Control of chaos in atomic force microscopes

M. Ashhab; M. V. Salapaka; M. Dahleh; I. Mezic

doi:10.1109/acc.1997.611784

Control of chaos in atomic force microscopes

M. Ashhab, M. V. Salapaka, M. Dahleh, I. Mezic

Electrical and Computer Engineering

Research output: Contribution to journal › Conference article › peer-review

15 Scopus citations

Abstract

In this paper, we study the dynamical behaviour of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the micro-cantilever by a single mode approximation and the interaction between the sample and cantilever by a van der Waals (vdW) potential. The cantilever is vibrated by a sinusoidal input, and its deflection is detected optically. We analyze the forced dynamics using Melnikov method, which reveals the region in the space of physical parameters where chaotic motion is possible. In addition, using a proportional and derivative controller we compute the Melnikov function in terms of the parameters of the controller. Using this relation it is possible to design controllers that will remove the possibility of chaos.

Original language	English (US)
Pages (from-to)	196-202
Number of pages	7
Journal	Proceedings of the American Control Conference
Volume	1
DOIs	https://doi.org/10.1109/acc.1997.611784
State	Published - 1997
Event	Proceedings of the 1997 American Control Conference. Part 3 (of 6) - Albuquerque, NM, USA Duration: Jun 4 1997 → Jun 6 1997

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title = "Control of chaos in atomic force microscopes",

abstract = "In this paper, we study the dynamical behaviour of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the micro-cantilever by a single mode approximation and the interaction between the sample and cantilever by a van der Waals (vdW) potential. The cantilever is vibrated by a sinusoidal input, and its deflection is detected optically. We analyze the forced dynamics using Melnikov method, which reveals the region in the space of physical parameters where chaotic motion is possible. In addition, using a proportional and derivative controller we compute the Melnikov function in terms of the parameters of the controller. Using this relation it is possible to design controllers that will remove the possibility of chaos.",

author = "M. Ashhab and Salapaka, {M. V.} and M. Dahleh and I. Mezic",

year = "1997",

doi = "10.1109/acc.1997.611784",

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journal = "Proceedings of the American Control Conference",

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T1 - Control of chaos in atomic force microscopes

AU - Ashhab, M.

AU - Salapaka, M. V.

AU - Dahleh, M.

AU - Mezic, I.

PY - 1997

Y1 - 1997

N2 - In this paper, we study the dynamical behaviour of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the micro-cantilever by a single mode approximation and the interaction between the sample and cantilever by a van der Waals (vdW) potential. The cantilever is vibrated by a sinusoidal input, and its deflection is detected optically. We analyze the forced dynamics using Melnikov method, which reveals the region in the space of physical parameters where chaotic motion is possible. In addition, using a proportional and derivative controller we compute the Melnikov function in terms of the parameters of the controller. Using this relation it is possible to design controllers that will remove the possibility of chaos.

AB - In this paper, we study the dynamical behaviour of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the micro-cantilever by a single mode approximation and the interaction between the sample and cantilever by a van der Waals (vdW) potential. The cantilever is vibrated by a sinusoidal input, and its deflection is detected optically. We analyze the forced dynamics using Melnikov method, which reveals the region in the space of physical parameters where chaotic motion is possible. In addition, using a proportional and derivative controller we compute the Melnikov function in terms of the parameters of the controller. Using this relation it is possible to design controllers that will remove the possibility of chaos.

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T2 - Proceedings of the 1997 American Control Conference. Part 3 (of 6)

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Control of chaos in atomic force microscopes

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