转台定位误差谐波函数计算方法研究

为了保障转台定位误差谐波补偿准确性,针对一种谐波误差函数计算方法开展研究。 首先分析了转台定位误差谐波补 偿方法,阐述了基于坐标旋转数字计算方法(CORDIC)的谐波误差函数计算原理可行性;针对算法原理误差进行分析,分别建 立了与迭代次数 n、数据位宽 b 的量化模型,明确了算法在谐波补偿值计算过程的总量化误差;根据计算精度要求对 n 和 b 取值 进行设计,在现场可编程门阵列(FPGA)中实现谐波误差函数计算并进行实时误差补偿。 以谐波误差函数理论值为参考,仿真 证明了计算方法的有效性;以自制电路板为实验平台,证明了计算方法的总量化误差模型正确性;搭建转台测试平台验证定位 误差补偿效果,实验结果证明采用本文提出的谐波误差函数计算方法进行补偿,使转台定位精度由 29. 0"提高至 5. 3" 。

A calculation method for positioning error of turntable based on harmonic function

To ensure the accuracy of harmonic compensation value for the turntable positioning error, a calculating method for the harmonic error function is proposed. The harmonic compensation method for turntable positioning is described and the feasibility of the CORDIC algorithm for harmonic error function calculation is introduced in detail. Based on the principle of the CORDIC, the quantitative models of the iteration number n and the data width b are established, respectively. The overall quantization error of calculating harmonic function is deduced. The calculating method is implemented by using the laboratory-made field-programmable gate array circuit. The value of n and b are determined to satisfy the calculation accuracy. Finally, a series of evaluation tests are performed to demonstrate the effectiveness of the method by comparing theoretical and computational values. The data of experiment performed on the test turntable platform confirm that the proposed method can calculate the value of harmonic function effectively. The positioning accuracy of turntable is improved from 29. 0" to 5. 3" with this method.