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

• Autorzy: Mandić P. D. , Lazarević M. P. , Šekara T. B.

Identyfikatory

DOI

10.1515/bpasts-2016-0021

• 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.

Słowa kluczowe

EN

fractional order; PID; D-decomposition; asymptotic stability; inverted pendulum

PL

PID; metoda D-dekompozycji; stabilność asymptotyczna; wahadło odwrócone

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2016
• Tom: Vol. 64, nr 1
• Strony: 189--196
• Opis fizyczny: Bibliogr. 21 poz., rys., wykr.

Twórcy

autor

Mandić P. D.

• Faculty of Mechanical Engineering, Department of Mechanics, University of Belgrade, 16 Kraljice Marije St., 11120 Belgrade, Serbia

autor

Lazarević M. P.

• Faculty of Mechanical Engineering, Department of Mechanics, University of Belgrade, 16 Kraljice Marije St., 11120 Belgrade, Serbia

autor

Šekara T. B.

• School of Electrical Engineering, Signals and Systems Department, University of Belgrade, 73 Bulevar Kralja Aleksandra St., 11120 Belgrade, Serbia

Bibliografia

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• [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).
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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.