Design and Parameter Identification for a Positioning Platform with a Large Stroke and High Precision for Segmented Mirrors.

An active optical system with three segmented mirrors was proposed to verify the co-focus and co-phase progress. In this system, a kind of large-stroke and high-precision parallel positioning platform was specially developed to help support the mirrors and reduce the error between them, which can move in three degrees of freedom out of plane. The positioning platform was composed of three flexible legs and three capacitive displacement sensors. For the flexible leg, a kind of forward-type amplification mechanism was specially designed to amplify the displacement of the piezoelectric actuator. The output stroke of the flexible leg was no less than 220 μm and the step resolution was up to 10 nm. Further, a linear model was established to identify the amplification ratio between the actuator and the flexible leg, which can increase the precision of the positioning platform. Moreover, three capacitive displacement sensors with a resolution of 2.5 nm were symmetrically installed in the platform to accurately measure the position and attitude of the platform. To improve the stability and precision of the platform, particle swarm optimization algorithm was applied to identify the control matrix, which can help the platform achieve ultra-high precision positioning. The results showed that the theoretical matrix parameters had a maximum deviation of 5.67% from the experimental ones. Finally, abundant experiments verified the excellent and stable performance of the platform. The results proved that while bearing the heavy mirror, which is no more than 5 kg, the platform can realize a 220 μm translation stroke and 2.0 mrad deflection stroke, with a high step resolution of 20 nm and 0.19 μrad. These indicators can perfectly cater to the requirements of the proposed segmented mirror system's co-focus and co-phase adjustment progress.