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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Adaptive Control of Atomic Force Microscope for Surface-Profile Estimation

Journal of Applied Nonlinear Dynamics 8(3) (2019) 327--344 | DOI:10.5890/JAND.2019.09.001

Nyesunthi Apiwattanalunggarn

Department of Mechanical Engineering, Kasetsart University, 50 Phaholyothin Road, Jatujak, Bangkok 10900, Thailand

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This paper describes a methodology for designing an adaptive tracking controller of an atomic force microscope to estimate a surface profile of a sample. A microbeam of the atomic force microscope is modeled as an Euler-Bernoulli beam with single mode considered. A tip-sample interaction force used here is a piecewise function described by the attractive van der Waals force and the repulsive Derjaguin-Muller-Toporov force which can represent the indentation made by a tip of the microbeam into the sample surface. The adaptive-tracking controllers for both regions are designed based on adaptive control Lyapunov functions. With the driving and measured signals, the controlled acceleration is generated and superimposed onto the harmonic excitation and the estimated surface profile is obtained. If the tip of the microbeam taps harder on the sample surface, the more estimation error is obtained. To reduce the estimated surface-profile error, the regression model needs more higher-order terms to approximate the repulsive Derjaguin-Muller-Toporov force.


  1. [1]  Binnig, G., Quate, C.F., and Gerber, C. (1986), Atomic force microscope, Physical Review Letters, 56(9), 930-933.
  2. [2]  Ashhab, M., Salapaka, M.V., Dahleh, M., and Mezic, I. (1999), Melnikov-based dynamical analysis of microcantilevers in scanning probe microscopy, Nonlinear Dynamics, 20(1999), 197-220.
  3. [3]  Xu, L.C. and Siedlecki, C.A. (2017), Atomic force microscopy, Comprehensive Biomaterials II, 3, 25-45.
  4. [4]  Rifai, O.M.E. and Youcef-Toumi, K. (2007), On automating atomic force microscopes: An adaptive control approach, Control Engineering Practice, 15, 349-361.
  5. [5]  Kuiper, S., Van den Hof, P.M.J., and Schitter, G. (2013), Integrated design of the feedback controller and topography estimator for atomic force microscopy, Control Engineering Practice, 21, 1110-1120.
  6. [6]  Albrecht, T.R., Grutter, P., Horne, D., and Rugar, D. (1991), Frequency modulation detection using high-Q cantilevers for enhanced force microscope sensitivity, J. Appl. Phys., 69(1991), 668-673.
  7. [7]  Yabuno, H., Kaneko, H., Kuroda, M., and Kobayashi, T. (2008), Van der Pol type self-excited micro-cantilever probe of atomic force microscopy, Nonlinear Dynamics, 54(2008), 137-149.
  8. [8]  Fang, Y., Feemster, M., Dawson, D., and Jalili, N.M. (2005), Nonlinear control techniques for an atomic force microscope system, Journal of Control Theory and Applications, 1(2005), 85-92.
  9. [9]  Lee, S.I., Howell, S.W., Raman, A., and Reifenberger, R. (2003), Nonlinear dynamic perspectives on dynamic force microscopy, Ultramicroscopy, 97(2003), 185-198.
  10. [10]  Apiwattanalunggarn, P. (N.) (2003), Finite-element-based nonlinear modal reduction of a rotating beam with large-amplitude motion, Journal of Vibration and Control, 9(2003), 235-263.
  11. [11]  Krstić, M., Kanellakopoulos, I., and Kokotović, P. (1995), Nonlinear and adaptive control design, John Wiley & Sons, Inc..