Influence of a locally-tailored external feedback control on the overall dynamics of a non-contact AFM model

•Non-linear dynamics of non-contact AFM with external feedback control is presented.•Bifurcation diagrams and behavior charts are obtained around main resonance regions.•Stability regions are detected as a function of the most relevant system parameters.•Effectiveness of control actuation on the overall dynamics is critically discussed.•Some hints to be properly taken into account in the design stage are provided.

The dynamical analysis of a single-mode model of non-contact AFM with external feedback control is carried out in the strongly non-linear regime. The aim of the study is to investigate and verify the effects of the control introduction on the system overall behavior, which could be unexpectedly influenced by the local nature of the control technique. For this purpose, a variety of behavior charts around primary and subharmonic resonances are obtained together with several bifurcation diagrams to detect the main local bifurcation thresholds as a function of the most relevant system parameters. The comparison with the results obtained for the corresponding uncontrolled system allows one to comprehensively evaluate the effectiveness and possible criticalities of the control actuation on the system dynamics, with also a view to the overall response scenario.