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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 ofa 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.