Fractional delayed control design for linear periodic systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Scopus citations

Abstract

In this paper, the fractional Chebyshev collocation (FCC) method is proposed to design fractional delay controllers for linear systems with periodic coefficients. In our previous study, it was shown that this method can be successfully used to stabilize fractional periodic time-delay systems with the delay terms being of integer orders. In the current paper, it is shown that this method can be extended successfully to design fractional delay controllers for fractional periodic systems. For this propose, the solution of linear periodic systems with fractional delay terms is expressed in a Banach space. The short memory principle is used to show that the actual response of the system can be approximated by an approximated monodromy operator. The approximated monodromy operator yields the solution of a fixed length interval by mapping the solution of the previous interval with the same length. Usually obtaining the approximated monodromy operator is complicated or even impossible. The spectral radius of the approximated monodromy matrix indicates the asymptotic stability of the system. The efficiency of the proposed fractional delayed control is illustrated in the case of a second order system with periodic coefficients.

Original languageEnglish (US)
Title of host publication12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers (ASME)
Volume6
ISBN (Electronic)9780791850183
DOIs
StatePublished - 2016
EventASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016 - Charlotte, United States
Duration: Aug 21 2016Aug 24 2016

Other

OtherASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016
CountryUnited States
CityCharlotte
Period8/21/168/24/16

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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    Dabiri, A., Butcher, E., & Poursina, M. (2016). Fractional delayed control design for linear periodic systems. In 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC201660322