Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The paper presents new methods for correcting the processing characteristics of measurement systems based on a modified Grünwald-Letnikov fractional calculus definition. The presented methods are based on the determination of the fractional order as an estimation factor. Two methods are presented: a fractional order array and a fractional order function. Both methods can be used in DSP systems as methods to correct the processing characteristics of systems with measuring transducers and measurement systems in general.
Słowa kluczowe
Rocznik
Tom
Strony
7--14
Opis fizyczny
Bibliogr. 23 poz., rys., tab., wykr.
Twórcy
autor
- Casimir Pulaski Radom University, Faculty of Transport, Electrical Engineering and Computer Science, Malczewskiego 29, 26-600 Radom, Poland,
Bibliografia
- [1] Oldham, K.B. Spanier, J. (2008) The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Dover Publications
- [2] Das, S. (2008) Functional Fractional Calculus for System Identification and Controls. Springer-Verlag
- [3] Jiao, Z., Chen, YQ., Podlubny I. (2012) Distributed-Order Dynamic Systems. Stability, Simulation, Applications and Perspectives; Springer London
- [4] Podlubny I. (1999) Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. Academic Press
- [5] Petráš, I. Terpák, J. (2023) Fractional calculus as a cimple tool for modeling and analysis of long memory process in industry, doi: 10.3390/math7060511
- [6] Hunek, W.P., Feliks T. (2021) “Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework”, FCAA 2021, 24(4):1257-1274. doi: 10.1515/fca-2021-0054
- [7] Mahata, S., Herencsar, N. and Maione G. (2023) “Optimal approximation of analog PID controllers of complex fractional-order”, FCAA 2023, 10.1007/s13540-023-00168-x
- [8] Oprzędkiewicz K. (2021) “Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator”, Bulletin of the Polish Academy of Sciences Technical Sciences 69(4)
- [9] Sowa M. and Majka L. and Wajda K. (2023) “Excitation system voltage regulator modeling with the use of fractional calculus”, AEU - International Journal of Electronics and Communications 159, doi: 10.1016/j.aeue.2022.154471
- [10] Matusiak M. , Bąkała, M., Wojciechowski, R. and Ostalczyk, P. (2020) „Fractional discrete model of an electrical drive with brushless micro-motor”, Bulletin of the Polish Academy of Sciences Technical Sciences 68(3)
- [11] Brouji H. El, Vinassa J.-M., et al. (2008) “Ultracapacitors self-discharge modelling using a physical description of porous electrode impedance”, IEEE Vehicle Power and Propulsion Conference 2008
- [12] Lopes, A.; Tenreiro Machado, J. (2021) “Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method” Sensors 2021, 21(22), 7736, doi: 10.3390/s21227736
- [13] Ullah, N. (2020) “Fractional order sliding mode control design for a buck converter feeding resistive power loads”, Mathematical Modelling of Engineering Problems 2020, Vol. 7, No. 4, pp. 649-658
- [14] Su, L.; Zhou, G.; Hu, D.; Liu, Y.; Zhu, Y. (2021) “Research on the State of Charge of Lithium-Ion Battery Based on the Fractional Order Model”, Energies 2021, 14, 6307, doi: 10.3390/en14196307
- [15] Magin, R.L., Hall, M. G., Karaman, M. M. and Vegh, V. (2016) “Fractional Calculus Models of Magnetic Resonance Phenomena: Relaxation and Diffusion”, Critical reviews in biomedical engineering 48(5), 10.1615/CritRevBiomedEng.2020033925
- [16] Yang Q., Chen D., Zhao T., Chen YQ. (2016) “Fractional calculus in image processing: a review”, Fractional Calculus and Applied Analysis 2016, vol. 19, No. 5, pp. 1222-1249, doi: 10.1515/fca-2016-0063
- [17] Kaczorek T. (2021) “Positive electrical circuits with the chain structure and cyclic Metzler state matrices”, Bulletin of the Polish Academy of Sciences Technical Sciences 69(4)
- [18] Dzieliński, A., Sierociuk, D. and Sarwas, G. (2010) „Some applications of fractional order calculus”, Bulletin of the Polish Academy of Sciences Technical Sciences 58(4)
- [19] Tarasov, V. E. (2020) “Mathematical Economics: Application of Fractional Calculus”, Mathematics 2020 8(5), doi: 10.3390/math8050660
- [20] Tarasov V. E. (2017) “Interpretation of Fractional Derivatives as Reconstruction from Sequence of Integer Derivatives”, Fundamenta Informaticae 2017 Vol. 151, No 1-4, pp. 431–442
- [21] Ortigueira, M.D., Machado J.T.M. (2018) “On fractional vectorial calculus”, Bulletin of the Polish Academy of Sciences: Technical Sciences 2018, No 4
- [22] Cioć R. (2016) “Physical and geometrical interpretation of Grünwald-Letnikov differintegrals: measurement of path and acceleration”, Fractional Calculus and Applied Analysis 2016, Vol. 19, No 1(2016), pp. 161-172, doi: 10.1515/fca-2016-0001
- [23] Cioć R., Chrzan M. (2019) “Fractional order model of measured quantity errors” Bull. Pol. Ac.: Tech. 2019, Vol. 67, No. 6, doi: 10.24425/bpasts.2019. 130887
Typ dokumentu
Bibliografia
Identyfikator YADDA
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