Robust, fragile, or optimal?

Author

Keel, L.H. ; Bhattacharyya, S.P.

Author_Institution

Center of Excellence in Inf. Syst., Tennessee State Univ., Nashville, TN, USA

Volume

42

Issue

8

fYear

1997

fDate

8/1/1997 12:00:00 AM

Firstpage

1098

Lastpage

1105

Abstract

We show by examples that optimum and robust controllers, designed by using the H₂, H_∞, l¹, and μ formulations, can produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed-loop control system. The examples show that this fragility usually manifests itself as extremely poor gain and phase margins of the closed-loop system. The calculations given here should raise a cautionary note and draw attention to the larger issue of controller sensitivity which may be important in other nonoptimal design techniques as well

Keywords

H^∞ control; Nyquist diagrams; closed loop systems; control system analysis; control system synthesis; poles and zeros; robust control; μ formulation; H_∞ control; H₂ control; closed-loop control; controller sensitivity; destabilization; fragile controllers; gain margins; l¹ formulation; nonoptimal design techniques; phase margins; robust controllers; vanishingly small perturbations; Analog-digital conversion; Control systems; Control theory; Digital-analog conversion; Hardware; Measurement uncertainty; Robust control; Robust stability; Robustness; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.618239

Filename

618239