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Stabilisation of LC ladder network with the help of delayed output feedback

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Języki publikacji
EN
Abstrakty
EN
The paper presents a method of stabilisation of an LC ladder network with a delayed output feedback. A discussion of certain properties of tridiagonal matrices and formulation of the considered system in state space equations is included. Formal stability of the arising infinite dimensional system is described and stability conditions are formulated based on properties of characteristic quasipolynomial. The method of D-partitions is used to determine the stability regions in the controller parameter space. Paper includes examples for ladders of dimensions 1, 2 and 3 and a comparison with Padé approximation.
Rocznik
Strony
13--34
Opis fizyczny
Bibliogr. 30 poz., wykr.
Twórcy
autor
  • AGH University of Science and Technology Al. Mickiewicza 30, 30-059 Cracow, Poland
Bibliografia
  • Abdallah, C.T., Dorato, P., Benitez-Read, J. and Byrne, R. (1993) Delayed Positive Feedback Can Stabilize Oscillatory Systems. In: Proceedings of the American Control Conference, San Francisco, CA. IEEE Conference Publications, 3106-3107.
  • Baranowski, J. and Mitkowski, W. (2009) Stabilisation of the second order system with a time delay controller. In: Papers. 24th IFIP TC7 Conference on System Modelling and Optimization, 48-49.
  • Baranowski, J., Mitkowski, W. and Skruch, P. (2009) Stability regions of time delay controller for LC ladder network. In: Materiały XXXII Międzynarodowej konferencji z podstaw elektrotechniki i teorii obwodów IC-SPETO, Ustroń. Extended version on CD, 103-104.
  • Cheng, J. and Berger, T. (2009) On minimal eigenvalues of a class of tri diagonal matrices. IEEE Transactions on Information Theory, 55(11), 5024-5031.
  • Delfour, M.C. (1980) The largest class of hereditary systems defining C0 semigroup on the product space. Can. J. Math. 32(4), 969-978.
  • Delfour, M.C. and Manitius, A. (1980a) The structural operator F and its role in theory of retarded systems. Part I. J. Math. Anal. Appl. 73(2), 466-490.
  • Delfour, M.C. and Manitius, A. (1980b) The structural operator F and its role in theory of retarded systems. Part II. J. Math. Anal. Appl. 74(2), 359-381.
  • Elsgolts, L.E. and Norkin, S.B. (1973) Introduction to the Theory and Application of Differential Equations with Deviating Arguments. Mathematics in Science and Engineering, 105. Academic Press, New York. Translated from Russian by John L. Casti.
  • Górecki, H. (1971) Analysis and Synthesis of Control Systems with Delay. Wydawnictwa Naukowo-Techniczne, Warszawa (in Polish).
  • Górecki, H., Fuksa, S., Grabowski, P. and Korytowski, A. (1989) Analysis and Synthesis of Time-delay Systems. J. Wiley & PWN, Chichester & Warsaw.
  • Ilin, W.P. and Kuznyetsow, Y.I. (1985) Tridiagonal matrices and their applications. Nauka, Moskva (in Russian).
  • Kaczorek, T. (2007) Polynomial and Rational Matrices. Applications in Dynamical Systems Theory. Springer-Verlag, London.
  • Klamka, J. (1990) Controllability of Dynamical Systems. PWN, Warszawa (in Polish, English language editio: Kluwer Academic Publishers, 1991).
  • Manitius, A. (1980) Completness and f-completness of eigenfunctions associated with retarded functional differential equations. J. Diff. Eq. 35(1), 1-29.
  • Mitkowski, W. (1973) Układy drabinkowe jednorodne R,L i G,C pasywne oraz aktywne (Passive and active uniform ladder networks of the R,L and G,C type). Arch. Elektrotechniki, 22(2), 387-395.
  • Mitkowski, W. (1976) Aproksymacja linii długiej układem drabinkowym (Approximation of an infinite line by a ladder network). Arch. Elektrotechniki 25(4), 943-953.
  • Miktowski, W. (1987a) Analysis of ladder networks with boundary feedback. Bulletin of the Polish Academy of Sciences - Technical Sciences, 32(11-12), 695-699.
  • Miktowski, W. (1987b) Uniform ladder networks with linear feedback. Arch. Elektrotechniki, 36(1-4), 7-18.
  • Miktowski, W. (1991a) Remarks on the eigenvalues of a Jacobi matrix with special perturbation. Kwartalnik AGH, Elektrotechnika, 10(2), 169-175.
  • Mitkowski, W. (1991b) Stabilizacja systemów dynamicznych (Stabilisation of dynamical systems; in Polish). WNT, Warszawa.
  • Mitkowski, W. (1996) Tridiagonal matrices and their applications in circuits theory. In: Proc. of Seminar on Electrical Engineering „Beskidy 96”, 2, Conference Archives PTETiS, 19-31.
  • Mitkowski, W. (2003) Dynamic Feedback in LC Ladder Network. Bulletin of the Polish Academy of Sciences - Technical Sciences 51(2), 173-180.
  • Mitkowski, W. (2004a) Analysis of undamped second order systems with dynamic feedback. Control and Cybernetics 33(4), 563-572.
  • Mitkowski, W. (2004b) Stabilisation of LC ladder network. Bulletin of the Polish Academy of Sciences - Technical Sciences 52(2), 109-114.
  • Mitkowski, W. and Skruch, P. (2009) Stabilization results of secondo-order systems with delayed positive feedback. In: W. Mitkowski and J. Kacprzyk, eds., Modelling Dynamics in Processes and Systems. Studies in Computational Intelligence, 180, Springer, Berlin - Heidelberg, 99-108.
  • Niculescu, S. and Abdallah, C. (2000) Delay effects on static output feedback stabilization. In: Proceedings of the 39th IEEE Conference on Decision and Control, 2000. IEEE, 3, 2811-2816.
  • Pandolfi, L. (1975) On feedback stabilisation of functional differential equations. Boll. Un. Mat. Ital. 11(4), 626-635.
  • Skruch,P. (2005) Stabilisation of linear infinitely dimensional oscillatory systems. Ph.D. thesis, Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, AGH University of Science and Technology. Supervisor: W. Mitkowski (in Polish).
  • Triggiani, R. (1975) Controlability and observability in Banach space with bounded operators. SIAM J. Control 13 (2), 462-491.
  • Turowicz, A. (2005) Teoria Macierzy (Matrix Theory; in Polish). Uczelniane Wydawnictwa Naukowo Dydaktyczne AGH, Kraków, 6th edition.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BATC-0009-0035
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