Active Shape Control Of Piezoelectric Laminated Membrane Mirrors

Due to their advantages of low surface density,easy folding and expansion,and low cost,membrane mirrors can effectively solve the contradiction between the need of high resolution space optical system and launch load and volume limitation.Therefore,they have great application prospect in future deep space det ection,space communication and earth observation.Since the 1960 s,foreign research institutes,represented by the United States,have carried out a lot of research work on space membrane mirrors and achieved outstanding results.In the past ten years,research institutions in China,represented by the Changchun Institute of Optics,Fine Mehcanics and Physics and Suzhou University,have also made some progress in the study of membrane mirrors.However,they paid most attention to the forming control mechanism and testing of the electrostatic tensile thin film reflectors.At present,there is still a gap in the research on the vibration and surface control of membrane mirrors when in orbit.At the same time,due to the rapid development of intelligent structure technology,it has become an important direction in the field of aviation and aerospace to attach/embed the shape memory materials,piezoelectric materials,photoelectric materials to/in spatial structures to realize their intelligent control.Thus,in this paper,we consider to combine the space membrane mirror with the intelligent materials by using the design idea of intelligent structural system in order to realize its dynamic and static active surface control.The constitutive relations of a generic laminated piezoelectric thin shell in thermo-electro-mechanical field are discussed.Based on the hypothesis of Love-Kirchhoff thin shell and the first-order shear deformation theory,mechanical model of piezoelectric laminated thin shell element is established.Expressions of resultant forces and moments of piezoelectric laminated thin shell element are also derived.General nonlinear dynamic system equations of piezoelectric laminated thin shell are then presented based on the Hamilton's principle and the basic hypothesis of thin shell theory.By susbstituting the corresponding Lame parameters and radii of curvature into the system equations,dynamic models of piezoelectric laminated membrane mirrors and single layer piezoelectric thin film mirrors are established,respectively.The numerical solution under an axisymmetric thermal load is given and compared with result of finite element method to verify the correctness of the model.Vibration characteristics of membrane mirrors are then investigated.Linear dynamic models are established considering of the effects of flexural rigidity and membrane tension.Frequency coefficients and transverse mode shape functions of different orders of the mirror with clamped boundary condition are obtained.Based on the Galerkin's method,a nonlinear dynamic model of membrane mirror is established.The model is then solved and compared with the relevant conclusions in the reference literature to prove its universality and correctness.The characteristics of distributed piezoelectric sensing and actuating signal of membrane mirrors are studied.Based on the structural equations of the membrane mirror,the expressions of micro-sensing signal and microscopic modal control force are derived.The influences of mode order,spatial distribution and tensioning force on micro-sensing signal and micro-control behavior are analyzed to provide references for the layout design of sensors and actuators.Optimal vibration control of the membrane mirror structronic system is studied.Distributed piezoelectric sensor and actuator patches are arranged symmetrically on the upper and lower surfaces of the membrane mirror.The linear quadratic optimal control algorithm is used and the state space equations of the system under optimal control theory is given.Independent active modal control of the mirror structronic system is carried out.The influences of mode order and tensioning force on control effects are analyzed,and the effects of each controller design parameters was evaluated.An experimental platform for active control of the membrane mirror is established.A new method for controlling the mirror surface based on the Influence Function Matrix(IFM)is proposed and the IFM are identified experimentally.Closed-loop surface tracking experiment and thermal deformation adaptive control experiment are performed.The results prove that the control strategy proposed can quickly and effectively eliminate the surface error caused by external thermal disturbance.A second order mathematical model of the membrane mirror system is obtained by parameter identification.Based on the positive position feedback control algorithm,vibration control experiments are carried out for the first two order modes of the membrane mirror with different control parameters.Experimental results demonstrate that the control strategy can effectively suppress the vibration of the membrane mirror.