Optimal resonant control of flexible structures

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

When introducing a resonant controller for a particular vibration mode in a structure this mode splits into two. A design principle is developed for resonant control based oil equal damping of these two modes. First the design principle is developed for control of a system with a single degree of freedom, and then it is extended to multi-mode structures. A root locus analysis of the controlled single-mode structure identifies the equal modal damping property as a condition oil the linear and Cubic terms of the characteristic equation. Particular solutions for filtered displacement feedback and filtered acceleration feedback are developed by combining the root locus analysis with optimal properties of the displacement amplification frequency curve. The results are then extended to multi-mode structures by including a quasi-static representation of the background modes in the equations for the damped mode. Applications to multi-degree-of-freedom systems are illustrated by idealized models of a piezoelectric sensor-actuator device on a beam and an accelerometer-actuator device oil a cable. In both cases near-ideal response characteristics are obtained, when including the quasi-static correction of the modal properties.
Original languageEnglish
JournalJournal of Sound and Vibration
Volume323
Issue number3-5
Pages (from-to)530-554
ISSN0022-460X
DOIs
Publication statusPublished - 2009

Cite this

@article{05cc8e81e8ea4d179932d616770aa307,
title = "Optimal resonant control of flexible structures",
abstract = "When introducing a resonant controller for a particular vibration mode in a structure this mode splits into two. A design principle is developed for resonant control based oil equal damping of these two modes. First the design principle is developed for control of a system with a single degree of freedom, and then it is extended to multi-mode structures. A root locus analysis of the controlled single-mode structure identifies the equal modal damping property as a condition oil the linear and Cubic terms of the characteristic equation. Particular solutions for filtered displacement feedback and filtered acceleration feedback are developed by combining the root locus analysis with optimal properties of the displacement amplification frequency curve. The results are then extended to multi-mode structures by including a quasi-static representation of the background modes in the equations for the damped mode. Applications to multi-degree-of-freedom systems are illustrated by idealized models of a piezoelectric sensor-actuator device on a beam and an accelerometer-actuator device oil a cable. In both cases near-ideal response characteristics are obtained, when including the quasi-static correction of the modal properties.",
author = "Steen Krenk and H{\o}gsberg, {Jan Becker}",
year = "2009",
doi = "10.1016/j.jsv.2009.01.031",
language = "English",
volume = "323",
pages = "530--554",
journal = "Journal of Sound and Vibration",
issn = "0022-460X",
publisher = "Elsevier",
number = "3-5",

}

Optimal resonant control of flexible structures. / Krenk, Steen; Høgsberg, Jan Becker.

In: Journal of Sound and Vibration, Vol. 323, No. 3-5, 2009, p. 530-554.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Optimal resonant control of flexible structures

AU - Krenk, Steen

AU - Høgsberg, Jan Becker

PY - 2009

Y1 - 2009

N2 - When introducing a resonant controller for a particular vibration mode in a structure this mode splits into two. A design principle is developed for resonant control based oil equal damping of these two modes. First the design principle is developed for control of a system with a single degree of freedom, and then it is extended to multi-mode structures. A root locus analysis of the controlled single-mode structure identifies the equal modal damping property as a condition oil the linear and Cubic terms of the characteristic equation. Particular solutions for filtered displacement feedback and filtered acceleration feedback are developed by combining the root locus analysis with optimal properties of the displacement amplification frequency curve. The results are then extended to multi-mode structures by including a quasi-static representation of the background modes in the equations for the damped mode. Applications to multi-degree-of-freedom systems are illustrated by idealized models of a piezoelectric sensor-actuator device on a beam and an accelerometer-actuator device oil a cable. In both cases near-ideal response characteristics are obtained, when including the quasi-static correction of the modal properties.

AB - When introducing a resonant controller for a particular vibration mode in a structure this mode splits into two. A design principle is developed for resonant control based oil equal damping of these two modes. First the design principle is developed for control of a system with a single degree of freedom, and then it is extended to multi-mode structures. A root locus analysis of the controlled single-mode structure identifies the equal modal damping property as a condition oil the linear and Cubic terms of the characteristic equation. Particular solutions for filtered displacement feedback and filtered acceleration feedback are developed by combining the root locus analysis with optimal properties of the displacement amplification frequency curve. The results are then extended to multi-mode structures by including a quasi-static representation of the background modes in the equations for the damped mode. Applications to multi-degree-of-freedom systems are illustrated by idealized models of a piezoelectric sensor-actuator device on a beam and an accelerometer-actuator device oil a cable. In both cases near-ideal response characteristics are obtained, when including the quasi-static correction of the modal properties.

U2 - 10.1016/j.jsv.2009.01.031

DO - 10.1016/j.jsv.2009.01.031

M3 - Journal article

VL - 323

SP - 530

EP - 554

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 3-5

ER -