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Stability and robustness analysis of discrete-time fractional-piecewise-constant-order PID controller

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Języki publikacji
EN
Abstrakty
EN
In the paper we propose a fractional-piecewise-constant-order PID controller and discuss the stability and robustness of a closed loop system. In stability analysis we use the transform method and include the Nyquist-like criteria. Simulations for designed controllers are performed for the second-order plant with a delay.
Rocznik
Strony
art. no. e137937
Opis fizyczny
Bibliogr. 29 poz., rys., tab.
Twórcy
  • Bialystok University of Technology, ul. Wiejska 45A, 15-351 Bialystok, Poland
  • Bialystok University of Technology, ul. Wiejska 45A, 15-351 Bialystok, Poland
  • Bialystok University of Technology, ul. Wiejska 45A, 15-351 Bialystok, Poland
Bibliografia
  • [1] R. Hilfer, Applications of Fractional Calculus in Physics, Singapore: World Scientific Publishing Company, 2000.
  • [2] R. Almeida, N.R.O. Bastos, and M.T.T. Monteiro, “A fractional Malthusian growth model with variable order using an optimization approach”, Stat. Optim. Inf. Comput. vol. 6, no. 1, pp. 4–11, 2018.
  • [3] R. Caponetto, G. Dongola, G. Fortuna, and I. Petras, Fractional Order Systems: Modeling and Control Applications, World Scientific, Singapore, 2010.
  • [4] I. Podlubny, “Fractional-order systems and PIlDm controllers”, IEEE Trans. Autom. Control, vol. 44, no. 1, pp. 208–214, 1999.
  • [5] D. Xue and Y.Q. Chen, “A Comparative Introduction of Four Fractional Order Controllers”, Proceedings of the 4th World Congress on Intelligent Control and Automation, Shanghai, P.R. China, 2002, pp. 3228–3235.
  • [6] Y.Q. Chen, “Ubiquitous fractional order controls?”, IFAC Proc. Vol., vol. 39, no. 11, pp. 481–492, 2006.
  • [7] C.A Monje, Y. Chen, B.M. Vinagre, and V. Feliubatlle, Fractional-Order Systems and Fractional-Order Controllers, Springer Science & Business Media, 2010.
  • [8] I. Petras, “Tuning and implementation methods for fractionalorder controllers”, Fract. Calc. Appl. Anal., vol. 15, no. 2, pp. 282–303, 2012.
  • [9] S. Debarma, L.C. Saikia, and N. Sinha, “Automatic generation control using two degree of freedom fractional order PID controller”, Int. J. Electr. Power Energy Syst., vol. 58, pp. 120–129, 2014.
  • [10] F. Padula and A. Visioli, “Set-point weight tuning rules for fractional order PID controllers”, Asian J. Control, vol. 15, no. 3, pp. 678–690, 2013.
  • [11] A. Tepljakov, E. Petlenkov, and J. Belikov, “A flexible MATLAB tool for optimal fractional-order PID controller design subject to specifications”, Proceedings of the 31st Chinese Control Conference, 2012, pp. 4698–4703.
  • [12] P. Shah and S. Agashe, “Review of fractional PID controller”, Mechatronics, vol. 38, pp. 29–41, 2016.
  • [13] A. Veloni and N. Miridakis, Digital Control Systems, Pearson Education Limited, 2017.
  • [14] P. Oziablo, D. Mozyrska, and M. Wyrwas, “A Digital PID Controller Based on Grünwald-Letnikov Fractional-, Variable-Order Operator”, 24th International Conference on Methods and Models in Automation and Robotics (MMAR), 2019, pp. 460–465.
  • [15] D. Mozyrska, P. Oziablo, and M.Wyrwas, “Fractional-, variableorder PID controller implementation based on two discretetime fractional order operators”, 7th International Conference on Control, Mechatronics and Automation (ICCMA), 2019, pp. 26–32.
  • [16] P. Oziablo, D. Mozyrska, and M. Wyrwas, “Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay”, Entropy, vol. 22, no. 7, p. 771, 2020.
  • [17] P. Ostalczyk, “Variable-, fractional-order discrete PID controllers”, 17th International Conference on Methods and Models in Automation and Robotics (MMAR), 2012, pp. 534–539.
  • [18] D. Sierociuk, W. Malesza, and M. Macias, “On a new definition of fractional variable-order derivative”, Proc. of the 14th International Carpathian Control Conference (ICCC), 2013, pp. 340–345.
  • [19] D. Sierociuk, and W. Malesza, “Fractional variable order antiwindup control strategy”, Bull. Pol. Acad. Sci. Tech. Sci., vol. 66, no. 4, pp. 427–432, 2018.
  • [20] D. Mozyrska and P. Ostalczyk, “Generalized Fractional-Order Discrete-Time Integrator”, Complexity, vol. 2017, p. 3452409, 2017.
  • [21] D. Mozyrska, and M. Wyrwas, “Systems with fractional variable-order difference operator of convolution type and its stability”, Elektronika i Elektrotechnika, vol. 24, no. 5, pp. 69‒73, 2018.
  • [22] F. Haugen, PID Control, Tapir Academic Press, 2004.
  • [23] R.C. Dorf and R.H. Bishop, Modern Control Systems, CRC Press, Taylor & Francis Group, 2018.
  • [24] O. Mayr, The origins in feedback control, MIT Press, Cambridge, Mass, 1970.
  • [25] F. Haugen, TechTeach: Discrete-time signals and systems, 2005.
  • [26] K. Chen, R. Tang, and Ch. Li, “Phase-constrained fractional order PI controller for second-order-plus dead time systems”, Trans. Inst. Meas. Control, vol. 39, no. 8, pp. 1225–1235, 2016.
  • [27] M. Micev, M. Calasan, and D. Oliva, “Fractional Order PID Controller Design for an AVR System Using Chaotic Yellow Saddle Goatfish Algorithm”, Mathematics, vol. 8, no. 7, p. 1182, 2020.
  • [28] MathWorks. [Online]. Available: https://www.mathworks.com/help/control/ref/stepinfo.html. [Accessed Aug. 28, 2020].
  • [29] G.F. Franklin, J.D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, Prentice Hall, 2004.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-97f4922a-3c20-468c-b09b-3b61da30e3f7
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