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Probabilistic learning technique for improved accuracy of sinusoidal encoders

Sinusoidal-encoder-based digital tachometers are often limited by nonidealities in both encoder construction and interface electronics. A probabilistically based compensation technique is presented which dispenses with the need for specialized calibration equipment. A code-density array, obtained during a learning phase, is utilized to yield a compensation function which approximates to the average relationship over the mechanical cycle between the calculated electrical angle (as determined by an arctangent-based algorithm) and the actual angle. An extended version of this probabilistically compensated sinusoidal encoder technique is used to compensate for variations in the encoder characteristics as it rotates through a mechanical cycle. An analysis of the learning-time requirements of the system is presented. Practical results, utilizing performance measures common in the testing of analog-to-digital converters, confirm the utility of the method. An example of the benefits which accrue from the inclusion of the enhanced sensor in closed-loop systems is also provided.