Selivanov, A. orcid.org/0000-0001-5075-7229 and Fridman, E. (Submitted: 2023) Disturbance attenuation in the Euler-Bernoulli beam using piezoelectric actuators. [Preprint - arXiv] (Submitted)
Abstract
We consider a simply-supported Euler-Bernoulli beam with viscous and Kelvin-Voigt damping. Our objective is to attenuate the effect of an unknown distributed disturbance using one piezoelectric actuator. We show how to design a suitable H∞ state-feedback controller based on a finite number of dominating modes. If the remaining (infinitely many) modes are ignored, the calculated L2 gain is wrong. This happens because of the spillover phenomenon that occurs when the effect of the control on truncated modes is not accounted for in the feedback design. We propose a simple modification of the H∞ cost that prevents spillover. The key idea is to treat the control as a disturbance in the truncated modes and find the corresponding L2 gains using the bounded real lemma. These L2 gains are added to the control weight in the H∞ cost for the dominating modes, which prevents spillover. A numerical simulation of an aluminum beam with realistic parameters demonstrates the effectiveness of the proposed method.
Metadata
Item Type: | Preprint |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2023 The Author(s). For reuse permissions, please contact the Author(s). |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 09 Jan 2024 11:11 |
Last Modified: | 09 Jan 2024 11:11 |
Status: | Submitted |
Identification Number: | 10.48550/arXiv.2308.05551 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:207311 |