柔性压电智能反射面的静态形状控制

王志; 曹玉岩; 周超; 范磊; 张丽敏

doi:10.3788/OPE.20142210.2715

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柔性压电智能反射面的静态形状控制

微纳技术与精密机械 | 更新时间：2020-08-13

- 柔性压电智能反射面的静态形状控制
- Static shape control of flexible piezoelectric smart reflectors
- 光学精密工程 2014年22卷第10期页码：2715-2724
- 作者机构：
  
  中国科学院长春光学精密机械与物理研究所,吉林长春,中国,130033
- 作者简介：
- 基金信息：
  
  吉林省科技发展计划资助项目(No.20130102018JC)()
- DOI：10.3788/OPE.20142210.2715
  中图分类号： O302;TN384
- 收稿日期：2013-10-15，
  
  修回日期：2013-11-18，
  
  纸质出版日期：2014-10-25
- 稿件说明：
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王志, 曹玉岩, 周超等. 柔性压电智能反射面的静态形状控制[J]. 光学精密工程, 2014,22(10): 2715-2724

WANG Zhi, CAO Yu-yan, ZHOU Chao etc. Static shape control of flexible piezoelectric smart reflectors[J]. Editorial Office of Optics and Precision Engineering, 2014,22(10): 2715-2724
王志, 曹玉岩, 周超等. 柔性压电智能反射面的静态形状控制[J]. 光学精密工程, 2014,22(10): 2715-2724 DOI： 10.3788/OPE.20142210.2715.

WANG Zhi, CAO Yu-yan, ZHOU Chao etc. Static shape control of flexible piezoelectric smart reflectors[J]. Editorial Office of Optics and Precision Engineering, 2014,22(10): 2715-2724 DOI： 10.3788/OPE.20142210.2715.

摘要

建立了柔性压电智能反射面系统的有限元模型和优化控制模型

给出了结构力学建模和形状控制方法以及相应的优化算法.首先

将蜂窝夹层结构的压电智能反射面等效为多层复合板;基于Kirchhoff假设和经典层合板理论

根据虚功原理推导了柔性压电智能反射面的有限元方程;采用蜂窝等效理论计算了反射面蜂窝夹芯等效弹性模量

有限元模型中的单元为四节点四边形压电板单元

每个作动器单元中引入额外的电势自由度.然后

根据建立的有限元方程

推导了反射面变形均方根误差与作动器控制电压的关系式;以均方根误差最小为优化目标

建立了柔性压电智能发射面的静态形状控制优化模型;采用Lagrange乘子法处理了压电作动器工作电压的限制.最后

用提出的方法分析已有模型并验证建模方法.以600 mm口径的平面柔性智能反射面为例

验证了采用压电陶瓷贴片对反射面静态形状控制的可行性及优化算法有效性.仿真结果表明:通过控制压电陶瓷贴片作动器

可以使反射面的静态形状误差减小97%以上

而且作动器的控制电压均在极限电压范围内.

Abstract

The finite element formulation of a flexible piezoelectric smart reflector was presented based on Kirchhoff classical laminated theory

and its structural mechanic modeling and optimization algorithms were investigated. Firstly

the smart reflector with the honeycomb core was modeled with the equivalent laminate plate theory

and its finite element formulation was derived according to virtual work theory. The honeycomb core equivalent elastic modulus was calculated by using equivalent theory. Then

a simple four-node quadrilateral element was used in the model

and one electric potential degree of freedom was introduced to each active element. Accordingly

the relation between the mean square root error of reflector and the control voltages of actuators was derived

the optimization model for static shape control was created and the voltage limitation for piezoelectric actuator patches was imposed to maintain its control voltage within a practical range. The optimal control voltages were determined by using Lagrange multipliers to minimize the Root Mean Square (RMS) error. Finally

a numerical example of plane smart reflector was given to demonstrate the feasibility of smart mirror concept and the effectiveness of optimization algorithm. Simulation results indicate that the square root error of the smart reflector is reduced by above 90%

and the control voltage of each actuator is in a practical range.

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references

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