Results of study of quantization and discretization error of digital tachometers with encoder

Abstract

The analysis of measuring channels of angular velocity with an encoder given by the authors made it possible for the first time to obtain an equation for estimating the quantization and sampling error for an exponential mathematical model describing the transient process of operation of electrical machines. The components of the mathematical model of this dynamic error are the sampling step and the derivative, which characterizes the rate of change of the measured value over time. It was found that the errors of quantization and sampling significantly depend on the value of the resolution z of the encoder. Moreover, an increase in z leads to a decrease in the sampling error, but the relative quantization error increases. To reconcile these components of errors, the laws of change in the distinguishing ability z of the encoder are adaptive to the dynamic properties of the change in angular velocity over time.

Proved  that to ensure the maximum speed of measuring the angular velocity during the transient process, it is advisable to implement the method of changing the distinguishing ability of the encoder on the internal timers of the microcontroller proposed adaptive to its dynamic properties, and the quantization of informative periods proportional to the measured angular velocity should be carried out in "adjoining intervals".