Chaos control in AFM systems using nonlinear delayed feedback via sliding mode control

In this paper a nonlinear delayed feedback control is proposed to control chaos in an Atomic Force Microscope (AFM) system. The chaotic behavior of the system is suppressed by stabilizing one of its first-order Unstable Periodic Orbits (UPOs). At first, it is assumed that the system parameters are known, and a nonlinear delayed feedback control is designed to stabilize the UPO of the system. Then, in the presence of model parameter uncertainties, the proposed delayed feedback control law is modified via sliding mode scheme. The effectiveness of the presented methods is numerically investigated by stabilizing the unstable first-order periodic orbit of the AFM system. Simulation results show the high performance of the methods for chaos elimination in AFM systems.