Journal of Applied Optics, Volume. 43, Issue 1, 23(2022)

Numerical simulation of piezoelectric bimorph mirror control strategy applied to synchrotron radiation

Ziqi WANG1,2, Kai FAN1,2, Junjian ZHANG1,2, and Zhihua FENG1,2、*
Author Affiliations
  • 1Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China
  • 2Key Laboratory of Precision Scientific Instrumentation of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei 230026, China
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    Figures & Tables(11)
    Finite element model of PBM
    Schematic diagram of PBM convergence
    Schematic of PBM piezoelectric response equations
    Schematic of ellipse coordinates reconstruction
    Displacement in vertical direction and slope changes of PBM under gravity
    L-curve and selection of regularization parameters
    Comparison of voltage inversion results
    Inversion target slope and comparison of control residual between LSM and Tikhonov regularization
    • Table 1. Parameters selection of ellipse surface shape

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      Table 1. Parameters selection of ellipse surface shape

      变量含义取值
      p面心距光源S的距离/m 30
      q面心距汇聚点F的距离/m 5
      $ \theta $面心处掠入射角/mrad4
    • Table 2. Influence of number of different partitions on condition number of transformation matrix H

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      Table 2. Influence of number of different partitions on condition number of transformation matrix H

      分区数量18243036
      条件数149.37331.77564.49954.16
    • Table 3. Comparison of inversion results of two methods

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      Table 3. Comparison of inversion results of two methods

      $\left\| {{\boldsymbol{H}}\overrightarrow {\boldsymbol{c}} - \overrightarrow { {{\boldsymbol{S}}_0} } } \right\|_2^2$*电压平均 值/kV 电压标准 差/kV 邻近电压波动 极大值/kV
      *注:二范数中 $\overrightarrow { {{\boldsymbol{S}}_0} }$不含噪声项ζζ只包含在反演斜率向量 $\overrightarrow { { {{\boldsymbol{S}}'}_0} }$中。
      LSM0.5940.3220.2251.019
      Tikhonov0.4650.3240.0750.174
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    Ziqi WANG, Kai FAN, Junjian ZHANG, Zhihua FENG. Numerical simulation of piezoelectric bimorph mirror control strategy applied to synchrotron radiation[J]. Journal of Applied Optics, 2022, 43(1): 23

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    Paper Information

    Category: OE SYSTEM AND ENGINEERING

    Received: Jun. 3, 2021

    Accepted: --

    Published Online: Mar. 7, 2022

    The Author Email: Zhihua FENG (fff@ustc.edu.cn)

    DOI:10.5768/JAO202243.0101004

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