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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 ± 0.1 μm and ± 0.5 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 ± 0.1 μm and ± 0.2 arcsec.

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