Manifold based control for a 1-dof beam with one-sided spring using feedback linearization

M.F. Heertjes; M.J.G. Molengraft, van de; A. Kraker, de; D.H. Campen, van; J.J. Kok

doi:10.1109/COC.1997.633438

Manifold based control for a 1-dof beam with one-sided spring using feedback linearization

M.F. Heertjes, M.J.G. Molengraft, van de, A. Kraker, de, D.H. Campen, van, J.J. Kok

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Hoofdstuk › Academic › peer review

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Vibration reduction in a harmonically excited 1-DOF beam with one-sided spring is realized by forcing the system from a long-term stable ½ subharmonic response towards a coexisting unstable harmonic response of lower vibration amplitude using feedback linearization. The control effort can be kept small once the unstable harmonic response is stabilized, because this response is a natural solution of the uncontrolled system. To reduce control effort, the approximated stable manifold is used to determine the desired trajectory for control. The stable manifold is approximated using the stable eigenvectors of the monodromy matrix. Due to the local validity of the approximation, a two-stage control strategy is implemented. In the first stage, the system state is controlled directly towards the unstable harmonic response, to reach the region where the stable manifold can be approximated accurately by the stable eigenvectors. In the second stage, the system state is controlled towards the stable eigenvectors, and evolves towards the unstable harmonic response with hardly any control effort.

Originele taal-2	Engels
Titel	Proceedings of the 1st International conference on Control of Oscillations and Chaos, 27-29 August 1997, St. Petersburg, Russia
Redacteuren	F.L. Chernousko, A.L. Fradkov
Plaats van productie	Piscataway
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	5-8
ISBN van geprinte versie	0-7803-4247-X
DOI's	https://doi.org/10.1109/COC.1997.633438
Status	Gepubliceerd - 1997

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Heertjes, M. F., Molengraft, van de, M. J. G., Kraker, de, A., Campen, van, D. H., & Kok, J. J. (1997). Manifold based control for a 1-dof beam with one-sided spring using feedback linearization. In F. L. Chernousko, & A. L. Fradkov (editors), Proceedings of the 1st International conference on Control of Oscillations and Chaos, 27-29 August 1997, St. Petersburg, Russia (blz. 5-8). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/COC.1997.633438

Heertjes, M.F. ; Molengraft, van de, M.J.G. ; Kraker, de, A. et al. / Manifold based control for a 1-dof beam with one-sided spring using feedback linearization. Proceedings of the 1st International conference on Control of Oscillations and Chaos, 27-29 August 1997, St. Petersburg, Russia. redacteur / F.L. Chernousko ; A.L. Fradkov. Piscataway : Institute of Electrical and Electronics Engineers, 1997. blz. 5-8

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title = "Manifold based control for a 1-dof beam with one-sided spring using feedback linearization",

abstract = "Vibration reduction in a harmonically excited 1-DOF beam with one-sided spring is realized by forcing the system from a long-term stable ½ subharmonic response towards a coexisting unstable harmonic response of lower vibration amplitude using feedback linearization. The control effort can be kept small once the unstable harmonic response is stabilized, because this response is a natural solution of the uncontrolled system. To reduce control effort, the approximated stable manifold is used to determine the desired trajectory for control. The stable manifold is approximated using the stable eigenvectors of the monodromy matrix. Due to the local validity of the approximation, a two-stage control strategy is implemented. In the first stage, the system state is controlled directly towards the unstable harmonic response, to reach the region where the stable manifold can be approximated accurately by the stable eigenvectors. In the second stage, the system state is controlled towards the stable eigenvectors, and evolves towards the unstable harmonic response with hardly any control effort.",

author = "M.F. Heertjes and {Molengraft, van de}, M.J.G. and {Kraker, de}, A. and {Campen, van}, D.H. and J.J. Kok",

year = "1997",

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Heertjes, MF , Molengraft, van de, MJG, Kraker, de, A, Campen, van, DH & Kok, JJ 1997, Manifold based control for a 1-dof beam with one-sided spring using feedback linearization. in FL Chernousko & AL Fradkov (uitgave), Proceedings of the 1st International conference on Control of Oscillations and Chaos, 27-29 August 1997, St. Petersburg, Russia. Institute of Electrical and Electronics Engineers, Piscataway, blz. 5-8. https://doi.org/10.1109/COC.1997.633438

Manifold based control for a 1-dof beam with one-sided spring using feedback linearization. / Heertjes, M.F.; Molengraft, van de, M.J.G.; Kraker, de, A. et al.
Proceedings of the 1st International conference on Control of Oscillations and Chaos, 27-29 August 1997, St. Petersburg, Russia. uitgave / F.L. Chernousko; A.L. Fradkov. Piscataway: Institute of Electrical and Electronics Engineers, 1997. blz. 5-8.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Hoofdstuk › Academic › peer review

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AU - Heertjes, M.F.

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N2 - Vibration reduction in a harmonically excited 1-DOF beam with one-sided spring is realized by forcing the system from a long-term stable ½ subharmonic response towards a coexisting unstable harmonic response of lower vibration amplitude using feedback linearization. The control effort can be kept small once the unstable harmonic response is stabilized, because this response is a natural solution of the uncontrolled system. To reduce control effort, the approximated stable manifold is used to determine the desired trajectory for control. The stable manifold is approximated using the stable eigenvectors of the monodromy matrix. Due to the local validity of the approximation, a two-stage control strategy is implemented. In the first stage, the system state is controlled directly towards the unstable harmonic response, to reach the region where the stable manifold can be approximated accurately by the stable eigenvectors. In the second stage, the system state is controlled towards the stable eigenvectors, and evolves towards the unstable harmonic response with hardly any control effort.

AB - Vibration reduction in a harmonically excited 1-DOF beam with one-sided spring is realized by forcing the system from a long-term stable ½ subharmonic response towards a coexisting unstable harmonic response of lower vibration amplitude using feedback linearization. The control effort can be kept small once the unstable harmonic response is stabilized, because this response is a natural solution of the uncontrolled system. To reduce control effort, the approximated stable manifold is used to determine the desired trajectory for control. The stable manifold is approximated using the stable eigenvectors of the monodromy matrix. Due to the local validity of the approximation, a two-stage control strategy is implemented. In the first stage, the system state is controlled directly towards the unstable harmonic response, to reach the region where the stable manifold can be approximated accurately by the stable eigenvectors. In the second stage, the system state is controlled towards the stable eigenvectors, and evolves towards the unstable harmonic response with hardly any control effort.

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Heertjes MF , Molengraft, van de MJG, Kraker, de A, Campen, van DH, Kok JJ. Manifold based control for a 1-dof beam with one-sided spring using feedback linearization. In Chernousko FL, Fradkov AL, redacteurs, Proceedings of the 1st International conference on Control of Oscillations and Chaos, 27-29 August 1997, St. Petersburg, Russia. Piscataway: Institute of Electrical and Electronics Engineers. 1997. blz. 5-8 doi: 10.1109/COC.1997.633438

Manifold based control for a 1-dof beam with one-sided spring using feedback linearization

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