Dynamical analysis and control of microcantilevers

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

doi:10.1016/S0005-1098(99)00077-1

Dynamical analysis and control of microcantilevers

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

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

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Abstract

In this paper, we study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever 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)	1663-1670
Number of pages	8
Journal	Automatica
Volume	35
Issue number	10
DOIs	https://doi.org/10.1016/S0005-1098(99)00077-1
State	Published - Oct 1999

Bibliographical note

Funding Information:
This research was partly supported by NSF ECS-9632820, NSF ECS-9733802 and AFOSR F49620-97-1-0168.

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10.1016/S0005-1098(99)00077-1

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title = "Dynamical analysis and control of microcantilevers",

abstract = "In this paper, we study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever 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. Mezi{\'c}",

note = "Funding Information: This research was partly supported by NSF ECS-9632820, NSF ECS-9733802 and AFOSR F49620-97-1-0168.",

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T1 - Dynamical analysis and control of microcantilevers

AU - Ashhab, M.

AU - Salapaka, M. V.

AU - Dahleh, M.

AU - Mezić, I.

N1 - Funding Information: This research was partly supported by NSF ECS-9632820, NSF ECS-9733802 and AFOSR F49620-97-1-0168.

PY - 1999/10

Y1 - 1999/10

N2 - In this paper, we study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever 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 behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever 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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DO - 10.1016/S0005-1098(99)00077-1

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VL - 35

SP - 1663

EP - 1670

JO - Automatica

JF - Automatica

IS - 10

ER -

Dynamical analysis and control of microcantilevers

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