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仿真实验采用的脉冲传递函数矩阵为:
为了使仿真更贴近真实环境,在输出信号上叠加通过白色噪声经过成型滤波器的方式生成的有色噪声信号。辨识实验的实验框图如图3所示。
辨识实验流程如图4所示。
a1 a2 b0 b1 b2 Static gain True value −1.55 0.72 0.212 0.389 0.248 4.99 Estimation −1.540 0.712 0.220 0.395 0.253 5.05 Table 1. Simulation results of α-X channel parameter estimation
a1 a2 b0 b1 b2 Static gain True value −1.55 0.72 0.212 0.389 0.248 4.99 Estimation −1.540 0.712 0.220 0.395 0.253 5.05 Table 2. Simulation results of α-Y channel parameter estimation
a1 a2 b0 b1 b2 Static gain True value −1.50 0.71 −0.212 −0.318 −0.354 4.21 Estimation −1.520 0.727 −0.188 −0.285 −0.345 3.95 Table 3. Simulation results of β-X channel parameter estimation
a1 a2 b0 b1 b2 Static gain True value −1.50 0.71 0.212 0.318 0.354 4.21 Estimation −1.495 0.709 0.222 0.321 0.357 4.21 Table 4. Simulation results of β-Y channel parameter estimation
经计算获得的耦合矩阵和伺服机构脉冲传递函数系数见表5~表7。
cos(θX ) cos(θY) sin(θX) sin(θY) True value 0.707 0.707 0.707 0.707 Estimation 0.707 0.674 0.707 0.739 Table 5. Calculation results for decoupling matrix
a1 a2 b0 b1 b2 Static gain True value −1.550 0.720 0.300 0.550 0.350 4.99 Estimation −1.540 0.712 0.311 0.559 0.358 5.04 Table 6. Results of pulse transfer function parameters for α drive axis
a1 a2 b0 b1 b2 Static gain True value −1.500 0.710 0.300 0.450 0.500 4.21 Estimation −1.508 0.718 0.291 0.430 0.496 4.10 Table 7. Results of pulse transfer function parameters for β drive axis
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辨识实验是在Matlab/dSPACE半实物仿真平台上进行的。伺服机构的输入信号通过半实物仿真平台D/A接口输出,并通过功率放大器放大后驱动伺服机构的两组音圈电机执行推拉工作;通过电涡流位置传感器测量并解算伺服机构反射镜转动的角度,并以模拟量的形式输出;通过A/D接口采集电涡流位置传感器输出的模拟信号以及D/A接口输出的输入信号,并转换成数字信号;Matlab对采集到的输入/输出信号利用m语言编程对脉冲传递函数进行辨识[17]。
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为了验证辨识算法的有效性和准确性,针对自行研制的一款口径为100 mm、行程±10 mrad的双轴快速反射镜原理样机进行了脉冲传递函数辨识。快速反射镜伺服机构实物如图9所示。
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采用COR-IV对伺服机构脉冲传递函数进行辨识。采用M序列作为辨识用激励信号,首先利用相关—最小二乘估计算法启动运算,再采用COR-IV进行参数辨识。辨识结果见表8~表11。
Parameter a1 a2 b0 b1 b2 Result −1.8070 0.9440 −0.0300 −0.1360 −0.0340 Table 8. Parameter estimation results for α-X channel
Parameter a1 a2 b0 b1 b2 Result −1.8390 0.9650 0.0406 0.1739 0.0360 Table 9. Parameter estimation results for α-Y channel
Parameter a1 a2 b0 b1 b2 Result −1.8398 0.9939 0.0302 0.1583 0.0255 Table 10. Parameter estimation results for β-X channel
Parameter a1 a2 b0 b1 b2 Result −1.8259 0.9636 0.0434 0.2029 0.0618 Table 11. Parameter estimation results for β-Y channel
辨识结束后,将辨识结果代入到差分方程中,获取伺服机构的阶跃响应曲线,对辨识结果进行验证,响应曲线如图14~图17所示。
对图14~图17的数据从振荡次数、振荡频率、最大振荡幅值以及稳态误差等四方面进行对比分析,结果如下:
(1)从“振荡次数”方面进行对比,以进入5%误差带作为评判标准,实测结果在9~10次之间,仿真结果在10~11次之间;
(2)从“振荡频率”方面进行对比,实测结果在29.4~31.3 Hz之间,仿真结果在29.4~31.3 Hz之间;
(3)从“振荡幅值”方面进行对比,实测结果和仿真结果的误差在3%~10%范围,其中阶跃响应的第一个振荡环节误差最大;
(4)从“稳态误差”方面进行对比,四个通道的稳态误差均在5%以内。
上述对比表明,通过参数辨识获得的脉冲传递函数可反映被测伺服机构的特性。
Servo mechanism parameter identification of fast steering mirror based on flexible supports
doi: 10.3788/IRLA20200303
- Received Date: 2020-08-06
- Rev Recd Date: 2020-10-31
- Publish Date: 2021-05-21
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Key words:
- system identification /
- transfer function /
- COS-IV /
- fast steering mirror /
- MIMO
Abstract: The problems of the two-axis fast steering mirror based on flexible support was put forward firstly, a servo mechanism structure of the two-axis fast steering mirror based on flexible support was introduced briefly, the pulse transfer function of the servo mechanism was established, the MIMO system parameter identification theory was discussed, and the method based on COR-IV method was analyzed. Based on the method, the identification method of servo mechanism based on flexible support for the two-axis fast steering mirror was proposed and simulated. The experiment for the identification of servo mechanism parameters was designed to verify the method and the experimental results were compared with theoretical calculations. The experimental results show that the MIMO system parameter identification algorithm based on the COR-IV method is effective, the identification accuracy is within the expected range, and the identification results can provide data support for the adaptive control of fast steering mirror.