Extending the root-locus method to fractional-order systems
type: Item
instance of: scholarly article
title: Extending the root-locus method to fractional-order systems
zbMATH Open document ID: 1262.93010
DOI: 10.1155/2008/528934
author: Farshad Merrikh-Bayat
author: Mahdi Afshar
published in: Journal of Applied Mathematics
publication date: 2008-08-15T00:00:00Z
review text: Summary: The well-known root-locus method is developed for special subset of linear time-invariant systems known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable \(s\). Such systems are defined on a Riemann surface because of their multivalued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis, and breakaway points are extended to fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm.
Mathematics Subject Classification ID: 93C80
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 5312419
zbMATH Keywords: root-locus method
zbMATH Keywords: linear time-invariant systems
zbMATH Keywords: fractional-order systems
zbMATH Keywords: transfer functions
zbMATH Keywords: closed-loop stability
Wikidata QID: Q58645958
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2008/528934
OpenAlex ID: W2042738128
cites work: Q4003780
cites work: The Root Locus Method: A Survey
cites work: A Closed Expression for the Root Locus Method
cites work: Numerical Technique to Trace the Loci of the Complex Roots of Characteristic Equations
cites work: Root-Locus and Boundary Feedback Design for a Class of Distributed Parameter Systems
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Applications of fractional calculus in physics
cites work: Continuous-time fractional ARMA processes
cites work: Identification of fractional systems using an output-error technique
cites work: Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
cites work: Tuning of fractional PID controllers with Ziegler-Nichols-type rules
cites work: State-space representation for fractional order controllers
cites work: Q3141902
cites work: Definition of Physically Consistent Damping Laws with Fractional Derivatives
cites work: Q3270793
cites work: Q3748518
cites work: Q5327977
cites work: Stability properties for generalized fractional differential systems
cites work: The Asymptotes of the Root Locus
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
DBLP publication ID: journals/jam/Merrikh-BayatA08
description: scientific article; zbMATH DE number 5312419