23. Sierociuk D., Malesza W., Macias M. (2013) On a new definition of fractional variable-order derivative, Proceedings of the 14th Interna-tional Carpathian Control Conference ICCC 2013, Rytro, Poland, 339–345.
  • 24. Sierociuk D., Malesza W., Macias M. (2015) Deviation, interpolation and analog modelling of fractional variable order derivative defini-tions, Applied Mathematics and Modelling, Vol. 39, 3876–3888.
  • 25. Stanislawski R., Latawiec K. (2012) Normalized finite fractional differences: computational and accuracy breakthrough, International Journal of Applied Mathematics and Computer Science, Vol. 22, No. 4, 907–919.
  • 26. Tepljakov A. (2017) Fractional-order modeling and control of dynamic systems, Springer-Verlag.
  • 27. Tepljakov A., Alagoz B.B. et al. (2018) FOPID controllers and their industrial applications: a survey of recent results, IFAC Papers On Line 51-4, 25–30.
  • 28. Tepljakov A., Petlekov E., Belikov J. (2012) A flexible Matlab tool for optimal fractional-order PID controller design subject to specifica-tions, Proceedings of the 31st Chinese Control Conference, 4698–4703.
  • 29. Valerio D., Sa da Costa J. (2001) Variable-order fractional deriva-tives and their numerical approximations, Signal Processing, Vol. 91, 470–483.
  • 30. Wang J.C. (1987) Realizations of generalized Warburg impedance with RC ladder networks and transmission lines, Journal of Electro-chemical Society, Vol. 134, No. 8, 1915–1920.
Uwagi
1. The work is supported with University Works No WZ/WM-IIM/1/2019 (A. Koszewnik and E. Pawluszewicz) and WI/WM-IIM/7/2020 (P. Burzyński) Faculty of Mechanical Engineering, Bialystok University of Technology.
2. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-42ae0987-b54a-4d95-8e65-e4fc3daf800a
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.