Shaft encoder characterisation through analysis of the mean-squared errors in nonideal quantised systems

Incremental shaft encoders with square outputs are characterised by quantisation of the sensed position and by additional errors caused by nonidealities in sensor construction that contribute to additional measurement error. Digital estimates of the velocity of a rotating mass are frequently calculated by the differentiation of successive quantised position estimates, derived from a digital sensor such as a shaft encoder. New formulae are presented for the associated mean-squared error. In particular, the combined influences of uniformly distributed noise, sinusoidal perturbations and quantisation error on a nominally constant rate system are treated in an analytical manner. Experimental data, obtained from encoder-based shaft velocity measurements, are utilised for sensor characterisation, using the theoretical models proposed. A 'figure-of-merit', defining the differential error caused by variations of transition locations from their nominal values over the circumference of the encoder, is obtained. It is shown that the influence of shaft velocity variation on the characterization process can be minimised by deriving the variation in the mean-squared velocity error due to the addition of a sinusoidal perturbation.