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The atomic force microscope (Binnig et al., 1986) utilizes a sharp tip moving over the surface of a sample in a raster scan mode to measure the topography and material properties of the surface. The tip is located at the free end of a cantilever microbeam (probe) which bends in response to the interaction forces between the tip and the sample. An estimate of the microbeam stiffness is used to determine the interaction forces from measurements of these deflections. A precision positioning device, usually made of a piezoelectric tube, is used to move the tip or the sample. AFMs can be operated in one of two principal modes: (i) with feedback control or (ii) without feedback control. Though widely practiced, open-loop operation has the potential for chaotic probe tip response, thus rendering erroneous topographical information. Therefore, in a typical imaging operation the cantilever deflection is maintained at a set point by means of a feedback controller, while scanning the sample surface. The control effort is used as a measure of the sample surface profile. Actuator creep, hysteresis, probe vibrations, modeling errors, and nonlinearities are major sources of error in AFM measurements (Barret & Quate, 1991; Devasia et al., 2007; Jung 7 Gwon, 2000). In addition to analytical methodologies for compensation of the above mentioned errors, feedback control strategies have been developed in order to improve AFM region of operation. Conventional PD, PI, and PID feedback controllers of the AFM probe were presented in (Ashhab et al., 1999) and (Sinha, 2005). Two nonlinear control techniques using a learning-based algorithm were presented in (Fang et al., 2005). H∞ and Glover-McFarlane controllers (Sebastian et al., 2003), (Salapaka et al., 2005) were also designed to achieve high bandwidth and robustness during AFM scanning. Other controllers based on inverse model control and combinations of feedforward and feedback and L1 and H∞ controllers were proposed to increase the scanning speed and overcome nonlinear effects in piezoelectric actuation (Jalili et al., 2004; Leang & Devasia, 2007; Pao et al., 2007; Rafai & Toumi, 2004; Salapaka et al., 2002; Schitter et al., 2004; Schitter et al., 2004; Sebastian et al., 2007). Although these methods can overcome modeling errors and have the robustness to overcome some parameter variations, they provide limited vibration compensation. In addition, in most of these methods, design complexity is combined with the use of linear

Control of Atomic Force Microscope Based on the Fuzzy Theory