Adaptive Shape Control for Thermal Deformation of Membrane Mirror with In-plane PVDF Actuators

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.

A Theoretical Study of Circular Orthotropic Membrane Under Concentrated Load: The Relation of Load and Deflection

“…A plate membrane model and a pure membrane model have been studied respectively to achieve active vibration control of plate membrane mirrors [20]. 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 [21]. To analyze the nonlinear dynamic characteristics of the membrane, the theoretical and approximate solutions of nonlinear frequencies of the membrane are obtained, and the discrepancies between the two solutions under different vibration amplitudes are discussed [22].…”

Mechanical, thermal, conductivity, and electrochemical behavior of poly(vinylidene fluoride)/poly(3,4-ethylenedioxythiophene)/polyaniline-grafted-nanodiamond nanocomposite

“…The results showed that PVDF/PEDT/PANI-ND nanocomposite have promising perspectives in Li-ion batteries. 7,15,32…”

“…Because of biocompatibility, flexibility, strength, conductivity, piezoelectric, and pyroelectric properties, PVDF-based nanocomposites have been found suitable for biomedical devices, lithium (Li) batteries, microelectronic devices, actuators, and energy harvesters. [5][6][7][8] Among a wide range of conducting polymers, polyaniline (PANI), polypyrrole, polythiophene, and polyphenylene are important. Mostly, conducting polymers are insoluble in common solvents.…”

Design of a Maglev Inertial Actuator with High Mass Power Ratio for Lateral Vibration Control of Propulsion Shafting

“…Under the influence of propeller hydrodynamic force, non-uniform wake excitation, machining accuracy and assembly accuracy, lateral vibration generated by propulsion shafting will be transmitted to the hull structure, thus producing underwater acoustic radiation [1][2][3]. The active control method implemented by actuators exhibit good performance on mechanical vibration control [4][5][6][7]. As the shafting system belongs to equipment with large mass and high stiffness, it is required that actuators with high mass power ratio are needed to conduct lateral vibration control of propulsion shafting [8].…”