46 Estimation of Instantaneous Speed for Rotating Systems: New Processing Techniques 527 Raw RPM estimate from Tach signal Raw RPM estimate from Tach signal Time (sec) Time (sec) Instantaneous speed estimate (rpm) Instantaneous speed estimate (rpm) 2.75 x 104 x 10 4 X: 15.26 Y: 2.521e+04 X: 15.25 Y: 2.433e+04 2.7 2.65 2.6 2.55 2.5 2.45 2.4 15 15.5 16 16.5 17 18 17.5 2.52 2.5 2.48 2.46 2.44 2.42 15.245 15.25 15.255 15.26 15.265 a b Fig. 46.7 (a) Fluctuations in the raw estimate at 25,000 RPM and (b) range of fluctuations in the raw estimate at 25,000 RPM Plugging in the values of time differences given in 46.A and 46.B into Eq. (46.9) gives, 22775:91 TrueA 26741:11 23331:37 TrueB 27510:06 The values might fluctuate anywhere within the specified range (almost 4000 RPM here). The time interval between these estimates is 0.002408 s. The fluctuation would not usually lie to the extremities of the error range but is around 650 RPM which is about 6.5 times lower than the maximum error possible. However, these are still unacceptable fluctuations which need to be minimized. Now, consider 18 pulses skipped during the above given time period: t.2745/ t.2725/ D0:048061 s (46.C) t.2746/ t.2726/ D0:048263 s (46.D) The corresponding speed ranges for 46.C and 46.D as estimated by Eq. (46.9) are, 24766:77 TrueC 24968:06 24763:54 TrueD 24964:78 Here, the values can fluctuate by a maximum of about 200 RPM. Again, the fluctuation usually does not lie in the extremities of this range and so, the change from one estimate to the next might be well under this maximum value. In fact, the corresponding RPM values are 24,867 RPM and 24,863 RPM assigned at 15.2883 s and 15.2907 s respectively. Hence within a time interval of 0.00238 s, the RPM changed by about 4 RPM which is a rate of change of about 1680 RPM/s which is much more believable given that the system goes from 0 to 25,000 RPM in 15 s. The resulting instantaneous speed curve for 18 pulses skipped is shown in Fig. 46.8.
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