Journal Article

On the computation and parametrization of proper denominator assigning compensators for strictly proper plants

E. N. Antoniou and A. I. G. Vardulakis

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 22, issue 1, pages 12-25
Published in print March 2005 | ISSN: 0265-0754
Published online March 2005 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dni002
On the computation and parametrization of proper denominator assigning compensators for strictly proper plants

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Given a right coprime MFD of a strictly proper plant P(s) = NR(s) DR(s)−1 with DR(s) column proper a simple numerical algorithm is derived for the computation of all polynomial solutions [XL(s), YL(s)] of the polynomial matrix Diophantine equation XL(s) DR(s) + YL(s) NR(s) = DC(s) which give rise to the class Φ (P, DC) of proper compensators C(s) ≔ XL(s)−1 YL(s) that when employed in a unity feedback loop, result in closed-loop systems S(P, C) with a desired denominator DC(s). The parametrization of the proper compensators C(s) ∈ Φ(P, DC) is obtained and the number of independent parameters in the parametrization is given.

Keywords: linear multivariable control; coprime factorizations; diophantine euqations

Journal Article.  0 words. 

Subjects: Mathematics

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