Encoder Calibration Method for High Precision Servo Systems with a Sinusoidal Encoder

Youngwoo Lee, Sang Hyun Kim, Seung Hi Lee, Chung Choo Chung

Research output: Contribution to journalArticlepeer-review


The sinusoidal encoder is used as an absolute position (velocity) transducer to implement the position (velocity) of actuators in many industrial applications. However, the performance of the position (velocity) can be degraded due to nonideal factors such as differential amplitudes of the encoder signals, offset, and phase shift. To analyze this problem, we formulate the relationship between the coefficients of ideal signals and the nonideal signals characteristic, which is an ellipse formed by plotting the encoder signals versus each other. In this article, we propose a nonideal signal calibration for the imperfect components of existing sinusoidal signals to improve position (velocity) regulation performance. The fictitious cosine function is used to detect the phase shift between the sine and cosine signals, and it can be designed by using the frequency of sinusoidal signals. The proposed method is validated by simulation and experimental implementation, showing noticeable improvement in estimating nonideal signal components, Lissajous error curve, phase distribution, and the position (velocity) error signal. Experimental results show that the proposed method is able to obtain the components of the nonideal signals and the accurate position (velocity) with a small error in real time, while other calibration methods are difficult to apply to fast motion.

Original languageEnglish
Pages (from-to)752-762
Number of pages11
JournalIEEE Transactions on Industrial Electronics
Issue number1
StatePublished - 2022 Jan 1


  • Fictitious cosine function
  • phase distribution
  • phase shift calibration
  • sinusoidal encoder


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