Piezoelectric tube scanners are widely used in scanning probe microscopes to position the sample or the probe. Fast and accurate scanning requires the suppression of dominant low-frequency resonances as well as the compensation of dynamics-coupling effects. The present article gives a detailed description of the fully coupled tube scanner dynamics over a wide frequency range modeled by finite element (FE) analysis using the commercially available software package ANSYS. The effect of a sample mass attached to the top of the tube is investigated by considering its added mass and local stiffening. A model order reduction scheme is applied to obtain a low order model that describes the lateral and vertical deflections as well as the voltage induced on quadrant electrodes. Comparison to experimental data demonstrates a good agreement for both the full FE model and reduced order model.
The operation speed and tracking accuracy of piezoelectric tube actuators in scanning probe microscopy is significantly reduced due to the excitation of the scanner eigenfrequencies by the driving voltages. Feedback control is a suitable method for vibration suppression but suffers from the required additional sensor equipment and high cost for generation of a displacement feedback signal. Operating the piezotube in single-electrode excitation mode allows the comparatively uncomplex measurement of the induced voltages at sensor electrodes. The Finite Element (FE) approach enables an accurate modeling of the voltage signals. Furthermore, geometrical details included in the dynamic FE-model are the sample mass attached to the top of the tube as well as tube eccentricity and dislocated electrodes. Additionally, the FEmodel accounts for dynamics-coupling effects along the separate axes of the three-dimensional tube motion. Comparison with experimental data demonstrates the accuracy of the FE-model. The controller employing the induced voltage as a feedback signal is designed by means of a reduced order model obtained from modal truncation. The efficacy of the controller is illustrated by closed-loop simulations.
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