Journal Article

Robust controller design based on generalized Bode envelopes

Arie Nakhmani, Ezra Zeheb and Michael Lichtsinder

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 2, pages 171-198
Published in print June 2012 | ISSN: 0265-0754
Published online December 2011 | e-ISSN: 1471-6887 | DOI:
Robust controller design based on generalized Bode envelopes

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We propose simple tools for robust design of controllers for single input single output linear systems with or without uncertainty. These tools are based on the generalization of frequency domain, where the uncertainty is defined by generalized Bode envelopes (GBEs). The utilization of generalized Nyquist and Mikhailov theorems, which uses the number of GBE crossings with certain predefined horizontal lines, to deduce stability allows to obtain stability as well as performance specifications simultaneously. The same design rules can be applied to continuous as well as discrete time systems. We provide examples to demonstrate our method of controller design for various control systems.

Keywords: controller design; synthesis; Bode envelope; robust; uncertain system; Nyquist theorem

Journal Article.  0 words. 

Subjects: Mathematics

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