Nonlinear vibrations control of a contact-mode AFM model via a time-delayed positive position feedback

Abstract

In this work, the nonlinear vibrations of a contact-mode atomic force microscopy (AFM) model subjected to multi excitations are controlled via a time-delayed positive position feedback (PPF) controller. A perturbation method is implemented to obtain the approximate nonlinear dynamical behavior of the AFM system. Different response curves, before and after control, are included utilizing frequency response equations. At multiple resonance cases (primary, sub-harmonic, and internal), the gain effects on the vibration amplitude and stability behavior of the controlled system are studied. The acquired results revealed that PPF controller is efficient in reducing the studied system oscillations. The efficiency of the controller Ea was about 193, means that the controller reduced the vibration by about 99.5%. For increasing feedback signal gain α2, the stability region in τ1-τ2 plane was shrinking. Finally, verification curves are plotted to depict the degree of closeness between analytical predictions and numerical simulation.