Numerical Exploratory Analysis of Dynamics and Control of an Atomic Force Microscopy in Tapping Mode with Fractional Order

In this paper, we investigate the mechanism of atomic force microscopy in tapping mode (AFM-TM) under the Casimir and van der Waals (VdW) forces. The dynamic behavior of the system is analyzed through a nonlinear dimensionless mathematical model. Numerical tools as Poincaré maps, Lyapunov exponents, and bifurcation diagrams are accounted for the analysis of the system. With that, the regions in which the system presents chaotic and periodic behaviors are obtained and investigated. Moreover, the fractional calculus is introduced into the mathematical model, employing the Riemann-Liouville kernel discretization in the viscoelastic term of the system. The 0-1 test is implemented to analyze the new dynamics of the system, allowing the identification of the chaotic and periodic regimes of the AFM system. The dynamic results of the conventional (integer derivative) and fractional models reveal the need for the application of control techniques such as Optimum Linear Feedback Control (OLFC), State-Dependent Riccati Equations (SDRE) by using feedback control, and the Time-Delayed Feedback Control. The results of the control techniques are efficient with and without the fractional-order derivative.

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Microcantilever chaotic motion suppression in tapping mode atomic force microscope

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406212467933 ◽

2012 ◽

Vol 227 (8) ◽

pp. 1730-1741 ◽

Cited By ~ 15

Author(s):

José Manoel Balthazar ◽

Angelo Marcelo Tusset ◽

Silvio Luiz Thomaz de Souza ◽

Atila Madureira Bueno

Keyword(s):

Atomic Force Microscopy ◽

Feedback Control ◽

Atomic Force Microscope ◽

Chaotic Motion ◽

Delayed Feedback Control ◽

Linear Feedback ◽

Tapping Mode ◽

Force Microscopy ◽

Atomic Force ◽

Wide Range

The tapping mode is one of the mostly employed techniques in atomic force microscopy due to its accurate imaging quality for a wide variety of surfaces. However, chaotic microcantilever motion impairs the obtention of accurate images from the sample surfaces. In order to investigate the problem the tapping mode atomic force microscope is modeled and chaotic motion is identified for a wide range of the parameter's values. Additionally, attempting to prevent the chaotic motion, two control techniques are implemented: the optimal linear feedback control and the time-delayed feedback control. The simulation results show the feasibility of the techniques for chaos control in the atomic force microscopy.

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Time Delayed Feedback Control Applied in an Atomic Force Microscopy (AFM) Model in Fractional-Order

Journal of Vibration Engineering & Technologies ◽

10.1007/s42417-019-00166-5 ◽

2019 ◽

Vol 8 (2) ◽

pp. 327-335 ◽

Cited By ~ 3

Author(s):

Angelo M. Tusset ◽

Mauricio A. Ribeiro ◽

Wagner B. Lenz ◽

Rodrigo T. Rocha ◽

Jose M. Balthazar

Keyword(s):

Atomic Force Microscopy ◽

Feedback Control ◽

Fractional Order ◽

Delayed Feedback ◽

Delayed Feedback Control ◽

Force Microscopy ◽

Atomic Force ◽

Time Delayed Feedback

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Control Techniques for Increasing the Scan Speed and Minimizing Image Artifacts in Tapping-Mode Atomic Force Microscopy: Toward Video-Rate Nanoscale Imaging

IEEE Control Systems Magazine ◽

10.1109/mcs.2013.2279471 ◽

2013 ◽

Vol 33 (6) ◽

pp. 46-67 ◽

Cited By ~ 8

Keyword(s):

Atomic Force Microscopy ◽

Image Artifacts ◽

Tapping Mode ◽

Force Microscopy ◽

Control Techniques ◽

Atomic Force ◽

Scan Speed ◽

Nanoscale Imaging ◽

Mode Atomic Force Microscopy

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Feedback-induced instability in tapping mode atomic force microscopy: theory and experiment

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2010.0451 ◽

2010 ◽

Vol 467 (2130) ◽

pp. 1801-1822 ◽

Cited By ~ 13

Author(s):

O. Payton ◽

A. R. Champneys ◽

M. E. Homer ◽

L. Picco ◽

M. J. Miles

Keyword(s):

Mathematical Model ◽

Atomic Force Microscopy ◽

Driving Frequency ◽

Integral Control ◽

Tapping Mode ◽

Force Microscopy ◽

Atomic Force ◽

Flat Sample ◽

Realistic Representation ◽

Mode Atomic Force Microscopy

We investigate a mathematical model of tapping mode atomic force microscopy (AFM), which includes surface interaction via both van der Waals and meniscus forces. We also take particular care to include a realistic representation of the integral control inherent to the real microscope. Varying driving amplitude, amplitude setpoint and driving frequency independently shows that the model can capture the qualitative features observed in AFM experiments on a flat sample and a calibration grid. In particular, the model predicts the onset of an instability, even on a flat sample, in which a large-amplitude beating-type motion is observed. Experimental results confirm this onset and also confirm the qualitative features of the dynamics suggested by the simulations. The simulations also suggest the mechanism behind the beating effect; that the control loop over-compensates for sufficiently high gains. The mathematical model is also used to offer recommendations on the effective use of AFMs in order to avoid unwanted artefacts.

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