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Analysis of Caputo-Fabrizio operator application for synthesis of fractional order PID-controller

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Warianty tytułu
PL
Analiza wykorzystania operatora Caputo-Fabrizio w syntezie regulatora PID ułamkowego rzędu
Języki publikacji
EN
Abstrakty
EN
Using the representation of Caputo and Fabrizio, the influence of substitution in the linear model of a two-mass system of integer derivatives on fractional order derivatives is shown in this paper. So, the change of parameters of PID-controller of fractional order in comparison with classical PID-controller is analyzed. The influence of the use of PID-controller of fractional order on the transient characteristics of the system is demonstrated in the results of this paper.
PL
Korzystając z reprezentacji Caputo i Fabrizio, ukazano wpływ zastąpienia pochodnych całkowitego rzędu w liniowym, modelu układu dwóch mas, pochodnymi ułamkowego rzędu. Przeanalizowano zmianę parametrów regulatora PID ułamkowego rzędu względem klasycznego regulatora PID. Zademonstrowano wyniki przedstawiające wpływ wykorzystania regulatora PID ułamkowego rzędu na charakterystykę przejściową układu.
Rocznik
Strony
66--71
Opis fizyczny
Bibliogr. 26 poz., rys.
Twórcy
  • Lviv Polytechnic National University, Institute of power engineering and control systems, 12’Stepana Bandery Str., 79013, Lviv, Ukraine
  • Lviv Polytechnic National University, Institute of power engineering and control systems, 12’Stepana Bandery Str., 79013, Lviv, Ukraine
autor
  • Lviv Polytechnic National University, Institute of power engineering and control systems, 12’Stepana Bandery Str., 79013, Lviv, Ukraine
  • Lviv Polytechnic National University, Institute of power engineering and control systems, 12’Stepana Bandery Str., 79013, Lviv, Ukraine
Bibliografia
  • [1] H.K. Khalil, Nonlinear Systems, Prentice Hall, New York, 2002.
  • [2] Garces F., Becerra V.M., Kambhampati C., Warwick K., Introduction to Feedback Linearisation. In: Strategies for Feedback Linearisation, Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-0065- 2_3.
  • [3] Ortega, R., Loría Perez, J.A., Nicklasson, P.J., Sira-Ramirez, H., Passivity-based Control of Euler-Lagrange Systems, Mechanical, Electrical and Electromechanical Applications. Springer-Verlag London. https://doi.org/10.1007/978-1-4471- 3603-3.
  • [4] K. Erenturk, Fractional-Order PIλDμ and Active Disturbance Rejection Control of Nonlinear Two-Mass Drive System, in IEEE Transactions on Industrial Electronics, vol. 60, no. 9, Sept. 2013, pp. 3806-3813.
  • [5] A. Oustaloup, B. Mathieu, and P. Lanusse, “The CRONE control of resonant plants: Application to a flexible transmission,” Eur. J. Control, vol. 1, no. 2, Feb. 1995, pp. 113–121.
  • [6] Bruzzone L., Belotti V., Fanghella P. Implementation of a Fractional-Order Control for Robotic Applications. In: Ferraresi C., Quaglia G. (eds) Advances in Service and Industrial Robotics. RAAD 2017. Mechanisms and Machine Science, vol. 49. Springer, Cham, 2018.
  • [7] R. Cajo, T. T. Mac, D. Plaza, C. Copot, R. De Keyser and C. Ionescu, A Survey on Fractional Order Control Techniques for Unmanned Aerial and Ground Vehicles, in IEEE Access, vol. 7, 2019, pp. 66864-66878.
  • [8] B. M. Vinagre, I. Podlubny, L. Dorcak, and V. Feliu, On fractional PID controllers: A frequency domain approach, in Proc. IFAC Workshop Digitalization Control PID, Terrassa, Spain, 2000, pp. 53–55.
  • [9] C. Yeroglu, N. Tan, Note on fractional-order proportionalintegral- differential controller design, IET Control Theory Application, vol. 5, no. 17, Nov. 2011, pp. 1978–1989.
  • [10] Pritesh Shah, Sudhir Agashe. Review of fractional PID controller, Mechatronics, 38, 2016, pp.29–41.
  • [11] V. Badri and M. S. Tavazoei, Some Analytical Results on Tuning Fractional-Order
  • [Proportional–Integral] Controllers for Fractional-Order Systems, in IEEE Transactions on Control Systems Technology, vol. 24, no. 3, May 2016, pp. 1059-1066.
  • [12] W. Yu and Y. Pi, Fractional order modeling and simulation experiment of Permanent Magnet Synchronous Motor, Proceedings of 2012 IEEE/ASME 8th IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications, Suzhou, 2012, pp. 114-118.
  • [13] S. Ghasemi, A. Tabesh and J. Askari-Marnani, Application of Fractional Calculus Theory to Robust Controller Design for Wind Turbine Generators, in IEEE Transactions on Energy Conversion, vol. 29, no. 3, Sept. 2014, pp. 780-787.
  • [14] Cipin R., Ondrusek C., Huzlík R. Fractional-Order Model of DC Motor. In: Březina T., Jabloński R. (eds) Mechatronics 2013. Springer, Cham, pp 363-370.
  • [15] N. Kianpoor, M. Yousefi, N. Bayati, A. Hajizadeh and M. Soltani, Fractional Order Modelling of DC-DC Boost Converters, 2019 IEEE 28th International Symposium on Industrial Electronics (ISIE), Vancouver, BC, Canada, 2019, pp. 864-869
  • [16] I. Birs, C. Muresan, I. Nascu and C. Ionescu, A Survey of Recent Advances in Fractional Order Control for Time Delay Systems,in IEEE Access, vol. 7, 2019, pp. 30951-30965.
  • [17] M. Caputo and M. Fabrizio, A New Definition of Fractional Derivative without Singular Kernel, Progress in Fractional Differentiation and Application 1:2, 2015, 1-13.
  • [18] J. Losada, J.J. Nieto. Properties of a new fractional derivative without singular kernel // Progress in Fractional Differentiation and Application, 1, 2016, pp. 87-92.
  • [19] Gürbüz, M., Akdemir, A.O., Rashid, S. et al. Hermite– Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities. J Inequal. Appl. 2020, 172 p. (2020). https://doi.org/10.1186/s13660-020-02438-1
  • [20] Gustavo Asumu Mboro Nchama, Angela Leon Mecıas, Mariano Rodrıguez Richard. The Caputo-Fabrizio Fractional Integral to Generate Some New Inequalities// Information Sciences Letters 8, No. 2, 2019, pp. 73-80
  • [21] Guy Jumarie. Laplace's transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative // Applied Mathematics Letters 22, 2009, pp. 1659– 1664.
  • [22] M. Caputo, M. Fabrizio, Applications of NewTime and Spatial Fractional Derivatives with Exponential Kernels// Progress in Fractional Differentiation and Application, 2002, pp. 7
  • [23] Kai Diethelm, Roberto Garrappa, Andrea Giusti and Martin Stynes. Why fractional derivatives with nonsingular kernels should not be used // Fractional Calculus and Applied Analysis, Volume 23, Issue 3, 610–634.
  • [24] Manuel D. Ortigueira, J. Tenreiro Machado. A critical analysis of the Caputo–Fabrizio operator // Communications in Nonlinear Science and Numerical Simulation, Volume 59, 2018, 608-61.
  • [25] Astrom K.J., Hagglund T. Advanced PID Control. – The Instrumentation, Systems, and Automation Society, 2005. — 461 p.
  • [26] Monje C.A , Vinagre B.M , Feliu V. , Chen Y . Tuning and autotuning of fractional order controllers for industry applications. Control Eng Prac , 2008;16(7), 798–812 .
Uwagi
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-9bea0267-dafc-4d2c-8a81-29f500ea5990
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