Robust spiral positioning control of a piezoelectric tube scanner

In this paper, a robust spiral positioning of a piezoelectric tube scanner (PTS) used in an atomic force microscope (AFM) is proposed. A minimax linear quadratic Gaussian (LQG) controller is designed based on an uncertainty system model which is constructed by measuring the modeling error between the measured and model frequency response. This controller is robust against uncertainties introduced as a result of spillover dynamics of the scanner at frequencies after the first resonance frequency (900 Hz) of the scanner and variation in plant transfer functions due to temperature and humidity. The proposed scheme provides sufficient damping at resonant modes to track the reference sinusoidal signal. The experimental results demonstrate that sufficiently high positioning accuracy is achieved using the proposed control scheme.