Event-driven feedback tracking and control of tapping-mode atomic force microscopy

This paper presents an event-driven, discrete-in-time feedback strategy for tracking and stabilizing naturally occurring periodic oscillations in the probe-tip dynamics of atomic force microscope (AFM) cantilevers in tapping-mode operation. Specifically, robust dynamic tracking and stabilization is achieved by the imposition of discrete changes in the vertical offset between the cantilever support and the sample surface based on an estimated linearization of the system dynamics about a dynamically generated reference trajectory. Here, use is made not only of the oscillation amplitude, as is typical in commercial control implementations for AFMs, but also of the instantaneous phase information. It is shown that stabilization and desirable performance during surface scanning is possible, even in the presence of uncertainty and limited state access. In particular, the methodology enables robust tracking and use of low-contact-velocity periodic system responses that are unstable in the absence of control.