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

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.