ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

The Atomic Force Microscope introduced the surface investigation with true atomic resolution. In the noncontact mode of operation both amplitude and frequency modulation methods can be implemented by using Phase-Locked Loops (PLLs). The Frequency Modulation - Atomic Force Microscope (FM-AFM) control system consists of two control loops, i. e, the amplitude and distance control loops. The amplitude loop controls the cantilever's oscillantion amplitude, and the distance loop controls the mean distance between tip and sample. The PLL performance is vital to FM-AFM control system since it generates the feedback signals to both the  amplitude and distance control loops. Nevertheless, little attention is drawn to PLL design and performance in atomic force microscopy literature. Perhaps because designing stable higher order PLLs, in contrast to second-order, demand some effort. A virtual FM-AFM is implemented and the calculations of FM-AFM images are presented. The results are compared considering the  various  PLL designs, attempting to determine the best characteristics of PLL response to the FM-AFM system.