光栅莫尔信号正交误差实时补偿研究

Study on quadrature error real-time compensation for grating Moiré signal

针对光栅读数头输出信号存在正交误差的问题,提出基于坐标旋转数字式计算机算法(CORDIC)的正交误差实时补偿方法。针对CORDIC算法在正余弦信号角度解算时存在误差较大区间以及在正余弦信号峰值区间角度解算灵敏度低的问题,引入向量模式双迭代方法抑制CORDIC算法因迭代收敛过快而带来的角度解算误差,并结合局部查表法消除信号峰值区间的角度解算误差。正交误差补偿过程包括相位解算、相位补偿和信号重构3个环节。以解算出的角度值为对象进行整周期误差角度的实时补偿,采用CORDIC算法旋转模式根据补偿后的角度值重构余弦信号,实现对莫尔信号正交误差的实时补偿。以FPGA为平台实现该补偿方法并验证其相位差检测和补偿效果,实验表明信号在正交误差[1°,10°]时,相位检测误差在±0.04°以内;信号在不同频率不同相位差时,补偿后其相位最大误差在±1°以内,平均误差在±0.1°以内,均方差在0.5°以内,证明该方法可有效实现对莫尔信号正交误差的实时补偿。

Aiming at the problem that quadrature error exists in the output signals of grating reading heads,a quadrature error real-time compensation method based on Coordinate Rotation Digital Computer,（ CORDIC） algorithm is proposed. Aiming at the problems that there exist large error interval in the sine-cosine signal angle solution and low angle solution sensitivity in the sine-cosine signal peak interval in the CORDIC algorithm,a vector pattern bi-iteration method is introduced to suppress the angle solution error caused by the CORDIC algorithm due to too quick iteration convergence speed,and the local table look-up method is used in combination to eliminate the angle solution error in the signal peak interval. The quadrature error compensation process consists of three steps： phase solution,phase compensation and signal reconstruction. Taking the solved angle value as the object,the angle errors are compensated in real time in complete period. The CORDIC rotation mode is used to reconstruct the cosine signals from the compensated angle values so as to realize the real-time compensation of the quadrature errors of Moiré signals. This compensation method was implemented on an FPGA platform,and the phase difference measurement and compensation performance of this method were verified. Test results indicate that with the signal quadrature error of [1°,10°],the phase measurement error is within ± 0. 04°; for the signals with different frequencies and phase differences,after compensation the maximum phase error is within ± 1°,the mean error is within ± 0. 1°,and the mean square deviation is within 0. 5°,which proves that the proposed method can effectively achieve the real-time compensation of the quadrature errors of Moiré signals.