High-precision spiral positioning control of a piezoelectric tube scanner used in an atomic force microscope

This paper considers a high-speed spiral scanning method using an atomic force microscope (AFM). In it, spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes in the X and Y-axes, respectively, of the AFM's piezoelectric tube (PZT) scanner. Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian (LQG) controller is designed to track the reference sinusoidal signal. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoid from the X and Y-PZTs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. Also, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors. A comparison of images scanned using the proposed controller (spiral) and the AFM proportional integral (PI) controller (raster) provide evidence of the efficacy of the proposed method.