Dynamic analysis of an atomic force microscopy (AFM) including fractional-order

2016 ◽  
Author(s):  
Angelo Marcelo Tusset ◽  
Frederic Conrad Janzen ◽  
Vinícius Piccirillo ◽  
Jose Manoel Balthazar ◽  
Rodrigo Tumolin Rocha
Keyword(s):  
Atomic Force Microscopy ◽  
Dynamic Analysis ◽  
Fractional Order ◽  
Force Microscopy ◽  
Atomic Force

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

2019 ◽  
Vol 8 (2) ◽  
pp. 327-335 ◽  
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

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

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Mauricio A. Ribeiro ◽  
Jose M. Balthazar ◽  
Wagner B. Lenz ◽  
Rodrigo T. Rocha ◽  
Angelo M. Tusset
Keyword(s):  
Mathematical Model ◽  
Atomic Force Microscopy ◽  
Feedback Control ◽  
Fractional Order ◽  
Delayed Feedback Control ◽  
Linear Feedback ◽  
Tapping Mode ◽  
Force Microscopy ◽  
Control Techniques ◽  
Atomic Force

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.

Chaos control of an atomic force microscopy model in fractional-order

2021 ◽  
Author(s):  
Angelo M. Tusset ◽  
Jose M. Balthazar ◽  
Mauricio A. Ribeiro ◽  
Wagner B. Lenz ◽  
Rodrigo T. Rocha
Keyword(s):  
Atomic Force Microscopy ◽  
Fractional Order ◽  
Chaos Control ◽  
Force Microscopy ◽  
Atomic Force
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