Disturbance Attenuation in the Euler-Bernoulli Beam with Viscous and Kelvin-Voigt Damping via Piezoelectric Actuators

Anton Selivanov; Emilia Fridman

doi:10.1109/CDC49753.2023.10383762

Disturbance Attenuation in the Euler-Bernoulli Beam with Viscous and Kelvin-Voigt Damping via Piezoelectric Actuators

Anton Selivanov, Emilia Fridman

School of Electrical Engineering

University of Sheffield

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We design a state-feedback controller, applied via piezoelectric actuators, that suppresses the effect of a distributed disturbance in the Euler-Bernoulli beam with viscous and Kelvin-Voigt damping. The controller is designed to improve performance on a finite number of modes. Its effect on the remaining (infinitely many) modes is analysed by constructing an appropriate Lyapunov functional, whose properties are guaranteed by the feasibility of linear matrix inequalities (LMIs). The LMIs allow us to design suitable controller gain and estimate the induced L2 gain. A numerical example demonstrates how this modal decomposition approach leads to a controller that significantly reduces the L2 gain.

Original language	English
Title of host publication	2023 62nd IEEE Conference on Decision and Control, CDC 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1961-1966
Number of pages	6
ISBN (Electronic)	9798350301243
DOIs	https://doi.org/10.1109/CDC49753.2023.10383762
State	Published - 2023
Event	62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: 13 Dec 2023 → 15 Dec 2023

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	62nd IEEE Conference on Decision and Control, CDC 2023
Country/Territory	Singapore
City	Singapore
Period	13/12/23 → 15/12/23

Access to Document

10.1109/CDC49753.2023.10383762

Cite this

Selivanov, A., & Fridman, E. (2023). Disturbance Attenuation in the Euler-Bernoulli Beam with Viscous and Kelvin-Voigt Damping via Piezoelectric Actuators. In 2023 62nd IEEE Conference on Decision and Control, CDC 2023 (pp. 1961-1966). (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC49753.2023.10383762

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abstract = "We design a state-feedback controller, applied via piezoelectric actuators, that suppresses the effect of a distributed disturbance in the Euler-Bernoulli beam with viscous and Kelvin-Voigt damping. The controller is designed to improve performance on a finite number of modes. Its effect on the remaining (infinitely many) modes is analysed by constructing an appropriate Lyapunov functional, whose properties are guaranteed by the feasibility of linear matrix inequalities (LMIs). The LMIs allow us to design suitable controller gain and estimate the induced L2 gain. A numerical example demonstrates how this modal decomposition approach leads to a controller that significantly reduces the L2 gain.",

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Selivanov, A & Fridman, E 2023, Disturbance Attenuation in the Euler-Bernoulli Beam with Viscous and Kelvin-Voigt Damping via Piezoelectric Actuators. in 2023 62nd IEEE Conference on Decision and Control, CDC 2023. Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 1961-1966, 62nd IEEE Conference on Decision and Control, CDC 2023, Singapore, Singapore, 13/12/23. https://doi.org/10.1109/CDC49753.2023.10383762

Disturbance Attenuation in the Euler-Bernoulli Beam with Viscous and Kelvin-Voigt Damping via Piezoelectric Actuators. / Selivanov, Anton; Fridman, Emilia.
2023 62nd IEEE Conference on Decision and Control, CDC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 1961-1966 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We design a state-feedback controller, applied via piezoelectric actuators, that suppresses the effect of a distributed disturbance in the Euler-Bernoulli beam with viscous and Kelvin-Voigt damping. The controller is designed to improve performance on a finite number of modes. Its effect on the remaining (infinitely many) modes is analysed by constructing an appropriate Lyapunov functional, whose properties are guaranteed by the feasibility of linear matrix inequalities (LMIs). The LMIs allow us to design suitable controller gain and estimate the induced L2 gain. A numerical example demonstrates how this modal decomposition approach leads to a controller that significantly reduces the L2 gain.

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Selivanov A, Fridman E. Disturbance Attenuation in the Euler-Bernoulli Beam with Viscous and Kelvin-Voigt Damping via Piezoelectric Actuators. In 2023 62nd IEEE Conference on Decision and Control, CDC 2023. Institute of Electrical and Electronics Engineers Inc. 2023. p. 1961-1966. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC49753.2023.10383762

Disturbance Attenuation in the Euler-Bernoulli Beam with Viscous and Kelvin-Voigt Damping via Piezoelectric Actuators

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