https://doi.org/10.1140/epjs/s11734-021-00242-6
Regular Article
Chaos control of an atomic force microscopy model in fractional-order
1
UTFPR, Federal University of Technology, Paraná, Ponta Grossa, Brazil
2
UNESP, Universidade Estadual Paulista Júlio Mesquita, Filho, São Paulo, Brazil
Received:
14
February
2021
Accepted:
8
July
2021
Published online:
26
July
2021
In this work, the nonlinear dynamics and control of an atomic force microscopy (AFM) in fractional-order are investigated. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space, whose behavior is characterized using the power spectral density and the 0-1 test. To bring the system from a chaotic state to a periodic one, the nonlinear saturation control (NLSC) and the time-delayed feedback control (TDFC) techniques for the fractional-order systems are applied with and without accounting for the fractional-order. Numerical results show the influence of fractional-order derivative on the dynamics of the AFM system. Due to that, some phenomena arise, which are confirmed through detailed numerical investigations by the 0-1 test. The NLSC and TDFC techniques showed to be efficient in controlling the chaotic behavior of the AFM in fractional-order.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021
