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Mathematical Problems in Engineering
Volume 2014, Article ID 523786, 16 pages
Research Article

Development of a Flat Type Six-Axis Stage Based on Piezoelectric Actuators

1Center for Measurement Standards, Industrial Technology Research Institute, Hsinchu 300, Taiwan
2Department of Mechanical Engineering, National Chung-Hsing University, Taichung 402, Taiwan
3Department of Industrial Education and Technology, National Changhua University of Education, Changhua 500, Taiwan

Received 18 May 2014; Accepted 1 July 2014; Published 25 September 2014

Academic Editor: Teen-Hang Meen

Copyright © 2014 Hau-Wei Lee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study presents and investigates a six-DOF (degrees of freedom) piezoelectric based stage for positioning error compensation. The relationship between the displacement of the piezoelectric actuators and the stage can be computed according to the geometric relationships of the actuators installed. In this study, a feedforward compensator based on the hysteresis model has been designed for compensation and a PI controller was used for positioning. The combination of a feedforward compensator and PI controller gives the stage good positioning and tracking performance. Stage position information is feedback from a six-DOF optical measurement system comprised of three modular two-dimensional measurement devices. Each module employs a quadrant photodiode (QPD), a laser diode, and a lens. The measurement signal is acquired and processed using an FPGA based processor for real time control. The linear and angular positioning resolution is 0.02 μm and 0.1 arcsec, respectively. When the stage is controlled in a closed loop, the positioning errors are in the range of μm and arcsec. The stage is controlled to track a sinusoidal wave with an amplitude of 2.5 μm and a frequency of 5 Hz; tracking errors were within μm and arcsec.