Extending the Root‐Locus Method to Fractional‐Order Systems

Merrikh-Bayat, Farshad; Afshar, Mahdi

doi:10.1155/2008/528934

Cited by 33 publications

(20 citation statements)

References 20 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, (16) and (17) imply that α and β are complex conjugates with nonzero imaginary parts. Moreover, (13) and (14) imply that for i = 1, . .…”

Section: Quadratic-root-locus Rulesmentioning

confidence: 99%

Quadratically Parameterized Root Locus Analysis

Wellman

Hoagg

2014

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Classical affine root locus applies to controllers that are linear in a parameter k and yield affinely parameterized closed-loop denominator polynomials. This paper presents root locus rules for controllers that are rational in k and yield quadratically parameterized closed-loop denominator polynomials. We show that the quadratic root locus has several advantages relative to the classical affine root locus. Specifically, the quadratic root locus is high-parameter stabilizing for minimum-phase systems that are relative degree 1, 2, or 3. Moreover, the quadratic root locus admits a wider variety of asymptote angles, which provides more controller design flexibility. The quadratic root locus is illustrated on several examples that are difficult to handle using affine root locus, such as high-parameter stabilization of the triple integrator.Index Terms-Affine root locus, quadratic root locus, stabilization.

show abstract

“…In addition, (16) and (17) imply that α and β are complex conjugates with nonzero imaginary parts. Moreover, (13) and (14) imply that for i = 1, . .…”

Section: Quadratic-root-locus Rulesmentioning

confidence: 99%

Quadratically Parameterized Root Locus Analysis

Wellman

Hoagg

2014

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

show abstract

“…T h e g e o m e t r i c m e t h o d s s u c h a s Nyquist type can be used for the stability check in the BIBO sense (bounded-input bounded-output). Root locus is another geometric method that can be used for analysis for FO systems [11], [14]. Also, for linear fractional differential systems of finite dimensions in state-space form, stability can be investigated.…”

Section: Stability Of Fractional-order Systemsmentioning

confidence: 99%

Time and Frequency Domain Analysis of the Linear Fractional-order Systems

Bhole¹,

Patil²,

Vyawahare³

2012

SpecialIssue

View full text Add to dashboard Cite

Abstract-Recent years have seen a tremendous upsurge inthe area related to the use of Fractional-order (FO) differential equations in modeling and control. FO differential equations are found to provide a more realistic, faithful, and compact representations of many real world, natural and manmade systems. FO controllers, on the other hand, have been able to achieve a better closed-loop performance and robustness, than their integer-order counterparts. In this paper, we provide a systematic and rigorous time and frequency domain analysis of linear FO systems. Various concepts like stability, step response, frequency response are discussed in detail for a variety of linear FO systems. We also give the state space representations for these systems and comment on the controllability and observability. The exercise presented here conveys the fact that the time and frequency domain analysis of FO linear systems are very similar to that of the integer-order linear systems.

show abstract

“…Therefore, researchers have mainly preferred to adopt frequency based methods, but we can mention several studies addressing the RL in the scope of fractional systems [20][21][22][23]. More recently the RL was considered for the stability analysis of fractional systems by tacking advantage of commensurable expressions that occur when truncating real valued integrodifferential orders up to a finite precision [24]. This strategy allows the use of built in routines available in several engineering packages, with a good level of integration of commands and editor, but, on the other hand, limits the precision and the type of symbolic expressions.…”

Section: Root Locus Of Fractional Systemsmentioning

confidence: 99%