Abstract
Purpose 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. Conclusions 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.