Local versus global dynamics and control of an AFM model in a safety perspective

The role of local and global dynamics to assess a system robustness and actual safety in operating conditions is investigated, by also studying the effect of different local and global control techniques on the nonlinear behavior of a noncontact AFM. Firstly, the nonlinear dynamical behavior of a single-mode model of noncontact AFM is analyzed in terms of stability of the main periodic solutions, as well as attractors robustness and basins integrity. To the same AFM model, an external feedback control is inserted during its nonlinear continuum formulation, with the aim to keep the system response to an operationally suitable one. The dynamical analysis of the controlled system is developed to investigate and verify the effects of control into the system overall behavior, which could be unexpectedly influenced by the local nature of the control technique. A different control technique is finally applied to the AFM model, acting on global bifurcation events to obtain an enlargement of the systems safe region in parameters space. The analytical procedure, based on Melnikov method, is applied to the homoclinic bifurcation involving the system hilltop saddle, and its practical effects as regards possibly increasing the system overall robustness are numerically investigated by means of a dynamical integrity analysis. Then, a fully numerical procedure is implemented to possibly control global bifurcations involving generic saddles. The method proves to succeed in delaying the drop down of the erosion profile, thus increasing the overall robustness of the system during operating conditions.