﻿ 大口径压电倾斜镜模型辨识与控制
 光电工程  2018, Vol. 45 Issue (3): 170704      DOI: 10.12086/oee.2018.170704

1. 中国科学院自适应光学重点实验室，四川 成都 610209;
2. 中国科学院光电技术研究所，四川 成都 610209

System identification and control for large aperture fast-steering mirror driven by PZT
Huang Linhai1,2, Fan Muwen1,2, Zhou Rui1,2, Zhang Haotian1,2, Huang Kui1,2, Hu Shijie1,2, Luo Xi1,2, Li Xinyang1,2
1. Key Laboratory of Adaptive Optics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China;
2. Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
Abstract: Novel system identification for large aperture fast-steering mirror (FSM) is presented in this paper. Using the stochastic parallel gradient descent method (SPGD), the new system identification method is able to identify the complex piezoelectric fast-steering mirror (PZT-FSM) model exactly and greatly improve the correction effect. The principle and mathematical model of the PZT-FSM are stated briefly in the paper firstly. Then the use process of the SPGD algorithm in the system identification for the large aperture PZT-FSM is presented. By using the identified model, the validity and feasibility of the proposed approach is confirmed by our close-loop experiments. To expand the usage of the new method, the input jitter spectrum is also identified using the similar method, which enables us to get a higher correction effect for the special frequency region.
Keywords: fast steering mirror    structural resonance    PZT    large aperture

1 引言

2 压电倾斜镜的机械谐振原理及数学模型

 $\omega = \frac{{8\alpha }}{{{D^2}}} \cdot {\left( {\frac{{SL}}{{\theta h}}} \right)^{\frac{1}{2}}},$ (1)

 ${F_k}(s) = \frac{{{s^2} + 2{\varepsilon _{{\rm{z}}k}}{\omega _{{\rm{z}}k}}s + \omega _{{\rm{z}}k}^2}}{{{s^2} + 2{\varepsilon _{{\rm{p}}k}}{\omega _{{\rm{p}}k}}s + \omega _{{\rm{p}}k}^2}},$ (2)

4 实例与分析

 图 1 用于辨识压电倾斜镜系统模型光路结构示意图 Fig. 1 Optical structure for piezoelectric fast-steering mirror system identification

 图 2 250 mm口径压电倾斜镜系统对不同频率的响应曲线 Fig. 2 Frequency response of piezoelectric fast-steering mirror with a 250 mm aperture

 图 3 辨识模型与实测模型对不同频率的响应曲线。(a) 7阶模型辨识结果；(b) 9阶模型辨识结果；(c) 7阶模型辨识局部细节；(d) 9阶模型辨识局部细节 Fig. 3 Frequency responses of identified model and detected models. (a) Identification of a 7th order model; (b) Identifi-cation of a 9th order model; (c) Local detail for the 7th order identification; (d) Local detail for the 9th order identification

 序号 极点频率 零点频率 极点振荡因子 零点振荡因子 1 1261.6 2243.2 0.021 0.384 2 715.2 1337.4 0.192 0.464 3 710.0 1186.8 0.020 0.030 4 661.6 664.5 0.018 0.055 5 625.9 649.3 0.019 0.117 6 576.2 643.2 0.021 0.023 7 528.2 577 0.822 0.047 8 527.6 577 0.046 0.063 9 298.6 304 0.016 0.020

 图 4 同样阶次条件下利用Levy方法辨识结果 Fig. 4 Identification result using Levy method with the same identified order

 图 5 250 mm压电倾斜镜系统中消谐振后，系统的实测响应曲线 Fig. 5 Actual detected frequency response after resonant depression for the 250 mm piezoelectric fast-steering mirror

 图 6 消谐振前后闭环误差控制曲线。(a)未消谐振闭环误差曲线；(b)消谐振后闭环误差曲线 Fig. 6 Close loop of the FSM before and after resonant depression. (a) Close loop of the FSM without resonant depression; (b) Close loop of the FSM with resonant depression

 图 7 输入测试抖动随时间的变化曲线 Fig. 7 The curl of input jitter against time

 图 8 消谐振前后倾斜镜校正残差分布 Fig. 8 Residual jitter error with and without resonant depression

 图 9 (a) 输入抖动频谱分布和校正后残余抖动频谱分布；(b)积分功率谱曲线 Fig. 9 (a) Power spectrums of input jitter and residual jitter error; (b) Power spectrum integral of (a)

 图 10 含输入抖动频谱成分的系统误差控制曲线 Fig. 10 The close loop of the FSM considering input jitter spectrum

 图 11 将入射抖动频谱进行辨识后结合PZT倾斜镜模型进行抖动抑制效果。(a)输入抖动频谱分布和校正后残余抖动频谱分布；(b)积分功率谱曲线 Fig. 11 The effect of jitter control combining identification of PZT-FSM and input jitter spectrum. (a) Power spectrum of input jitter and residual jitter error; (b) Corresponding power spectrum integral of (a)
5 小结

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