Global dynamics and integrity in noncontacting atomic force microscopy with feedback control

Dynamical integrity of a noncontact AFM model with external feedback control is investigated to evaluate the effects of such local control procedure on the erosion of the basins of attraction of the system bounded solutions. Two-dimensional cross sections of the five-dimensional basins of attraction have been systematically constructed, and the relevant erosion profiles are obtained for the parametrically excited system. The outcomes, summarized by the so-called isointegrity curves (i.e., frequency-dependent thresholds with constant residual integrity which actually represent the system practical safety), highlight that around the resonance frequencies, the system undergoes a worsening of its practical stability, with respect to variations in the forcing amplitude and the tip–sample distance, as well, thus underlining the importance of a global analysis to assess the system actual safety in operating conditions.