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

  • Angelo M. TussetEmail author
  • Mauricio A. Ribeiro
  • Wagner B. Lenz
  • Rodrigo T. Rocha
  • Jose M. Balthazar
Original Paper



In this work, the nonlinear dynamics and control of an Atomic Force Microscopy (AFM) model in fractional-order were investigated.

Methods and Results

For analyse of the chaos behaviour, the 0–1 test was used, since this is a good tool to characterise fractional-order differential systems. To bring the system from a chaotic state to a periodic orbit, the time-delayed feedback control technique for the fractional-order systems is applied, thus controlling the chaotic behaviour.


For fractional-order case, the results showed the influence of derivative order on the dynamics of the AFM system. Due to the fractional order, some phenomena comes up, which were confirmed through detailed numerical investigations by 0–1 test. The time-delayed feedback control technique was efficient to control the chaotic motion of the AFM in fractional order. In addition, the robustness of the proposed time-delayed feedback control was tested by a sensitivity analysis to parametric uncertainties.


Time Delay Feedback control AFM system 0-1 test Nonlinear system Fractional-order 



The authors acknowledge support by CNPq, FAPES, FA and CAPES, all Brazilian research funding agencies. In addition, the authors thank the organizing committee of the 14th International Conference on Vibration Engineering and Technology of Machinery (VETOMAC XIV), where part of this work was presented.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


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Authors and Affiliations

  1. 1.Federal University of Technology - ParanáPonta GrossaBrazil

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