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Tytuł artykułu

State estimators and observers for continuous and discrete linear systems. Part 2. Integral observers for exact state reconstruction

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper, the exact state observers will be presented. The state estimators and observers can be used in technical processes for many purposes like the fault detection and diagnosis, the implementation of the state controllers, and soft reconstruction of inaccessible for measurements variables of the system. As the standard, for continuous systems the differential estimators of Kalman filter or Luenberger type observer are commonly used. However, if the initial conditions of the real state are unknown, both estimators guarantee only an asymptotic quality of the real state tracking. The paper presents another type of the state observers, which for continuous system have the structure given by two integral operators. Based on measurements of the system input and output signals on some predefined finite time interval T, they can reconstruct the initial state exactly. In on-line version, the exact state reconstruction is performed continuously for every t, based on special procedure executed within two moving windows of width T, on sliding time interval [t-T, t].
Rocznik
Strony
23--33
Opis fizyczny
Bibliogr. 27 poz., rys.
Twórcy
  • Department of Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, Krakow 30-059, Poland
  • Department of Automatic Control and Robotics, AGH University of Science and Technology, al. Mickiewicza 30, Krakow 30-059, Poland
Bibliografia
  • 1. Byrski J. Algorytmy ze skończoną pamięcią do przetwarzania sygnałów w diagnostyce procesów, Monografie, Wydawnictwa AGH, Kraków, 2016.
  • 2. Byrski J, Byrski W, State estimators and observers for continuous and discrete linear systems. Part 1. Differential asymptotic state estimators, Sci, Tech. Innov., 2018;3(2):62-68.
  • 3. Kalman R. A new approach to linear filtering and prediction problems, Journal of Basic Engineering, 1960.
  • 4. Luenberger D. Observers for multivariable systems. IEEE TAC-11. 1966, p.190.
  • 5. Kwakernaak H, Sivan R. Linear Optimal Control Systems. Wiley; 1972.
  • 6. Franklin G, Powell D, Workman M. Digital Control of Dynamic System. Addison Wesley;1990.
  • 7. Byrski W, Fuksa S. Optimal finite parameter observer. An application to synthesis of stabilizing feedback for a linear system. Control and Cybernetics. 1984;13,(1).
  • 8. Fuksa S, Byrski W. General approach to linear optimal estimator of finite number of parameters. IEEE Transaction on AC-29, 1984.
  • 9. Halmos P, Hilbert A. Space Problem Book. New York: Springer; 1982.
  • 10. Byrski W. Optimal State Observers with Moving and Expanding Observation Window. Proc. of Intern.Conference on Modeling & Simulation, IASTED, Innsbruck, Austria, 1993.
  • 11. Byrski J, Byrski W. An Optimal Identification of the Input-Output Disturbances in Linear Dynamic Systems by the Use of the Exact Observation of the State. Hindawi. Mathematical Problems in Engineering. Article ID 8048567, 2018.
  • 12. Byrski W, Pelc M. The finite time state observer and its cooperation with Kalman Filter algorithm. Modelling, Identification, and Control MIC 2004. Proceedings of the 23rd IASTED International Conference; 2004 Feb 23–25; Grindelwald, CH. ACTA Press. pp. 160–165, 412-084.
  • 13. Byrski W. Integral Description of the Optimal State Observers. II European Control Conference, ECC’93; 1993; Groningen, NL.
  • 14. Byrski W. Theory and Application of the Optimal Integral State Observers. III European Control Conference. ECC; 1995; Roma, IT, p.526-531.
  • 15. Byrski W, Kubik P. Integral Observer of Finite State in Heat Equation Approximated by ODE. IFAC/IMACS Large Scale Systems Symposium LSS’98; 1998; Patras, GR.
  • 16. Byrski W. The Survey For The Exact and Optimal State Observers In Hilbert Spaces. VII European Control Conference, ECC’03; 2003; Cambridge, UK.
  • 17. Pelc M, Byrski W. Full parallel decomposition of computational algorithm with discrete state estimator. 19th IASTED International Conference on Parallel and Distributed Computing and Systems; 2007; Cambridge, MA, USA.
  • 18. Byrski J, Byrski W. A double window state observer for detection and isolation of abrupt changes in parameters. Int. Journal of Appl. Math. And Computer Sci. 2016;26(3):585–602. DOI: 10.1515/amcs-2016-0041.
  • 19. James M.R. Finite time observers and observability, Proc.29th IEEE Conf.on Decision & .Contr.; 1990; Honolulu, HI, USA.
  • 20. Medvedev A, Toivonen H.T. A continuous finite-memory deadbeat observer. American Control Conference; 1992; Chicago, USA.
  • 21. Medvedev A. Fault detection and isolation by functional continuous deadbeat observers. Int. J. Control. 1996;64.
  • 22. Medvedev A. State estimation and fault detection by a bank of continuous finite-memory filters. International Journal of Control. 1998;69(4);499-517. DOI: 10.1080/002071798222668.
  • 23. Nuninger W, Kratz F, Ragot J. Finite Memory Generalized State Observer for failure Detection in Dynamic Systems, IEEE Conf. on Decision & Control; 1998; Tampa, USA
  • 24. Engel R, Kreisselmeier G. A Continuous –Time Observer which Converges in Finite Time. IEEE Trans. AC–47, 2002;7:1202.
  • 25. Reger J, Jouffroy J. On Algebraic Time-Derivative Estimation and Deadbeat State Reconstruction. 48th IEEE Conference on Decision and Control; 2010; Shanghai, CN.
  • 26. Fliess M, Sira-Ramirez H.J. State reconstructors: a possible alternative to asymptotic observers and Kalman filters, CESA Conference, 2003.
  • 27. Hocine A, Maquin D, Ragot J. Finite memory observer for switching systems, IFAC World Congress, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9176754b-0b4c-489d-b508-6c6ab398b833
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