Cantilever Dynamics Modelling for the Transverse Dynamic Force Microscope

Thang Nguyen Tien; C Edwards; Guido Herrmann; Toshiaki Hatano; Stuart C Burgess; Mervyn J Miles

doi:10.1109/CDC.2014.7039564

Cantilever Dynamics Modelling for the Transverse Dynamic Force Microscope

Thang Nguyen Tien, C Edwards, Guido Herrmann, Toshiaki Hatano, Stuart C Burgess, Mervyn J Miles

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

3 Citations (Scopus)

Abstract

This paper studies the dynamics of the cantilever
in a Transverse Dynamic Force Microscope (TDFM). A series
expansion approach for the irrational transfer functions of
modelling the cantilever dynamics is presented in terms of
an infinite sum of second-order rational transfer functions
and a finite dimensional linear time invariant (LTI) system
model is developed. An approximate model of the cantilever
can then be obtained using a finite number of rational transfer functions. This approach preserves the physical constants from the underlying partial differential equation, and retains them in the approximate model. Future work will use these finite dimensional LTI systems as the basis for the design of observers and controllers for the TDFM at the NSQI centre at the University of Bristol.

Original language	English
Title of host publication	Proceedings of the 53rd Annual Conference on Decision and Control, Los Angeles, USA
DOIs	https://doi.org/10.1109/CDC.2014.7039564
Publication status	Published - 2014

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Robustness and adaptivity: advanced control and estimation algorithms for the transverse dynamic atomic force microscope
Herrmann, G. (Principal Investigator)
1/11/11 → 1/05/15
Project: Research

Cite this

@inproceedings{bbf6a95294af4309827a852ad6abedf9,

title = "Cantilever Dynamics Modelling for the Transverse Dynamic Force Microscope",

abstract = "This paper studies the dynamics of the cantileverin a Transverse Dynamic Force Microscope (TDFM). A seriesexpansion approach for the irrational transfer functions ofmodelling the cantilever dynamics is presented in terms ofan infinite sum of second-order rational transfer functionsand a finite dimensional linear time invariant (LTI) systemmodel is developed. An approximate model of the cantilevercan then be obtained using a finite number of rational transfer functions. This approach preserves the physical constants from the underlying partial differential equation, and retains them in the approximate model. Future work will use these finite dimensional LTI systems as the basis for the design of observers and controllers for the TDFM at the NSQI centre at the University of Bristol.",

author = "{Nguyen Tien}, Thang and C Edwards and Guido Herrmann and Toshiaki Hatano and Burgess, {Stuart C} and Miles, {Mervyn J}",

year = "2014",

doi = "10.1109/CDC.2014.7039564",

language = "English",

booktitle = "Proceedings of the 53rd Annual Conference on Decision and Control, Los Angeles, USA",

}

TY - GEN

T1 - Cantilever Dynamics Modelling for the Transverse Dynamic Force Microscope

AU - Nguyen Tien, Thang

AU - Edwards, C

AU - Herrmann, Guido

AU - Hatano, Toshiaki

AU - Burgess, Stuart C

AU - Miles, Mervyn J

PY - 2014

Y1 - 2014

N2 - This paper studies the dynamics of the cantileverin a Transverse Dynamic Force Microscope (TDFM). A seriesexpansion approach for the irrational transfer functions ofmodelling the cantilever dynamics is presented in terms ofan infinite sum of second-order rational transfer functionsand a finite dimensional linear time invariant (LTI) systemmodel is developed. An approximate model of the cantilevercan then be obtained using a finite number of rational transfer functions. This approach preserves the physical constants from the underlying partial differential equation, and retains them in the approximate model. Future work will use these finite dimensional LTI systems as the basis for the design of observers and controllers for the TDFM at the NSQI centre at the University of Bristol.

AB - This paper studies the dynamics of the cantileverin a Transverse Dynamic Force Microscope (TDFM). A seriesexpansion approach for the irrational transfer functions ofmodelling the cantilever dynamics is presented in terms ofan infinite sum of second-order rational transfer functionsand a finite dimensional linear time invariant (LTI) systemmodel is developed. An approximate model of the cantilevercan then be obtained using a finite number of rational transfer functions. This approach preserves the physical constants from the underlying partial differential equation, and retains them in the approximate model. Future work will use these finite dimensional LTI systems as the basis for the design of observers and controllers for the TDFM at the NSQI centre at the University of Bristol.

U2 - 10.1109/CDC.2014.7039564

DO - 10.1109/CDC.2014.7039564

M3 - Conference Contribution (Conference Proceeding)

BT - Proceedings of the 53rd Annual Conference on Decision and Control, Los Angeles, USA

ER -

Cantilever Dynamics Modelling for the Transverse Dynamic Force Microscope

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Projects

Robustness and adaptivity: advanced control and estimation algorithms for the transverse dynamic atomic force microscope

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