Explicit harmonic balance method for transition curve analysis of linear fractional periodic time-delayed systems

Arman Dabiri; Morad Nazari; Eric A. Butcher

doi:10.1016/j.ifacol.2015.09.350

Explicit harmonic balance method for transition curve analysis of linear fractional periodic time-delayed systems

Arman Dabiri, Morad Nazari, Eric A. Butcher

Research output: Contribution to journal › Conference article › peer-review

15 Scopus citations

Abstract

This paper presents an explicit harmonic balance (EHB) method for the analysis of transition curves of linear fractional periodic time delayed (FPTD) systems. The EHB method has advantages in computational efficiency in obtaining transition curves of a FPTD system compared with conventional techniques. The proposed technique is illustrated with parametrically excited single and double pendulum systems, with both time-delayed states and fractional damping.

Original language	English (US)
Pages (from-to)	39-44
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	28
Issue number	12
DOIs	https://doi.org/10.1016/j.ifacol.2015.09.350
State	Published - Jul 1 2015
Event	12th IFAC Workshop on Time Delay Systems, TDS 2015 - Ann Arbor, United States Duration: Jun 28 2015 → Jun 30 2015

Keywords

Floquet theory
Fractional derivative
Harmonic balance
Parametric excitation
Stability
Time delay
Time periodic
Transition curves

ASJC Scopus subject areas

Control and Systems Engineering

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10.1016/j.ifacol.2015.09.350

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title = "Explicit harmonic balance method for transition curve analysis of linear fractional periodic time-delayed systems",

abstract = "This paper presents an explicit harmonic balance (EHB) method for the analysis of transition curves of linear fractional periodic time delayed (FPTD) systems. The EHB method has advantages in computational efficiency in obtaining transition curves of a FPTD system compared with conventional techniques. The proposed technique is illustrated with parametrically excited single and double pendulum systems, with both time-delayed states and fractional damping.",

keywords = "Floquet theory, Fractional derivative, Harmonic balance, Parametric excitation, Stability, Time delay, Time periodic, Transition curves",

author = "Arman Dabiri and Morad Nazari and Butcher, {Eric A.}",

note = "Publisher Copyright: {\textcopyright} 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.; 12th IFAC Workshop on Time Delay Systems, TDS 2015 ; Conference date: 28-06-2015 Through 30-06-2015",

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doi = "10.1016/j.ifacol.2015.09.350",

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TY - JOUR

T1 - Explicit harmonic balance method for transition curve analysis of linear fractional periodic time-delayed systems

AU - Dabiri, Arman

AU - Nazari, Morad

AU - Butcher, Eric A.

PY - 2015/7/1

Y1 - 2015/7/1

N2 - This paper presents an explicit harmonic balance (EHB) method for the analysis of transition curves of linear fractional periodic time delayed (FPTD) systems. The EHB method has advantages in computational efficiency in obtaining transition curves of a FPTD system compared with conventional techniques. The proposed technique is illustrated with parametrically excited single and double pendulum systems, with both time-delayed states and fractional damping.

AB - This paper presents an explicit harmonic balance (EHB) method for the analysis of transition curves of linear fractional periodic time delayed (FPTD) systems. The EHB method has advantages in computational efficiency in obtaining transition curves of a FPTD system compared with conventional techniques. The proposed technique is illustrated with parametrically excited single and double pendulum systems, with both time-delayed states and fractional damping.

KW - Floquet theory

KW - Fractional derivative

KW - Harmonic balance

KW - Parametric excitation

KW - Stability

KW - Time delay

KW - Time periodic

KW - Transition curves

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U2 - 10.1016/j.ifacol.2015.09.350

DO - 10.1016/j.ifacol.2015.09.350

M3 - Conference article

SN - 2405-8963

VL - 28

SP - 39

EP - 44

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 12

T2 - 12th IFAC Workshop on Time Delay Systems, TDS 2015

Y2 - 28 June 2015 through 30 June 2015

ER -

Explicit harmonic balance method for transition curve analysis of linear fractional periodic time-delayed systems

Abstract

Keywords

ASJC Scopus subject areas

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