On an optimal control applied in atomic force microscopy (AFM) including fractional-order

In this work, the nonlinear dynamics of an Atomic Force Microscope (AFM) operating in tapping mode is investigated, considering the influence of squeeze film damping in fractional-order. Its influence plays an important role because the dynamics of the AFM can be led to different responses, e.g., periodic and chaotic motions, specially the influence of the derivative order when in fractional-order. In a way to characterize the type of behavior, the 0-1 test was used once this is a good tool to characterize fractional-order differential systems. In addition, the linear feedback control technique for fractional-order systems is applied to control the chaotic behaviors. Therefore, the results showed a nonlinear behavior presented by the AFM system. In addition, the feedback control technique was efficient to control the chaotic motion of the micro cantilever beam of the AFM, whose results included variation of parameters of the fractional derivative of the squeeze film damping.