High-precision Nanopositioning Control of a Piezoelectric Tube Scanner: Atomic Force Microscopy

Abstract

A piezoelectric tube scanner (PTS) is made of a piezoelectric material (PZM) is used in an atomic force microscopy (AFM) for sub-nanometre range positioning of a sample. High-precision nanopositioning of the PTS is a major requirement for a high-speed imaging using the AFM. The main motivation to this thesis is to propose suitable control methods for high-speed imaging using an AFM. The scanning speed of a commercial AFM is limited by the positioning accuracy of its scanner which has the following problems: i) creep effect in slow-speed scanning; ii) hysteresis effect during large range scanning (which both result in inaccurate reference motion tracking); iii) cross-coupling effect among the axes of the scanner; and iv) vibration effect at high frequencies due to its mechanical properties. Over the last two decades, high-speed imaging using an AFM has been attempted to achieve either by applying suitable controller, using alternative scanning methods, or changing hardware setup. This thesis demonstrates, the first two approaches to achieve high-speed AFM image scanning. According to the objectives of this thesis, three steps high-precision nanopositioning controls are designed, experimentally implemented on an AFM and results for high-precision nanopositioning are demonstrated. The three unique contributions of this thesis are mentioned in brief.

Firstly, as an alternative to the traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM scanner. A phase-locked loop (PLL)-based proportional-integral (PI) controller is designed for compensating phase error between motions from the lateral axes of the PTS during spiral scanning.

Secondly, for further improvement, a linear quadratic Gaussian (LQG) controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and to reduce the tracking error, an integrator is introduced.

Finally, a robust minimax linear quadratic Gaussian (LQG) controller is designed and implemented on the AFM. The minimax LQG controller is designed based on an uncertain system model which is constructed by measuring the plant variations due to variations of sample mass and modelling error between the measured and model frequency responses.