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2005 | 15 | 4 | 493-507
Tytuł artykułu

Proper feedback compensators for a strictly proper plant by polynomial equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction C = (X_l)^{−1}Y_l . We recall first the class of all polynomial matrix pairs (X_l, Y_l) solving (COMP) and then single out those pairs which result in a proper rational compensator. An important role is hereby played by the assumptions that (a) the plant denominator D_r is column-reduced, and (b) the closed-loop characteristic matrix Dk is row-column-reduced, e.g., monically diagonally degree-dominant. This allows us to get all solution pairs (X_l, Y_l) giving a proper compensator with a row-reduced denominator X_l having (sufficiently large) row degrees prescribed a priori. Two examples enhance the tutorial value of the paper, revealing also a novel computational method.
Rocznik
Tom
15
Numer
4
Strony
493-507
Opis fizyczny
Daty
wydano
2005
otrzymano
2005-05-18
poprawiono
2005-10-08
Twórcy
  • Department of Mathematics, University of Namur (FUNDP), Rempart de la Vierge 8, B-5000 Namur, Belgium
  • UTIA, Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, POB 18, 18208 Prague, Czech Republic
Bibliografia
  • Antoniou E.N. and Vardulakis A.I.G. (2005): On the computation and parametrization of proper denominator assigning compensators for strictly proper plants. - IMA J. Math. Contr. Inf., Vol. 22, pp. 12-25.
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  • Callier F.M. (2000): Proper feedback compensators for a strictly proper plant by solving polynomial equations. - Proc. Conf. Math. Models. Automat. Robot., MMAR, Miedzyzdroje, Poland, Vol. 1, pp. 55-59.
  • Callier F.M. (2001): Polynomial equations giving a proper feedback compensator for a strictly proper plant. - Prep. 1st IFAC/IEEE Symp. System Structure and Control, Prague, (CD-ROM)
  • Callier F.M. and Desoer C.A. (1982): Multivariable Feedback Systems. -New York: Springer.
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  • Kucera V. (1979): Discrete Linear Control: The Polynomial Equation Approach. -Chichester, UK: Wiley.
  • Kucera V. (1991): Analysis and Design of Discrete Linear Control Systems. -London: Prentice-Hall.
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  • ProTyS, Inc. (2003): Personal communication.
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Bibliografia
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