Extending the Root-Locus Method to Fractional-Order Systems. (15th June 2008)

• Record Type: Journal Article
• Authors: Merrikh-Bayat, Farshad; Afshar, Mahdi
• Other Names: Tesi Alberto Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2008(2008)
• Publication Date: 2008-06-15
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2008/528934
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : 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.