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Discrete-time feedback stabilization

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents an algorithm for designing dynamic compensator for infinitedimensional systems with bounded input and bounded output operators using finite dimensional approximation. The proposed method was then implemented in order to find the control function for thin rod heating process. The optimal sampling time was found depending on discrete output measurements.
Rocznik
Strony
309--322
Opis fizyczny
Bibliogr. 35 poz., rys., schem., tab., wykr., wzory
Twórcy
autor
  • AGH University of Science and Technology, krakow, Poland
autor
  • AGH University of Science and Technology, Krakow, Poland
  • AGH University of Science and Technology, Krakow, Poland
Bibliografia
  • [1] K. J. Astrom: Computer Controlled Systems. Theory and Design. Second Edition. Prentice-Hall, 1990.
  • [2] M. J. Balas: The Galerkin method and feedback control of linear distributed parameter systems. J. Mathematical Analysis and Application, 91(2), (1983), 527-546.
  • [3] E. Bini and G. M. Buttazzo: The optimal sampling pattern for linear control systems. IEEE Trans. On Automatic Control, 59(1), (2014), 78-90.
  • [4] R. F. Curtain: Finite dimensional compensators for parabolic distributed systems with unbounded control and observation. SIAM J. Control and Optimization, 22(2), (1984), 255-276.
  • [5] R. F. Curtain and D. Salomon: Finite dimensional compensators for infinite dimensional systems with unbounded input operators. SIAM J. Control and Optimization, 24(4), (1986), 797-816.
  • [6] R. F. Curtain: Linear-quadratic control problem with fixed endpoints in infinite dimensions, J. of Optimization Theory and its Applications, 44(1), (1984), 55-74.
  • [7] R. F. Curtain and A. J. Pritchard: Infinite-Dimensional Linear Systems Theory. Springer, Berlin, 1978.
  • [8] R. F. Curtain and H. Zwart: An Introduction to Infinite-Dimensional Linear Systems Theory. Springer, New York, NY, 1995.
  • [9] Z. Emirsajłow: Feedback control in LQCP with a terminal inequality constraint. J. of Optimization Theory and Applications, 62(3), (1989), 387-403.
  • [10] K. P. Evans and N. Jacob: Feller semigroups obtained by variable order subordination. Revista Matematica Complutense, 20(2), (2007), 293-307.
  • [11] H. O. Fattorini: On complete controllability of linear systems. J. Differential Equations, 3(3), (1967), 391-402.
  • [12] C. Gal and M. Warma: Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evolution Equations and Control Theory, 5(1), (2016), 61-103.
  • [13] J. S. Gibson: An analysis of optimal modal regulation: convergence and stability. SIAM J. Control and Optimization, 19(5), (1981), 686-707.
  • [14] E. W. Kamen, P. P. Khargonekar and A. Tannenbaum: Stabilization of time-delay systems using finite-dimensional compensators. IEEE Trans. on Automatic Control, 30(1), (1985), 75-78.
  • [15] T. Kato: Perturbation Theory for Linear Operators. Springer, Berlin, 1966.
  • [16] T. Kobayashi: Discrete-time observers and parameter determination for distributed parameter systems with discrete-time input-output data. SIAM J. on Control and Optimization, 21(3), (1983), 331-351.
  • [17] W. Mitkowski: Stabilization of linear distributed systems. 3rd Symp. IFAC, Control of Distributed Parameter Systems, Toulouse, France, (1982), p. IV.10-IV.13.
  • [18] W. Mitkowski: Feedback stabilization of second order evolution equations with damping by discrete-time input-output data. IMACS-IFAC Symp. on Modelling and Simulation for Control of Lumped and Distributed Parameter Systems, Lille, France, (1986), 355-358.
  • [19] W. Mitkowski: Stabilizacja liniowych układów nieskończenie wymiarowych za pomocą dynamicznego sprzężenia zwrotnego (Stabilization of infinite-dimensional linear systems by dynamic feedback). Archiwum Automatyki i Telemechaniki, 33(4), (1988), 515-528, (in Polish).
  • [20] W. Mitkowski: Stabilizacja systemów dynamicznych (Stabilization of Dynamic Systems). WNT, Warszawa, 1991.
  • [21] W. Mitkowski and K. Oprzędkiewicz A sample time assign for a discrete interval parabolic system with the two-dimensionalmuncertain parameter space. Systems Science, 30(1), (2004), 43-50.
  • [22] A. Obrączka and W. Mitkowski: The comparison of parameter identification methods for fractional partial differential equation. Solid State Phenomena, 21 (2014), 265-270.
  • [23] K. Oprzędkiewicz: The interval parabolic system. Archives of Control Sciences, 13(4), (2003), 415-430.
  • [24] K. Oprzędkiewicz, E. Gawin and W. Mitkowski: Modeling of heat distribution with the use of non-integer order, state space model. Int. J. of Applied Mathematics and Computer Science, 26(4), (2016), 749-756.
  • [25] A. Pazy Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York, 1983.
  • [26] K. M. Przyłuski: On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question. Int. J. of Applied Mathematics and Computer Science, 24(4), 723-733.
  • [27] Y. Sakawa: Feedback stabilization of linear diffusion systems. SIAM J. Control and Optimization, 21(5), (1983), 667-676.
  • [28] Y. Sakawa: Feedback control of second order evolution equations with damping. SIAM J. Control and Optimization, 22(3), (1984), 343-361.
  • [29] Y. Sakawa: Feedback control of second-order evolution equations with unbounded observation. Int. J. Control, 41(3), (1985), 717-731.
  • [30] J. M. Schumacher: Dynamic Feedback in Finite- and Infinite -dimensional Linear Systems. Ph. D. dissertation, Dep. Math., Vrije Universiteit, Amsterdam, The Netherlands, 1981.
  • [31] J. M. Schumacher: A direct approach to compensator design for distributed parameter systems. SIAM J. Control and Optimization, 21(6), (1983), 823-836.
  • [32] D. Sierociuk, T. Skovranek, M. Macias, I. Podlubny, I. Petras, A. Dzielinski and P. Ziubinski: Diffusion process modeling by using fractionalorder models. Applied Mathematics and Computation, 257(1), (2015), 2-11.
  • [33] M. Slemrod: A note on complete controllability and stabilizability for linear control systems in Hilbert space. SIAM J. Control, 12(3), (1974).
  • [34] R. Triggiani: On the stabilization problem in Banach space. J. of Mathematical Analysis and Applications, 52(3), (1975), 383-403.
  • [35] P. K. C. Wang: Model feedback stabilization of linear distributed system. IEEE Trans. on Automatic Control, 17(4), (1972), 552-553.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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