Controller synthesis for stabilizing oscillations in tapping-mode atomic force microscopes

The atomic force microscope operating in tapping-mode can be properly described by a sinusoidally forced second order mechanical oscillator, which is nonlinearly interacting with the sample. Due to interaction forces, which strongly depend on the separation between the AFM tip and the sample profile, the cantilever oscillations may present chaotic behaviors, rising when the separation decreases. The stabilization of such periodic solutions is critical for achieving the correct sample topography. In this work, an LMI-based synthesis technique is proposed for determining the controller which guarantees stability of the cantilever oscillation for a wider range of tip-sample separations, thus eliminating unwanted complex dynamics