Numerical Exploratory Analysis of Dynamics and Control of an Atomic Force Microscopy in Tapping Mode with Fractional Order
Joint Authors
Ribeiro, Mauricio A.
Balthazar, Jose M.
Lenz, Wagner B.
Rocha, Rodrigo T.
Tusset, Angelo M.
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-06-22
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Ribeiro, Mauricio A.& Balthazar, Jose M.& Lenz, Wagner B.& Rocha, Rodrigo T.& Tusset, Angelo M.. 2020. Numerical Exploratory Analysis of Dynamics and Control of an Atomic Force Microscopy in Tapping Mode with Fractional Order. Shock and Vibration،Vol. 2020, no. 2020, pp.1-18.
https://search.emarefa.net/detail/BIM-1209876
Modern Language Association (MLA)
Ribeiro, Mauricio A.…[et al.]. Numerical Exploratory Analysis of Dynamics and Control of an Atomic Force Microscopy in Tapping Mode with Fractional Order. Shock and Vibration No. 2020 (2020), pp.1-18.
https://search.emarefa.net/detail/BIM-1209876
American Medical Association (AMA)
Ribeiro, Mauricio A.& Balthazar, Jose M.& Lenz, Wagner B.& Rocha, Rodrigo T.& Tusset, Angelo M.. Numerical Exploratory Analysis of Dynamics and Control of an Atomic Force Microscopy in Tapping Mode with Fractional Order. Shock and Vibration. 2020. Vol. 2020, no. 2020, pp.1-18.
https://search.emarefa.net/detail/BIM-1209876
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209876