Model-based vibration suppression in piezoelectric tube scanners through induced voltage feedback

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 FE- model 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.