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Research Papers

Analysis of Oscillations in Relay Feedback Systems With Fractional-Order Integrating Plants

[+] Author and Article Information
Davood Rezaei

Electrical Engineering Department,
Sharif University of Technology,
Tehran 1458889694, Iran

Mohammad Saleh Tavazoei

Electrical Engineering Department,
Sharif University of Technology,
Tehran 1458889694, Iran
e-mail: tavazoei@sharif.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 1, 2016; final manuscript received June 2, 2017; published online July 12, 2017. Assoc. Editor: Bernard Brogliato.

J. Comput. Nonlinear Dynam 12(5), 051023 (Jul 12, 2017) (7 pages) Paper No: CND-16-1315; doi: 10.1115/1.4037103 History: Received July 01, 2016; Revised June 02, 2017

Oscillatory behavior and transfer properties of relay feedback systems with a linear plant including a fractional-order integrator are studied in this paper. An expression for system response in the time domain is obtained by means of short memory principle, Poincare return map, and Mittag–Leffler functions. On the basis of this expression, the frequency of self-excited oscillations is approximated. In addition, the locus of perturbed relay system (LPRS) is derived to analyze the input–output properties of the relay system. The presented analysis is supported by a numerical example.

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Figures

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Fig. 1

A relay feedback system with fractional-order integrating plant

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Fig. 2

LPRS functions for four values of α in the complex plane

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Fig. 3

System response to a sinusoidal input

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