Error Compensation for Optical Encoder via Local-Sinusoidal-Assisted Empirical Mode Decomposition With an Optimization Scheme

Abstract

The measurement precision of the optical encoder is influenced by coupling interferences from the system and the environment. To further improve the measurement precision of the optical encoder, in this article, a nonlinear error compensation method is proposed to extract the optimal underlying trend of the measurement error, which is based on the empirical mode decomposition (EMD) with a local-sinusoidal-assisted (LSA) scheme and an adaptive intrinsic mode function (IMF) selection scheme. To solve the inherent problem of mode-mixing phenomena existing in the decomposed IMFs from the measurement error, an LSA scheme is proposed to adaptively change the extreme distribution of the measurement error, which is based on an abnormal segment discrimination rule. An adaptive IMF selection scheme is proposed to construct the optimal underlying trend of the measurement error, which is first formulated as an optimization problem. Next, a significant factor is defined to select the eligible IMFs with more contributions to the underlying trend. Comparison experiments indicate that the eligible IMFs can be adaptively selected, and the proposed compensation method achieves an excellent compensation performance with the root-mean-square error of 0.380 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m in the 95% confidence interval of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> 0.017–0.016 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m, which is superior to the previous EMD-based compensation methods.