Simple answers to usual questions about unusual forms of the Evans' root locus plot

Monteiro, Luiz Henrique Alves; Cruz, José Jaime da

doi:10.1590/s0103-17592008000400007

Sba Controle & Automação

2008

DOI: 10.1590/s0103-17592008000400007

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Simple answers to usual questions about unusual forms of the Evans' root locus plot

Luiz Henrique Alves Monteiro

José Jaime da Cruz

Abstract: After a first contact with Evans' root locus plots, in an introductory course about classical control theory, students usually pose questions for which the answers are not trivially found in the usual textbooks. Examples of such questions are: Can a branch intersect itself? Can two or more branches be coincident? Can a branch intersect its asymptote? In this paper devoted to helping teaching, numerical examples and an incremental property are used for answering some questions about unusual forms of root loci r… Show more

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Cited by 2 publications

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“…The alternative iteration formulas Eqns. (10) to (16) were subjected to tests to determine the most reliable or effective. The results and conclusion of the tests are presented and discussed in section 3.1.…”

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confidence: 99%

Computer-aided root -locus numerical technique

Zubair¹,

Olatunbosun²

2014

Nig. J. Tech.

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The existing technique of manual calcu The existing technique of manual calcu The existing technique of manual calcu The existing technique of manual calcu studies studies studies studies is laborious and time consuming. is laborious and time consuming. is laborious and time consuming. is laborious and time consuming. simple fast mathematical iteration is simple fast mathematical iteration is simple fast mathematical iteration is simple fast mathematical iteration is were formed and te were formed and te were formed and te were formed and tested for convergence. A pair of complementary formulas with highest rate of sted for convergence. A pair of complementary formulas with highest rate of sted for convergence. A pair of complementary formulas with highest rate of sted for convergence. A pair of complementary formulas with highest rate of convergence was selected. The process of convergence was selected. The process of convergence was selected. The process of convergence was selected. The process of were divided into steps which were were divided into steps which were were divided into steps which were were divided into steps which were g g g geometric properties of the root eometric properties of the root eometric properties of the root eometric properties of the root-de de de described in the literature. Root scribed in the literature. Root scribed in the literature. Root scribed in the literature. Root-loci are drawn to scale instead of rough sketches. loci are drawn to scale instead of rough sketches. loci are drawn to scale instead of rough sketches. loci are drawn to scale instead of rough sketches.

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confidence: 99%

Computer-aided root -locus numerical technique

Zubair¹,

Olatunbosun²

2014

Nig. J. Tech.

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On Complementary Root Locus of Biproper Transfer Functions

Teixeira

Assunção

Cardim

et al. 2009

Mathematical Problems in Engineering

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This paper addresses the root locus (locus of positive gain) and the complementary root locus (locus of negative gain) of biproper transfer functions (transfer functions with the same number of poles and zeros). It is shown that the root locus and complementary root locus of a biproper transfer function can be directly obtained from the plot of a suitable strictly proper transfer function (transfer function with more poles than zeros). There exists a lack of sources on the complementary root locus plots. The proposed procedure avoids the problems pointed out by Eydgahi and Ghavamzadeh, is a new method to plot complementary root locus of biproper transfer functions, and offers a better comprehension on this subject. It also extends to biproper open-loop transfer functions, previous results about the exact plot of the complementary root locus using only the well-known root locus rules.

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Simple answers to usual questions about unusual forms of the Evans' root locus plot

Cited by 2 publications

References 9 publications

Computer-aided root -locus numerical technique

Computer-aided root -locus numerical technique

On Complementary Root Locus of Biproper Transfer Functions

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