Root locus practical sketching rules for fractional-order systems
type: Item
instance of: scholarly article
title: Root locus practical sketching rules for fractional-order systems
zbMATH Open document ID: 1293.93368
DOI: 10.1155/2013/102068
author: António M. Lopes
author: José A. Tenreiro Machado
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: For integer-order systems, there are well-known practical rules for Root Locus (RL) sketching. Nevertheless, these rules cannot be directly applied to Fractional-Order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalizes several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 6306022
zbMATH Keywords: root locus rules
zbMATH Keywords: fractional-order (FO) systems
zbMATH Keywords: noninteger polynomials
zbMATH Keywords: FO zeros and poles
Wikidata QID: Q58915279
describes a project that uses: sysdfod
describes a project that uses: CRONE
describes a project that uses: DFOC
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/102068
OpenAlex ID: W1984039574
cites work: The Root Locus Method: A Survey
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: Stability properties for generalized fractional differential systems
cites work: Stability of Fractional-Order Systems with Rational Orders
cites work: Extending the root-locus method to fractional-order systems
cites work: Root locus of fractional linear systems
cites work: Q3141895
cites work: Q3141902
cites work: Q4233638
cites work: Q5699297
cites work: The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
cites work: Q4844958
cites work: Q5302855
cites work: Q5190149
cites work: Fractional-order systems and controls. Fundamentals and applications
cites work: Recent history of fractional calculus
cites work: Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order $\alpha$: The $0≪\alpha≪1$ Case
cites work: Newtonian law with memory
cites work: Dynamics of the dow Jones and the NASDAQ stock indexes
cites work: Mechanical properties and impedance model for the branching network of the sapping system in the leaf of Hydrangea macrophylla
cites work: Dynamical analysis of the global warming
cites work: Fractional dynamics in DNA
cites work: Fractional variational calculus in terms of Riesz fractional derivatives
cites work: Design equations for fractional-order sinusoidal oscillators: Four practical circuit examples
cites work: Fractional-order nonlinear systems. Modeling, analysis and simulation
cites work: Q5327977
Recommended article: Extending the root-locus method to fractional-order systems
Recommended article: Root locus of fractional linear systems
Recommended article: Mathematical Techniques of Fractional Order Systems
Recommended article: Order and pole locator estimation in fractional order systems using bode diagram
Recommended article: Q4698585
Recommended article: Fractional-order Systems and the Internal Model Principle
Recommended article: Fraction representations of non-linear systems: a simplified approach
Recommended article: Fractional order polytopic systems: robust stability and stabilisation
Recommended article: Q4260146
Recommended article: Partial practical stability for fractional‐order nonlinear systems
description: scientific article; zbMATH DE number 6306022