TY - JOUR

T1 - Pole-zero cancellations and closed-loop properties of an H∞ mixed sensitivity design problem

AU - Tsai, M. C.

AU - Geddes, E. J.M.

AU - Postlethwaite, I.

N1 - Funding Information:
Acknowledgement--The authors are grateful to the U.K. Science and Engineering Research Council for financial support.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1992/5

Y1 - 1992/5

N2 - We examine an H∞ mixed sensitivity design problem in order to gain an understanding of the pole-zero cancellation phenomenon that is known to occur with such designs. It is shown how the pole-zero cancellation phenomenon is dependent upon the choice of weighting functions used in the problem formulation, and a particular construction of weighting function is given that gives the designer freedom to exploit or prevent the phenomenon. Furthermore, this weighting function is then a mechanism for (partial) pole placement. As a consequence of the construction of this weighting function, it is shown that for a certain class of plant, the Normalized Coprime Factor design procedure of Glover and McFarlane (1989, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Springer-Verlag, Berlin) gives rise to (possibly undesirable) pole-zero cancellations. The results are presented for multivariable systems, and are illustrated with a simple design example.

AB - We examine an H∞ mixed sensitivity design problem in order to gain an understanding of the pole-zero cancellation phenomenon that is known to occur with such designs. It is shown how the pole-zero cancellation phenomenon is dependent upon the choice of weighting functions used in the problem formulation, and a particular construction of weighting function is given that gives the designer freedom to exploit or prevent the phenomenon. Furthermore, this weighting function is then a mechanism for (partial) pole placement. As a consequence of the construction of this weighting function, it is shown that for a certain class of plant, the Normalized Coprime Factor design procedure of Glover and McFarlane (1989, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Springer-Verlag, Berlin) gives rise to (possibly undesirable) pole-zero cancellations. The results are presented for multivariable systems, and are illustrated with a simple design example.

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U2 - 10.1016/0005-1098(92)90176-G

DO - 10.1016/0005-1098(92)90176-G

M3 - Article

AN - SCOPUS:0026868142

VL - 28

SP - 519

EP - 530

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 3

ER -