Abstract
Optical membrane mirrors are promising key components for future space telescopes. Due to their ultra-thin and high flexible properties, the surfaces of these membrane mirrors are susceptible to temperature variations. Therefore adaptive shape control of the mirror is essential to maintain the surface precision and to ensure its working performance. However, researches on modeling and control of membrane mirrors under thermal loads are sparse in open literatures. A 0.2 m diameter scale model of a polyimide membrane mirror is developed in this study. Three Polyvinylidene fluoride (PVDF) patches are laminated on the non-reflective side of the membrane mirror to serve as in-plane actuators. A new mathematical model of the piezoelectric actuated membrane mirror in multiple fields, (i.e., thermal, mechanical, and electrical field) is established, with which dynamic and static behaviors of the mirror can be analyzed. A closed-loop membrane mirror shape control system is set up and a surface shape control method based on an influence function matrix of the mirror is then investigated. Several experiments including surface displacement tracking and thermal deformation alleviation are performed. The deviations range from 15 μm to 20 μm are eliminated within 0.1 s and the residual deformation is controlled to micron level, which demonstrates the effectiveness of the proposed membrane shape control strategy and shows a satisfactory real-time performance. The proposed research provides a technological support and instruction for shape control of optical membrane mirrors.
Highlights
1 Introduction Along with the development of deep space exploration, space communication, and earth observation technology, there is an increasing demand for high-resolution and wide-field optical mirrors used in space telescopes, radars, antennas, and energy collectors [1]
Three laser displacement sensors produced by Keyence Corporation are used for measuring the surface deviation of the mirror for feedback shape control, and three Polyvi‐ nylidene fluoride (PVDF) patches are laminated to the nonreflective side of the mirror to serve as actuators for surface shape control
4 Implementation and Results From the mathematical model established previously, we can find that the transverse deflection of the mirror is caused by the piezoelectric forces and moments induced by the PVDF actuators
Summary
Along with the development of deep space exploration, space communication, and earth observation technology, there is an increasing demand for high-resolution and wide-field optical mirrors used in space telescopes, radars, antennas, and energy collectors [1]. Many flatness control methods have been explored including in-plane patching-on/embedding-in, boundary actuation, and out-of-plane electrostatic actuation to ensure the surface accuracy of membrane mirrors. Various smart materials such as shape-memory alloys (SMAs) [4], polyvinylidene fluoride (PVDF) films [5,6,7], piezoelectric polymer actuators [8], macrofiber composites [9, 10], and microelectromechanical system transducers [11] have been used to control the surface shape of membrane structures. A generic algorithm-based control system was developed and tested on a square membrane by Peng et al [14,15,16,17] and Wang et al [18,19,20] investigated active flatness control of membrane structures under thermal and mechanical loads with SMA actuators.
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