A review of the systems approach to the analysis of dynamic-mode atomic force microscopy

Abu Sebastian, Anil Gannepalli, Murti V. Salapaka

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37 Scopus citations


The atomic force microscope (AFM) is one of the foremost tools for imaging, measuring and manipulating matter at the nanoscale. This brief presents a review of the systems and control approach to analyzing the challenging dynamic-mode operation of the AFM. A Luré system perspective of the AFM dynamics facilitates the application of powerful tools from systems theory for the analysis. The harmonic balance method provides significant insights into the steady-state behavior as well as a framework for identifying the tip-sample interaction force. A simple piecewise-linear tip-sample interaction model and its identification using the harmonic balance method is presented. The dominant first harmonic is analyzed using multivalued frequency responses and the corresponding stability conditions. The ability of the simple tip-sample interaction model to capture the intricate nonlinear behavior of the first harmonic is demonstrated. This also points to the importance of studying the higher harmonics to obtain finer details of the tip-sample interaction. The suitability of the Luré system perspective for the analysis of the higher harmonics is demonstrated.

Original languageEnglish (US)
Pages (from-to)952-959
Number of pages8
JournalIEEE Transactions on Control Systems Technology
Issue number5 SPEC. ISS.
StatePublished - 2007

Bibliographical note

Funding Information:
Manuscript received February 19, 2007. Manuscript received in final form April 20, 2007. Recommended by Guest Editor S. Devasia. The work of M. Salapaka was supported by the National Science Foundation under Grant CMS 0626171 and Grant ECS 0601571. A. Sebastian is with IBM Research GmbH, Zurich Research Laboratory, 8803 Rüschlikon, Switzerland (e-mail: ase@zurich.ibm.com). A. Gannepalli is with Asylum Research Inc., Santa Barbara, CA 93117 USA (e-mail: ganil@rasy.com). M. V. Salapaka is with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 USA (e-mail: murti@iastate. edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2007.902959


  • Asymptotic methods
  • Atomic force microscopy (AFM)
  • Dynamic-mode AFM
  • Harmonic balance
  • Integral quadratic constraints
  • Luré system

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