Performance of sinusoidal scanning with MPC in AFM imaging

An atomic force microscope (AFM) is an extremely versatile investigative tool in the field of nanotechnology, the performance of which is significantly influenced by its conventional zig-zag raster pattern scanning method. In this paper, in order to increase its imaging speed, we consider the use of a sinusoidal scanning method, i.e., a spiral scanning method with an improved model predictive control (MPC) scheme. In this approach, spirals are generated by applying waves, each with a single frequency and slowly varying amplitude, in the X-piezo (sine wave) and Y -piezo (cosine wave) of the piezoelectric tube scanner (PTS) of the AFM. As these input signals are single frequencies, the scanning can proceed faster than traditional raster scanning, without exciting the resonant mode of the PTS. The proposed MPC controller reduces the phase error between the reference position input and measured output sinusoids and provides better tracking of the reference signal. Also, a notch filter is designed and included in the feedback loop to suppress vibrations of the PTS at the resonant frequency. The experimental results show that, using the proposed method, the AFM is able to scan a 6 μm radius image within 2.04 s with a quality better than that obtained using the conventional raster pattern scanning method.