Analysis and application of real-time compensation of positioning precision of the turntable with a harmonic function

Authors

  • Yi Zhou China Jiliang University, School of Measurement and Testing Engineering, Hangzhou, 310018, China
  • Weibin Zhu China Jiliang University, School of Measurement and Testing Engineering, Hangzhou, 310018, China
  • Yi Shu China Jiliang University, School of Measurement and Testing Engineering, Hangzhou, 310018, China
  • Yao Huang Zhejiang University, College of Optical Science and Engineering, State Key Laboratory of Modern Optical Instrumentation, Hangzhou 310027, China https://orcid.org/0000-0001-5070-1778
  • Wei Zou National Institute of Metrology, Beijing, 100029, China
  • Zi Xue National Institute of Metrology, Beijing, 100029, China

DOI:

https://doi.org/10.24425/mms.2022.142269

Keywords

harmonic function, positioning error, compensation, real-time, CORDIC

Abstract

In order to guarantee the accuracy of turntable angle measurement, a real-time compensation method for turntable positioning precision based on harmonic analysis is proposed in this paper. Firstly, the principle and feasibility of the real-time compensation method are analysed, and a detailed description of harmonic compensation is provided herein. Secondly, we analyse the relationships between the surface number of the polygon with the compensation order of the harmonic function and its corresponding compensation accuracy. The effects of the iterations number and the data width on calculation accuracy in the coordinate rotation digital computer (CORDIC) algorithm are analysed and the quantization models of the approximation error and rounding error of the CORDIC algorithm are established. Then, the calculation of the harmonic error function and real-time compensation processes are implemented on a field programmable gate array (FPGA) chip. The resource occupation and time delay of the phase angle calculation and the harmonic component calculation are discussed separately. Finally, the validity of the harmonic compensation method is proven through comparing the compensation effect with that of linear interpolation and the polynomial compensation method. The influences of the compensation order, the iterations number and the data width on the compensation results are demonstrated by simulation. A test platform with a laboratory-made FPGA circuit is built to evaluate the effect of real-time compensation with the harmonic function and the positioning error compensation can be performed within 760 ns. The results confirmed the effectiveness of the harmonic compensation method, revealing an improvement of the positioning precision from 54.21ʹʹ to 1.63ʹʹ, equivalent to 96.99% reduction in positioning error.

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Published

2022-09-30

How to Cite

Zhou, Yi, et al. “Analysis and Application of Real-Time Compensation of Positioning Precision of the Turntable With a Harmonic Function”. Metrology and Measurement Systems, vol. 29, no. 3, Sept. 2022, pp. 553-71, doi:10.24425/mms.2022.142269.

Issue

Vol. 29 No. 3 (2022)

Section

Articles

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