Optimal strictly positive real approximations for stable transfer functions

Author

Damaren, C.J. ; Marquez, H.J. ; Buckley, A.G.

Author_Institution

Dept. of Mech. Eng., Canterbury Univ., Christchurch, New Zealand

Volume

143

Issue

6

fYear

1996

fDate

11/1/1996 12:00:00 AM

Firstpage

537

Lastpage

542

Abstract

The problem of finding the optimal strictly positive real (SPR) approximation to a given stable transfer function is considered. The transfer function is further assumed to be strictly proper and the SPR approximation is constrained to have the same pole structure. The optimisation is carried out using the (weighted) H₂-norm and the problem is reduced to a strictly convex quadratic programming problem with linear inequality constraints. At the heart of the method is a parametrisation for all SPR compensators which possess a given denominator polynomial. Motivation for the problem stems from the robust stability provided by SPR compensation for passive plants such as flexible structures with collocated sensing and actuation. Numerical examples are provided, as well as the experimental implementation of an optimal approximation to the control of a single-flexible-link manipulator

Keywords

H^∞ control; approximation theory; poles and zeros; quadratic programming; stability; transfer functions; SPR compensators; denominator polynomial; flexible structures; linear inequality constraints; optimal strictly positive real approximations; pole structure; robust stability; single-flexible-link manipulator; stable transfer functions; strictly convex quadratic programming problem; strictly proper transfer function; weighted H₂-norm;

fLanguage

English

Journal_Title

Control Theory and Applications, IEE Proceedings -

Publisher

iet

ISSN

1350-2379

Type

jour

DOI

10.1049/ip-cta:19960720

Filename

579196