Exploiting Global Dynamics of a Noncontact Atomic Force Microcantilever to Enhance Its Dynamical Robustness via Numerical Control

A control technique exploiting the global dynamical features is applied to a reduced order model of noncontact AFM, aiming to obtain an enlargement of the system's safe region in parameters space. The method consists of optimally modifying the shape of the system excitation by adding controlling superharmonics, to delay the occurrence of the global events (i.e. homo/heteroclinic bifurcations of some saddle) which trigger the erosion of the basins of attraction leading to loss in safety. The system's main saddles and the bifurcations involving the relevant manifolds are detected through accurate numerical investigations, and their topological characterization allows the determination of the global event responsible for the sharp reduction in the system dynamical integrity. Since an analytical treatment is impossible in applying the control, a fully numerical procedure is implemented. Besides being effective in detecting the value of the optimal superharmonic to be added for shifting the global bifurcation to a higher value of forcing amplitude, the method also proves to succeed in delaying the drop down of the erosion profile, thus increasing the overall robustness of the system during operating conditions.