压电式快速反射镜系统建模与传递函数辨识
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摘要
为在高精度跟瞄系统中对压电式快速反射镜(PFSM)实现稳定、精确的控制,构建了PFSM系统的传递函数模型,并结合实测的PFSM系统幅频和相频响应特性,使用非线性最小二乘曲线拟合法,针对不同频率特性进行分段拟合,得到了精确的PFSM系统传递函数。与实测结果相比,在中低频段,幅度辨识误差在0.1 dB以内,相位辨识误差小于1°。由此设计的双二阶滤波器和经典比例积分(PI)相结合的控制算法有效降低了机械谐振的影响,使系统的幅值裕度提高了10.94 dB,相位裕度提高了47.2°,开环截止频率提高了181 Hz。结果表明:通过理论推导建立的PFSM模型是合理的,辨识方法具有可行性,且精度很高,为PFSM系统的复杂控制器设计提供了依据。
The piezoelectric fast steering mirror(PFSM) is widely used in the high precision tracking system. In order to ensure that the PFSM system can work more stably and precisely, the transfer function model is deduced. Combined with actual measured data of PFSM's amplitude frequency response characteristics and phase frequency response characteristics, the exact transfer function of the PFSM system is obtained by carrying out piecewise fitting for different frequency characteristics which uses the nonlinear least square curve fitting method. Compared with the actual measured result, the error of the transfer function obtained by identification is less than 0.1 dB in magnitude and 1° in phase within the low and intermediate frequency. The dual two-order filter assisted PI control algorithm which is designed based on the identified transfer function effectively eliminates the mechanical resonance. The amplitude margin of the PFSM system is increased by 10.94 dB, the phase margin is increased by 47.2°, and the open loop cut-off frequency is increased by 181 Hz with the designed control algorithm. The results show that the PFSM model established by theoretical deduction is reasonable, and the identification method is feasible and highly accurate, providing the basis for the design of the complex controller of the PFSM system.
The piezoelectric fast steering mirror(PFSM) is widely used in the high precision tracking system. In order to ensure that the PFSM system can work more stably and precisely, the transfer function model is deduced. Combined with actual measured data of PFSM's amplitude frequency response characteristics and phase frequency response characteristics, the exact transfer function of the PFSM system is obtained by carrying out piecewise fitting for different frequency characteristics which uses the nonlinear least square curve fitting method. Compared with the actual measured result, the error of the transfer function obtained by identification is less than 0.1 dB in magnitude and 1° in phase within the low and intermediate frequency. The dual two-order filter assisted PI control algorithm which is designed based on the identified transfer function effectively eliminates the mechanical resonance. The amplitude margin of the PFSM system is increased by 10.94 dB, the phase margin is increased by 47.2°, and the open loop cut-off frequency is increased by 181 Hz with the designed control algorithm. The results show that the PFSM model established by theoretical deduction is reasonable, and the identification method is feasible and highly accurate, providing the basis for the design of the complex controller of the PFSM system.
引文
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[8] 蔡骞, 周云耀, 吕永清, 等. 摆式倾斜仪传递函数的识别与仿真研究[J]. 测绘地理信息, 2013, 38(1): 60-62.
[9] 刘金星, 李洪文, 年朋, 等. 伺服系统传递函数的全数字测量方法[J]. 电子测量技术, 2010, 33(9): 8-10.
[10] 黄海波, 左韬, 陈晶, 等. 复合轴精跟踪系统伺服带宽的优化设计[J]. 红外与激光工程, 2012, 41(6): 1561-1565.
[11] 周辉, 杨明冬, 贾建军, 等. 压电驱动FSM的动态性能分析[J]. 科学技术与工程, 2013, 13(18): 5168-5171.
[2] WATKINS R J, CHEN H J, AGRAWAL B N, et al. Optical beam jitter control[C]// Proceedings of SPIE. [S.l.]: SPIE, 2004: 204-213.
[3] 向思桦, 陈四海, 吴鑫, 等. 基于新型压电驱动器的快速扫描反射镜[J]. 中国激光, 2009, 36(增刊1): 208-212.
[4] CHEN N, POTSAID B, WEN J T, et al. Modeling and control of a fast steering mirror in imaging applications[C]// IEEE International Conference on Automation Science and Engineering. Toronto: IEEE, 2010: 27-32.
[5] LI N, PAN W, YAN L, et al. Analysis of nonlinear dynamics and detecting messages embedded in chaotic carriers using sample entropy algorithm[J]. Journal of the Optical Society of America B, 2011, 28(8): 2018-2024.
[6] 凡木文, 黄林海, 李梅, 等. 抑制光束抖动的压电倾斜镜高带宽控制[J]. 物理学报, 2016, 65(2): 154-161.
[7] WASSOM S R. Low-cost large-angle steering mirror development[C]//Advances in Optomechanics. San Diego: SPIE, 2009: 74240L1-74240L12.
[8] 蔡骞, 周云耀, 吕永清, 等. 摆式倾斜仪传递函数的识别与仿真研究[J]. 测绘地理信息, 2013, 38(1): 60-62.
[9] 刘金星, 李洪文, 年朋, 等. 伺服系统传递函数的全数字测量方法[J]. 电子测量技术, 2010, 33(9): 8-10.
[10] 黄海波, 左韬, 陈晶, 等. 复合轴精跟踪系统伺服带宽的优化设计[J]. 红外与激光工程, 2012, 41(6): 1561-1565.
[11] 周辉, 杨明冬, 贾建军, 等. 压电驱动FSM的动态性能分析[J]. 科学技术与工程, 2013, 13(18): 5168-5171.
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