Imaginary-axis crossing points in root loci that depend polynomially on the gain

This technical note discusses the crossing with the stability boundary for the root loci that polynomially depend on the gain. A simple calculation method based on reflected polynomials is provided. The trend of the roots is also determined, which allows studying the gain margin as well as the minim...

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Bibliographic Details
Published in:Automatica (Oxford) 2021-12, Vol.134, p.109959, Article 109959
Main Author: Mulero-Martínez, Juan Ignacio
Format: Article
Language:English
Subjects:
Crossover frequencies
Gain margin
Polynomial root locus
Reflected polynomials
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Summary:This technical note discusses the crossing with the stability boundary for the root loci that polynomially depend on the gain. A simple calculation method based on reflected polynomials is provided. The trend of the roots is also determined, which allows studying the gain margin as well as the minimum gain so that all the roots are within the stable region. Finally, these concepts are illustrated with two case studies.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2021.109959