Summary
In the present work we show experimental frequency-response curves in the near resonant regime of dynamic mode atomic force microscopy that are obtained through a control-based continuation method. In dynamic mode atomic force microscopy a microcantilever is monoharmonically forced in proximity (nanometer regime) of a sample. Highly nonlinear interaction forces between tip and sample induce unstable periodic orbits in the displacement motion of the tip, manifesting in nonlinear frequency response curves with fold bifurcations. By utilizing adaptive filters to estimate Fourier coefficients online, we are experimentally able to stabilize formerly unstable periodic orbits in lab experiments of dynamic mode atomic force microscopy by a non-invasive phase-locked loop controller and measure complete frequency-response curves. In addition, we change the distance between the cantilever tip and sample and show the transition from linear to nonlinear frequency-response curves.
