An optimal controller for high-precision spiral positioning of a piezoelectric tube scanner used in an atomic force microscope (AFM) is proposed in this paper. In the proposed control scheme, a second-order vibration compensator is incorporated with the piezoelectric tube scanner (PTS) to suppress the vibration of the PTS at the resonant frequency. An internal model of a reference sinusoidal signal is included with the augmented plant model and an integrator is introduced with a linear quadratic Gaussian controller which reduces the phase error between the input and output sinusoids. The proposed method allows a commercial AFM to scan at high scanning speeds as an alternative to the raster scanning approach. The performance of this controller is assessed with closed-loop frequency response, tracking accuracy, and a set of spiral scanned images. The raster scanned images obtained using the standard AFM PI controller is also presented for comparison with the spiral images. Experimental results prove the effectiveness of the proposed method.
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