The control of a typical commercial Atomic Force Microscope (AFM) is through some variant on a Proportional, Integral, Derivative (PID) controller. Typically, the gains are hand tuned so as to keep the bandwidth of the system far below the first resonant frequency of the actuator. This paper shows a straightforward method of selecting PID gains from the actuator model so as to allow considerably higher bandwidths.
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Abramovitch et al. (2008) studied this question.
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