Proper feedback compensators for a strictly proper plant by polynomial equations

Callier, F. M. ; Kraffer, F.

International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 4, pp. 493-507.

Résumé

We review the polynomial matrix compensator equation XlDr + YlNr = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (Nr,Dr) is given by the strictly proper rational plant right matrix-fraction P = NrD-1 r , (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (Xl, Yl) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction C = X-1 l Yl. We recall first the class of all polynomial matrix pairs (Xl, Yl) 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 Dr 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 (Xl, Yl) giving a proper compensator with a row-reduced denominator Xl having (sufficiently large) row degrees prescribed a priori. Two examples enhance the tutorial value of the paper, revealing also a novel computational method.

Détail

Keywords: linear time-invariant feedback control systems, polynomial matrix systems, row-column-reduced polynomial matrices, feedback compensator design, flexible belt device
Mots-clés : liniowy układ stacjonarny, sprzężenie zwrotne, macierz wielomianowa, równanie wielomianowe

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