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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 5, OCTOBER 2002

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New Interpolation Method for Quadrature Encoder Signals
K. K. Tan, Member, IEEE, Huixing X. Zhou, and Tong Heng Lee, Member, IEEE
Abstract—This paper presents a new interpolation method suitable for increasing the measurement resolution obtainable from quadrature encoder signals. Based on the existingsinusoidal signals, high-order sinusoids can be derived, from which binary pulses can be generated, which can be decoded using only standard servo controllers for position information. A look-up table, constructed off-line, serves as the inferencing engine for the proposed method. Imperfections in the encoder signals can be directly compensated for in the look-up table, including mean and phaseoffsets, amplitude difference, and waveform distortion. Simulation and experimental results are provided in this paper. Index Terms—Encoder resolution, interpolation errors, look-up tables, measurement interpolation, quadrature encoder signals.

I. INTRODUCTION IGH-PRECISION and resolution motion control relies critically on the precision and resolution achievable from the encoders. These factorsare in turn limited by the technology behind the manufacturing of encoders. To date, the scale grating on linear optical encoders can be manufactured to less than four micrometers in pitch, but, clearly, further reduction in pitch is greatly constrained by physical considerations. This implies an optical resolution of one micrometer is currently achievable. Interpolation using soft techniques willprovide an interesting possibility to further improve on the encoder resolution, by processing the analog encoder signals online to yield the small intermediate positions. The error sources associated with position information obtained this way can be classified under pitch and interpolation errors. Pitch errors are due to scale manufacturing tolerances and mounting distortion. They can becompensated via the same procedures that will be carried out for general geometrical error compensation. Interpolation errors are associated with the accuracy of subdivision within a pitch, affecting any calibration performed. Ideal signals from encoders are a pair of sinusoids with a quadrature phase difference between them. Interpolation operates on the relative difference in amplitude and phase ofthese paired sinusoids. Therefore, interpolation errors will occur if the pair-periodic signals deviate from the ideal waveforms on which the interpolation computations are based. These deviations must be corrected before interpolation, using digital signal processing techniques, to reduce the interpolation errors. The technology to compensate the mean value errors, phase and amplitude errors fortwo quadrature sinusoidal signals was

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first introduced by Heydemann [1]. He used least squares fitting to compute these error components efficiently and made correction for the two nonideal sinusoidal signals. Using this method, K. P. Birch [2] was able to calculate optical fringe fractions to nanometric accuracy. By making use of the amplitude variation with angle, Birch divided one periodof the sinusoidal signal into equiangular segments to increase the effective electrical angle resolution. The micro step controller [3] and encoder code compensation technology [4] have been developed based on this method. Relevant applications can also be found in [5], [6]. These interpolation approaches generally require explicit high-precision analog-to-digital converters in the control system,and a high-speed DSP to compute the electrical angle to the required resolution. Therefore, they are inapplicable to the typical servo controller with only digital incremental encoder interface. Furthermore, it is cumbersome to integrate sinusoidal correction with interpolation since the correction parameters must be calibrated off-line. As a result, most servo controllers that are able to...