Adaptive Algorithms for Quantization Error Normalization of Digital Encoder-Based Tachometers

The authors’ analysis of the instantaneous and average values digital tachometer quantization error assessment in the dynamic measurements of angular velocity with an encoder allowed to create an innovative a mathematical model for calculating the critical speed numerical value for an exponential mathematical model that adequately describes the transient process of the electric machine’s operation. The authors discovered that the value of the critical speed depends on the resolution ƶ of the encoder, the quantization frequency \({f}_{0}\) , and the duration of the sample time interval \({t}_{0}\) , which variation allows to measure the angular velocity with a predetermined normalized value of the quantization error during the transient process of the electric machine from the lower to the upper measurement limit. The practical significance of the proposed approach is as follows. At the beginning of measurements \(n{\le n}_{c}\) , the transient characteristics of electric machines are characterized by dips, jumps, synchronous dips in angular velocity, the amplitude and duration of which must be determined with high accuracy. The most effective here is the structure and algorithm of the digital tachometer of instantaneous values. In the section of the transition characteristic, when \(n{>n}_{c}\) , such dips are not significant. In addition, the quantization error of instantaneous values also increases with the increase in angular velocity. Therefore, in this section of the transient characteristic, we advise to configure the hardware and software for the tachometer by using an average value.