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1 Opto-Electronic Engineering Article DOI: 1.186/oee Scan signal HV e PZTTM i Controller 1 619; 619 r CCD TH74 A. [J]. 1845(3): 1774 Systemidentificationandcontrolforlarge aperturefaststeeringmirrordrivenbypzt 1 Key Laboratory of Adaptive Optics, Chinese Academy of Sciences, Chengdu, Sichuan 619, China; Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 619, 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 Citation: Huang L H, Fan M W, Zhou R, et al. System identification and control for large aperture fast-steering mirror driven by PZT[J]. Opto-Electronic Engineering, 18, 45(3): (116438) (198-) hlhai@ioe.ac.cn

2 DOI: 1.186/oee () [1-4] [1][] [3-4] [5-1] PID [] Levy [11-14] [3] 8 SL, (1) D h ω=πf f D h θ L S (1) [3] (1) k F ( s) k 1 s s zk zk zk, () s pkpks pk k 1,,, L s j Laplace zk pk zk pk () F FSM( 1 s) F ( s) F ( s) F ( s), (3) M (stochastic parallel gradient descentspgd) 3 SPGD M 1774-

3 DOI: 1.186/oee [15-17] SPGD J J J J J (, ), (4),,, } { 1 N { 1,,, N } N=M SPGD 1),,, } { 1 N,,, } { 1 N 1 N 1 N ) (3) J J, ) ( J J (, ) 3) ( J J ) ( J J ) (5) {,,, } {,,, } 1 N 1 N J 4 5 mm 5 mm3 mm 1 CCD CCD ( ) Scan signal i HV r e PZTTM Controller CCD 1 Fig. 1 Optical structure for piezoelectric fast-steering mirror system identification i() (high voltage amplifierhv) e=ir r 3 Hz 5 Hz 7 Hz [3] ( 14 mm 5 mm) 5 Hz 3 Hz PI 5 Hz SPGD 7 9 (3) M=

1774 7 9 7 SPGD 7 1 3 9 ( 5 Hz 7 Hz ) 1 5 Hz 3 1-1 - -3 Phase/deg

-36 Phase/deg -7 5 1 15 (d) Phase/deg - -36-7 5 1 15 3 7 9 (c) 7 (d) 9

4 DOI: 1.186/oee SPGD ( 5 Hz 7 Hz ) 1 5 Hz Phase/deg mm Fig. Frequency response of piezoelectric fast-steering mirror with a 5 mm aperture Phase/deg Phase/deg (c) Phase/deg (d) Phase/deg (c) 7 (d) 9 Fig. 3 Frequency responses of identified model and detected models. Identification of a 7th order model; Identification of a 9th order model; (c) Local detail for the 7th order identification; (d) Local detail for the 9th order identification

5 DOI: 1.186/oee Table 1 Identification results for the 9 th order model Levi Levy Levy Fig. 4 Identification result using Levy method with the same identified d SPGD 7 9 J.6.55 Levy 4 Levy e 5 Hz ± db e=i-r 6 15 Hz 1 Hz

5 Actual detected frequency response after resonant depression for

Phase/deg -5-1 6 3-3 1 1 3-3 1 1 3 6 Fig.

Close loop of the FSM without resonant depression; Close loop of

6 DOI: 1.186/oee Phase/deg mm Fig. 5 Actual detected frequency response after resonant depression for the 5 mm piezoelectric fast-steering mirror 5 5 Phase/deg Phase/deg Fig. 6 Close loop of the FSM before and after resonant depression. Close loop of the FSM without resonant depression; Close loop of the FSM with resonant depression PZT Hz Hz 5 1 Hz =3.4 Hz 5 Hz 7 Hz RMS 11.6 rad RMS 7.9 rad RMS 3.5 rad 9 8 Hz 1 Hz 1 Hz Hz 3 Hz

1774 Position measurement/rad 6 4 - -4 4 8 1 16 Time/s Position measurement/rad

8 Residual jitter error with and without resonant depression 1 1-1 -4 1 1 1 PI

9 Power spectrums of input jitter and residual jitter error; Power spectrum

1 The close loop of the FSM considering input jitter spectrum 1 PI 1-1 -4 1 1 1

7 DOI: 1.186/oee Position measurement/rad Time/s Position measurement/rad Time/s 7 Fig. 7 The curl of input jitter against time 8 Fig. 8 Residual jitter error with and without resonant depression PI PI PSD for total tilt/(rad /Hz) PI PI Fig. 9 Power spectrums of input jitter and residual jitter error; Power spectrum integral of Phase/deg Fig. 1 The close loop of the FSM considering input jitter spectrum 1 PI PSD for total tilt/(rad /Hz) PI PI PZT Fig. 11 The effect of jitter control combining identification of PZT-FSM and input jitter spectrum. Power spectrum of input jitter and residual jitter error; Corresponding power spectrum integral of

8 DOI: 1.186/oee PZT 35 Hz Hz Hz 35 Hz Hz PZT 1 35 Hz Hz Hz 5 db Hz Hz RMS.3 rad 5 SPGD SPGD PZT LQG(linear quadratic gaussian) [1] Wu Q Y, Wang Q, Peng Q, et al. Wide bandwidth control of fast-steering mirror driven by voice coil motor[j]. Opto-Electronic Engineering, 4, 31(8): ,,,. [J]., 4, 31(8): [] Zhou Q K, Ben-Tzvi P, Fan D P, et al. Design of Fast Steering Mirror systems for precision laser beams steering[c]//international Workshop on Robotic and Sensors Environments, 8: [3] Li X Y, Ling N, Chen D H, et al. Stable control of the fast steering mirror in adaptive optics system[j]. High Power Laser and Particle Beams, 1999, 11(1): ,,,. [J]., 1999, 11(1): [4] Li X Y, Jiang W H. Effective bandwidth analysis of adaptive optics control system[j]. Acta Optica Sinica, 1997, 17(1): ,. [J]., 1997, 17(1): [5] Ding K, Huang Y M, Ma J G, et al. Error adaptive feedforward composite control of fast-steering-mirror[j]. Chinese Journal of Lasers, 11, 38(7): 757.,,,. [J]., 11, 38(7): 757. [6] Monirabbasi S, Gibson S. Adaptive control in an adaptive optics experiment[j]. Journal of the Optical Society of America A Optics Image Science, and Vision, 1, 7(11): A84 A96. [7] Kim B S, Gibson S, Tsao T C. Adaptive control of a tilt mirror for laser beam steering[c]//proceedings of the 4 American Control Conference, 4, 4: [8] Wang Q, Chen K, Fu C Y. Method for controlling fast-steering mirror driven by voice coil motor based on the closed-loop performance[j]. Opto-Electronic Engineering, 5, 3(): 9 11, 18.,,. [J]., 5, 3(): 9 11, 18. [9] Kim J J, Nagashima M, Agrawal B N. Optical beam jitter control for the NPS HEL beam control testbed[r]. Monterey, CA: Naval Postgraduate School Monterey CA, 11. [1] Watkins R J, Chen H J, Agrawal B N, et al. Optical beam jitter control[j]. Proceedings of SPIE, 4, 5338: [11] Shi J J, Yao B D, Lu J G. Modeling and transfer function identification of FSM system[j]. Infrared and Laser Engineering, 13, 4(1): ,,. [J]., 13, 4(1): [1] Hu H J, Ma J G, Wang Q, et al. Transfer function identification in a fast steering mirror system[j]. Opto-Electronic Engineering, 5, 3(7): 1 3, 1.,,,. [J]., 5, 3(7): 1 3, 1. [13] Fan M W, Huang L H, Li M, et al. High-voltage drive and control for piezoelectric fast steering mirror[j]. Optics and Precision Engineering, 15, 3(1): ,,,. [J]., 15, 3(1): [14] Fan M W, Huang L H, Li M, et al. High-bandwidth control of piezoelectric steering mirror for suppression of laser beam jitter[j]. Acta Physica Sinica, 16, 65(): 49.,,,. [J]., 16, 65(): 49. [15] Geng C, Tan Y, Mu J B, et al. Experimental research of tip/tilt control of a multi-channel fiber-laser array[j]. Acta Physica Sinica, 13, 6(): 46.,,,. [J]., 13, 6(): 46. [16] Zheng Y, Shen F. Simulation and analysis of stochastic parallel gradient descent control algorithm for coherent combining[j]. Proceedings of SPIE, 9, 7156: 71563C. [17] Zheng Y, Shen F. Research on phase-locking technique for -channels fiber laser coherent beam combination based on stochastic parallel gradient descent algorithm[j]. Chinese Journal of Lasers, 1, 37(3): ,. [J]., 1, 37(3):

9 DOI: 1.186/oee Systemidentificationandcontrolforlarge aperturefaststeeringmirrordrivenbypzt 1 Key Laboratory of Adaptive Optics, Chinese Academy of Sciences, Chengdu, Sichuan 619, China; Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 619, China Phase/deg System identification using SPGD method 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 5 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 ± db in the range of Hz to 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 15 Hz to 1 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 rad to 7.9 rad. However, after the resonance elimination and correction, the RMS of the jitter amplitude decreased to 3.5 rad. 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. Citation: Huang L H, Fan M W, Zhou R, et al. System identification and control for large aperture fast-steering mirror driven by PZT[J]. Opto-Electronic Engineering, 18, 45(3): 1774 Supported by National Natural Science Foundation of China (116438) * hlhai@ioe.ac.cn

[1-3] (Smile) [4] 808 nm (CW) W 1 50% 1 W 1 W Fig.1 Thermal design of semiconductor laser vertical stack ; Ansys 20 bar ; bar 2 25 Fig

[1-3] (Smile) [4] 808 nm (CW) W 1 50% 1 W 1 W Fig.1 Thermal design of semiconductor laser vertical stack ; Ansys 20 bar ; bar 2 25 Fig 40 6 2011 6 Vol.40 No.6 Infrared and Laser Engineering Jun. 2011 808 nm 2000 W 1 1 1 1 2 2 2 2 2 12 (1. 710119 2. 710119) : bar 808 nm bar 100 W 808 nm 20 bar 2 000 W bar LIV bar 808 nm : : TN248.4 TN365