2. Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
Overview: Fast steering mirror driven by piezoelectric material has been used widely for control of opto-axis stabilization. The system identification for such fast steering mirror is very important. It has decided whether we are able to reach the mirror's full correction potential. However, the system identification is difficult for mirror with large aperture, because we found that the larger aperture, the more complex of the mirror responding.
Novel system identification method based on the stochastic parallel gradient descent (SPGD) algorithm is presented for the large aperture fast-steering mirror (FSM). The proposed method can identify the complicated frequency response of the large aperture FSM accurately and improve the correcting effect of the system. The principle and mathematical model of the piezoelectric fast-steering mirror (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. A PZT-FSM with the diameter of 250 mm is taken as an example to test the effectiveness of the proposed method. Compared with the actual frequency response curves, the frequency response curves of the two kinds of models identified by different order (7th-order and 9th-order) are consistent with the actual curves. Especially for the 9th-order identified model, both the overall distribution of the curves and the local details are highly consistent with the actual curves. As a contrast, the results using the Levy method for identification are also presented. Levy method cannot accurately identify complex models. Even if the order of identification is increased, there is no significant improvement in performance.
In order to verify the accuracy of the identified model, we conduct two confirmatory experiments. First, we explore the resonance elimination of PZT-FSM by the identified model. After the resonance elimination, the frequency response is close to the frequency response of a pure-delay system. The amplitude response of the system is close to the ideal case, and the fluctuation of the amplitude response is within ± 2 dB in the range of 0 Hz to 2000 Hz. The closed-loop control effects of PZT-FSM before and after the resonance elimination are presented in the next section, where we found that the error bandwidth of the PZT-FSM has been significantly improved after the resonance elimination. Under the same condition of overshoot, the closed-loop error bandwidth increases from 105 Hz to 210 Hz. We compared the correction capability of beam jitter before and after the resonance elimination. After the correction without resonance elimination, the root mean square (RMS) of the jitter amplitude declined from 11.6 μrad to 7.9 μrad. However, after the resonance elimination and correction, the RMS of the jitter amplitude decreased to 3.5 μrad. The experimental results show that the proposed method can not only eliminate the resonance, but also improve the closed-loop error bandwidth.
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. Accurate model identification for the large aperture FSM is also meaningful to advanced control methods, such as LQG control and adaptive filters control method. Through the combination of these advanced control methods, on-line identification and correction of specific resonance frequency can be realized.