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Root locus for SISO dead-time systems: A continuation based approach

Authors
  • Gumussoy, Suat
  • Michiels, Wim
Type
Published Article
Journal
Automatica
Publisher
Elsevier
Publication Date
Jan 01, 2012
Accepted Date
Aug 10, 2011
Volume
48
Issue
3
Pages
480–489
Identifiers
DOI: 10.1016/j.automatica.2012.01.010
Source
Elsevier
Keywords
License
Unknown

Abstract

We present a numerical method to plot the root locus of Single-Input–Single-Output (SISO) dead-time systems with respect to the controller gain or the system delay. We compute the trajectories of characteristic roots of the closed-loop system on a prescribed complex right half-plane. We calculate the starting, branch and boundary crossing roots of root-locus branches inside the region. We compute the root locus of each characteristic root based on a predictor–corrector type continuation method. To avoid the high sensitivity of roots with respect to the locus parameter in the neighborhood of branch points, the continuation method relies on a natural parameterization of the root-locus trajectory in terms of a distance in the (characteristic root, locus parameter)-space. The method is numerically stable for high order SISO dead-time systems.

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