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D-decomposition technique for stabilization of Furuta pendulum: fractional approach

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Języki publikacji
EN
Abstrakty
EN
In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out.
Rocznik
Strony
189--196
Opis fizyczny
Bibliogr. 21 poz., rys., wykr.
Twórcy
  • Faculty of Mechanical Engineering, Department of Mechanics, University of Belgrade, 16 Kraljice Marije St., 11120 Belgrade, Serbia
  • Faculty of Mechanical Engineering, Department of Mechanics, University of Belgrade, 16 Kraljice Marije St., 11120 Belgrade, Serbia
  • School of Electrical Engineering, Signals and Systems Department, University of Belgrade, 73 Bulevar Kralja Aleksandra St., 11120 Belgrade, Serbia
Bibliografia
  • [1] Yu.I. Neimark, “On the problem of the distribution of the roots of polynomials”, Dokl. Akad. Nauk SSSR 58, 357-360 (1947), (in Russian).
  • [2] Yu.I. Neimark, “D-decomposition of the space of the quasipolynomials”, Appl. Math. Mech 13, 349-380 (1949), (in Russian).
  • [3] J.A. Acosta, “Furuta’s pendulum: a conservative nonlinear model for theory and practise”, Mathematical Problems in Engineering 2010, 742-894 (2010).
  • [4] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [5] S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, London, 1993.
  • [6] K.B. Oldham and J. Spanier, Fractional Calculus: Theory and Applications, Differentiation and Integration to Arbitrary Order, Academic Press, New York, 1974.
  • [7] I. Podlubny, “Fractional-order systems and PI_Dμ controllers”, IEEE Trans. Automatic Control 44, 208-214 (1999).
  • [8] V. Čović and M.P. Lazarević, Robot Mechanics, Faculty of Mechanical Engineering, Belgrade, 2009, (in Serbian).
  • [9] M.P. Lazarević, M. Rapaić, and T.B. Šekara, “Introduction to fractional calculus”, in: Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, pp. 3-18, WSEAS Press, Athens, 2014.
  • [10] M. Cajić and M.P. Lazarević, “Fractional order spring/springpot/ actuator element in a multibody system: application of an expansion formula”, Mechanics Research Communications 62, 44-56 (2014).
  • [11] H. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, 2002.
  • [12] K. Furuta, M. Yamakita, and S. Kobayashi, “Swing-up control of inverted pendulum using pseudo-state feedback”, J. Systems and Control Engineering 206 (6), 263-269 (1992).
  • [13] A. Ruszewski, “Stability regions of closed loop system with time delay inertial plant of fractional order and fractional order PI controller”, Bull. Pol. Ac.: Tech. 56 (4), 329-332 (2008).
  • [14] P.D. Mandić, M.P. Lazarević, and T.B. Šekara, “Fractional order PD control of Furuta pendulum: D-decomposition approach”, Proc. IEEE International Conf. on Fractional Differentiation and Its Applications 1, CD-ROM (2014).
  • [15] P.D. Mandić, M.P Lazarević, and T.B. Šekara, “Ddecomposition method for stabilization of inverted pendulum using fractional order PD controller”, Proc. First Int Conf. on Electrical, Electronic and Computing Eng. 1, CD-ROM(2014).
  • [16] E.N. Gryazina, B.T. Polyak, and A.A. Tremba, “Ddecomposition technique state-of-the-art”, Automation and Remote Control 69, 1991-2026 (2008).
  • [17] T.B. Šekara, Fractional Order Control Systems, Faculty of Electrical Engineering, East Sarajevo, 2011, (in Serbian).
  • [18] M. Stojić, Continuous Control Systems, Nauka, Belgrade, 1996, (in Serbian).
  • [19] S. E. Hamamci, “An algorithm for stabilization of fractionalorder time delay systems using fractional-order PID controllers”, IEEE Trans. Automatic Control 52, 1964-1969 (2007).
  • [20] M. Buslowicz “Frequency domain method for stability analysis of linear continuous time fractional systems”, in: Recent Advances in Control and Automation, eds.: K. Malinowski and L. Rutkowski, pp. 83-92, Academic Publishing House Exit, Warsaw, 2008.
  • [21] L. Brančik, “Numerical inverse Laplace transforms for electrical engineering simulation”, in: Matlab for Engineeris - Applications in Control, Electrical Engineering, IT and Robotics, pp. 51-74 , InTech, Rijeka, 2011.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-5011a545-9309-4828-a113-5db991bbb050
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