PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

PI observer design for a class of nondifferentially flat systems

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents a methodology and design of a model-free-based proportional-integral reduced-order observer for a class of nondifferentially flat systems. The problem is tackled from a differential algebra point of view, that is, the state observer for nondifferentially flat systems is based on algebraic differential polynomials of the output. The observation problem is treated together with that of a synchronization between a chaotic system and the designed observer. Some basic notions of differential algebra and concepts related to chaotic synchronization are introduced. The PI observer design methodology is given and it is proven that the estimation error is uniformly ultimately bounded. To exemplify the effectiveness of the PI observer, some cases and their respective numerical simulation results are presented.
Rocznik
Strony
655--665
Opis fizyczny
Bibliogr. 20 poz., wykr.
Twórcy
  • Department of Automatic Control, CINVESTAV-IPN, Av. Instituto Politecnico Nacional 2508, La Laguna Ticoman, 07360 Mexico City, Mexico, jflores@ctrl.cinvestav.mx
  • Department of Automatic Control, CINVESTAV-IPN, Av. Instituto Politecnico Nacional 2508, La Laguna Ticoman, 07360 Mexico City, Mexico, rguerra@ctrl.cinvestav.mx
Bibliografia
  • [1] Boutayeb, M., Darouach, M. and Rafaralahy, H. (2002). Generalized state-space observers for chaotic synchronization and secure communication, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49(3): 345–349.
  • [2] Claude, D., Fliess, M. and Isidori, A. (1983). Immersion directe et par bouclage d’un système non linéaire dans un linéaire, Comptes Rendus Des Seances De L’Academie Des Sciences 296(I): 237–240.
  • [3] Corless, M. and Leitmann, G. (1981). Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE Transactions on Automatic Control 26(5): 1139–1144.
  • [4] Gauthier, J.P., Hammouri, H. and Othman, S. (1992). A simple observer for nonlinear systems applications to bioreactors, IEEE Transactions on Automatic Control 37(6): 875–880.
  • [5] Gensior, A., Woywode, O., Rudolph, J. and Guldner, H. (2006). On differential flatness, trajectory planning, observers, and stabilization for dc-dc converters, IEEE Transactions on Circuits and Systems I: Regular Papers 53(9): 2000–2010.
  • [6] Karagiannis, D., Astolfi, A. and Ortega, R. (2005). Nonlinear stabilization via system immersion and manifold invariance: Survey and new results, Multiscale Modeling & Simulation 3(4): 801–817.
  • [7] Kolchin, E.R. (1973). Differential Algebra and Algebraic Groups, Academic Press, New York City, NY.
  • [8] Layek, G. (2015). An Introduction to Dynamical Systems and Chaos, Springer, New York City, NY.
  • [9] Martínez-Guerra, R. and Cruz-Ancona, C.D. (2017). Algorithms of Estimation for Nonlinear Systems, Springer, New York City, NY.
  • [10] Martínez-Guerra, R., Cruz-Victoria, J., Gonzalez-Galan, R. and Aguilar-Lopez, R. (2006). A new reduced-order observer design for the synchronization of Lorenz systems, Chaos, Solitons & Fractals 28(2): 511–517.
  • [11] Martinez-Guerra, R. and Flores-Flores, J.P. (2018). Synchronization for a class of nondifferentially flat chaotic systems by means of a PI observer, 15th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico City, Mexico, pp. 1–5, paper 25.
  • [12] Martínez-Guerra, R., Gómez-Cortés, G. and Pérez-Pinacho, C. (2015). Synchronization of Integral and Fractional Order Chaotic Systems: A Differential Algebraic and Differential Geometric Approach with Selected Applications in Real-Time, Springer, New York City, NY.
  • [13] Martínez-Guerra, R., González-Galan, R., Luviano-Juárez, A. and Cruz-Victoria, J. (2007). Diagnosis for a class of non-differentially flat and Liouvillian systems, IMA Journal of Mathematical Control and Information 24(2): 177–195.
  • [14] Martinez-Guerra, R. and Mendoza-Camargo, J. (2004). Observers for a class of Liouvillian and non-differentially flat systems, IMA Journal of Mathematical Control and Information 21(4): 493–509.
  • [15] Martínez-Guerra, R. and Pérez-Pinacho, C.A. (2018). Advances in Synchronization of Coupled Fractional Order Systems: Fundamentals and Methods, Springer, New York City, NY.
  • [16] Nijmeijer, H. and Mareels, I.M. (1997). An observer looks at synchronization, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 44(10): 882–890.
  • [17] Pecora, L.M. and Carroll, T.L. (1990). Synchronization in chaotic systems, Physical Review Letters 64: 821–824.
  • [18] Pledgie, S.T., Hao, Y., Ferreira, A.M., Agrawal, S.K. and Murphey, R. (2002). Groups of unmanned vehicles: Differential flatness, trajectory planning, and control, IEEE International Conference on Robotics and Automation, ICRA’02, Washington, DC, USA, pp. 3461–3466.
  • [19] Ritt, J.F. (1950). Differential Algebra, American Mathematical Society, New York City, NY.
  • [20] Sira-Ramirez, H. (2002). A flatness based generalized PI control approach to liquid sloshing regulation in a moving container, American Control Conference, Anchorage, AK, USA, pp. 2909–2914.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7a9ec6a6-0517-4eb8-bb39-48ddbf6b5541
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.