基于遗传算法的光栅信号辨识与偏差补偿研究

为减小圆光栅测量过程中叠栅条纹信号的细分误差, 提出了一种对叠栅条纹采样信号进行参数辨识与偏差补偿的方法。该方法运用遗传算法参数辨识理论, 不受信号模型参数初值选取影响, 寻优特性和适用性良好, 使复现的信号模型较好地拟合原始采样信号。信号采样实验中控制光栅匀速转动, 采样两个栅距内的周期信号, 其次对采样得到的离散数据进行频谱分析, 建立光栅信号的数学模型, 进而通过遗传算法对引起细分误差的信号参数进行识别并对细分误差进行数值补偿。实验结果表明, 遗传算法对构建的信号模型参数辨识准确; 对比补偿前后李萨如图形, 验证了该方法对叠栅条纹信号正弦性误差具有良好的补偿效果; 检测单个栅距内的细分误差, 补偿前后误差值由10.65″减小到3.31″。该方法适用于光栅编码器等位移测量系统, 保证测量精度和可靠性。

Abstract

In order to eliminate the subdivision error of moiré fringe signals in the circular grating measurement process, a parameter identification and deviation compensation method for grating sampled signal is proposed. The method is based on the parameter identification theory of the genetic algorithm and cannot be affected by initial signal model parameters with characteristics of optimization and applicability. The regenerated signal model can fit the original signal well. The periodic signals between two grating pitches are sampled with grating rotating at a constant speed in sampling experiments. From the sampled discrete data, the frequency spectra are obtained and analyzed for establishing the mathematical model of grating signals. The parameters which cause the subdivision error are identified by using the genetic algorithm to compensate the subdivision error. The experimental results show that the parameters of signal model constructed by genetic algorithm are identified accurately. The sine deviation of moiré fringe signals is compensated by comparing the Lissajous figures with and without compensation. The subdivision error detected in one grating pitch decreases from 10.65″ to 3.31″. This method can actually be used in grating encoder system and other displacement measuring systems, which ensures the measurement accuracy and reliability.

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