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Numerical solution of fractional variable order linear control system in state-space form

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to introduce a matrix approach for approximate solving of non-commensurate fractional variable order linear control systems in state-space form. The approach is based on switching schemes that realize variable order derivatives. The obtained numerical solution is compared with simulation and analog model results.
Rocznik
Strony
715--724
Opis fizyczny
Bibliogr. 29 poz., wykr.
Twórcy
autor
  • Warsaw University of Technology, Faculty of Electrical Engineering, 75 Koszykowa St., 00-625 Warszawa, Poland
autor
  • Warsaw University of Technology, Faculty of Electrical Engineering, 75 Koszykowa St., 00-625 Warszawa, Poland
Bibliografia
  • [1] I. Podlubny, Fractional Differential Eąuations. Academic Press, 1999.
  • [2] S. Samko, A. Kilbas, and O, Maritchev, Fractional Integrals and Deri vat ive. Theory and Applications. Gordon & Breach Sci. Publishers, 1987.
  • [3] T. Kaczorek, Selected Problems of Fractional Systems Theory. Heidelberg, Springer, 2011.
  • [4] H. El Brouji, J.-M. Yinassa, O. Briat, N. Bertrand, and E.Woir-gard, "Ultracapacitors self discharge modelling using a physical description of porous electrode impedance", Vehicle Power and Propulsion Conference, IEEE, 1-6 (2008).
  • [5] R. Martin, J.J. Quintana, A. Ramos, and I. de la Nuez, "Modeling electrochemical double layer capacitor, from classical to fractional impedance", The 14th IEEE Mediterranean Electro-technical Conference, 61-66 (2008).
  • [6] H. Sheng, H. Sun, C. Coopmans, Y. Chen, and G.W. Bohannan, "Physical experimental study of variable-order fractional integrator and differentiator", in Proceedings of The 4th IFACWorkshop Fractional Differentiation and its Applications (2010).
  • [7] L. Ramirez and C. Coimbra, "On the Variable order dynamics of the nonlinear wake caused by a sedimenting particle", Physica D-Nonlinear Phenomena 240 (13), 1111-1118 (2011).
  • [8] C.-C. Tseng, "Design and application of variable fractional order differentiator", Proceedings of The 2004 IEEE Asia- Pacific Conference on Circuits and Systems l, 405-408 (2004).
  • [9] C.-C. Tseng and S.-L. Lee, "Design of variable fractional order differentiator using infinite product expansion", Proceedings of 20th European Conference on Circuit Theory and Design, 17—20 (2011).
  • [10] H. Sheng, H. Sun, Y. Chen, and T. Qiu, "Synthesis of mul-tifractional gaussian noises based on variable-order fractional operators", Signal Processing 91 (7), 1645-1650 (2011).
  • [11] D. Sierociuk, 1. Podlubny, and I. Petras, "Experimental eyidence of yariable-order behayior of ladders and nested ladders", IEEE Transactions on Control Systems Technology 21 (2), 459-466 (2013).
  • [12] P. Ostalczyk and T. Rybicki, "Variable-fractional-order deadbeat control of an electromagnetic servo", Journal of Vibration and Control 14 (9-10), 1457-1471 (2008).
  • [13] P. Ostalczyk, "Variable-, fractional-order discrete PID control -lers", Proceedings of the IEEE/IFAC 17th Internationa] Conference on Methods and Models in Automation and Robotics Międzyzdroje, 534-539 (2012).
  • [14] P. Ostalczyk and P. Duch, "Closed-loop system synthesis with the variable-, fractional- order PID controller", Proceedings of the IEEE/IFAC 17th International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, 589-594 (2012).
  • [15] C. Lorenzo and T. Hartley, "Variable order and distributed order fractional operators", Nonlinear Dynamics 29 (1-4), 57-98 (2002).
  • [16] D. Yalerio and J.S. da Costa, "Yariable-order fractional deriva-tives and their numerical approximations", Signal Processing 91 (3), 470-483(2011).
  • [17] D. Sierociuk, W. Malesza, and M. Macias, "On a new definition offractional variable-orderderivative",Proceedingsof the 14th International Carpathian Control Conference, 340-345 (2013).
  • [18] M. Macias and D. Sierociuk, "An alternative recursive fractional yariable-order derivative definition and its analog yalidation", Proceedings of International Conference on Fractional Differentiation and its Applications, Catania (2014).
  • [19] W. Malesza, M. Macias, and D. Sierociuk, "Matrix approach and analog modeling for solying fractional yariable order differential equations", Advances in Modelling and Control of Non-integer-Order Systems, Lecture Notes in Electrical Engineering, eds. K.J. Latawiec, M. Lukaniszyn, and R. Stanislawski, Springer International Publishing, 71-80, 2015.
  • [20] D. Sierociuk, W. Malesza, and M. Macias, "Practical analog realization of multiple order switching for recursive fractional yariable order derivative", in 20th International Conference on Methods and Models in Automation and Robotics, 573-578 (2015).
  • [21] W. Malesza, D. Sierociuk, and M. Macias, "Solution of fractional variable order differential eąuation", Proceedings of the American Control Conference IEEE, 1537-1542 (2015).
  • [22] P. Ostalczyk, D. Brzeziński, P. Duch, M. Łaski, and D. Sankowski, "The variable, fractional-order discrete-time pd controller in the iisvl.3 robot arm control", Central European Journal of Physics 11 (6), 750-759, (2013).
  • [23] P. Sakrajda and D. Sierociuk, Modeling Heat Transfer Process in Grid-Holes Structure Changed in Time Using Fractional Variable Order Calculus. Springer International Publishing, 297-306 (2017).
  • [24] D. Sierociuk and M. Twardy, "Duality of yariable fractional order difference operators and its application to identification", Buli. Poi. Ac.: Tech. 62 (4), 809-815 (2014).
  • [25] I. Podlubny, "Matrix approach to discrete fractional calculus", Fractional Calculus and Applied Analysis 3, 359-386 (2000).
  • [26] I.Podlubny,A.Chechkm,T.Skovranek,Y.Chen,andB.M. Vinagre Jara, "Matrix approach to discrete fractional calculus. II: Partial fractional differential equations", Journal of Computational Physics 228 (8), 3137-3153 (2009).
  • [27] D. Sierociuk, W. Malesza, and M. Macias, "On the recursive fractional variable-order derivative: Equivalent switching strategy, duality, and analog modeling", Circuits, Systems, and Signal Processing 34 (4), 1077 1113 (2015).
  • [28] D. Sierociuk, W. Malesza, and M. Macias, "Practical analog realization of multiple order switching for recursive fractional variable order derivative", 20th International Conference on Methods and Models in Automation and Robotics, 573-578 (2015).
  • [29] D. Sierociuk and A. Dzielinski, "New method of fractional order integrator analog modeling for orders 0.5 and 0.25", Proc. of the I6th International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, 137-141 (2011).
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-045e5f69-1119-4446-93ac-f2a486a9ec52
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