Optimal fractional state feedback control for linear fractional periodic time-delayed systems

Arman Dabiri, Morad Nazari, Eric Butcher

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

24 Citations (Scopus)

Abstract

This paper proposes a new strategy to design an optimal fractional state feedback control for linear fractional periodic time-delayed (FPTD) systems. Although there exist different techniques to design the state feedback control for linear ordinary periodic time-delayed (OPTD) systems such as discretizing their monodromy matrix, there is no systematic method to design state feedback control for FPTD systems. Moreover, linear OPTD systems have the monodromy operator defined explicitly in a Banach space, and can be discretized in arbitrary basis functions. However, linear FPTD systems do not have any monodromy operator because of the nonlocal properties of fractional operators. In the proposed method, a monodromy matrix is defined for the steady state solution. Then, the efficiency of the proposed control technique is shown by implementing the method to a double inverted pendulum with fractional dampers subject to a periodic retarded follower force.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2778-2783
Number of pages6
Volume2016-July
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Other

Other2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period7/6/167/8/16

Fingerprint

State feedback
Feedback control
Banach spaces
Pendulums
Mathematical operators

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Dabiri, A., Nazari, M., & Butcher, E. (2016). Optimal fractional state feedback control for linear fractional periodic time-delayed systems. In 2016 American Control Conference, ACC 2016 (Vol. 2016-July, pp. 2778-2783). [7525339] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525339

Optimal fractional state feedback control for linear fractional periodic time-delayed systems. / Dabiri, Arman; Nazari, Morad; Butcher, Eric.

2016 American Control Conference, ACC 2016. Vol. 2016-July Institute of Electrical and Electronics Engineers Inc., 2016. p. 2778-2783 7525339.

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

Dabiri, A, Nazari, M & Butcher, E 2016, Optimal fractional state feedback control for linear fractional periodic time-delayed systems. in 2016 American Control Conference, ACC 2016. vol. 2016-July, 7525339, Institute of Electrical and Electronics Engineers Inc., pp. 2778-2783, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7525339
Dabiri A, Nazari M, Butcher E. Optimal fractional state feedback control for linear fractional periodic time-delayed systems. In 2016 American Control Conference, ACC 2016. Vol. 2016-July. Institute of Electrical and Electronics Engineers Inc. 2016. p. 2778-2783. 7525339 https://doi.org/10.1109/ACC.2016.7525339
Dabiri, Arman ; Nazari, Morad ; Butcher, Eric. / Optimal fractional state feedback control for linear fractional periodic time-delayed systems. 2016 American Control Conference, ACC 2016. Vol. 2016-July Institute of Electrical and Electronics Engineers Inc., 2016. pp. 2778-2783
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