Page 379 - Mechatronics with Experiments

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JWST499-Cetinkunt
JWST499-c06
SENSORS 365 254mm×178mm
on when that happens (right before the T sampling period expired or right after it), can vary
estimated velocity by 100%.
Instead of keeping a fixed time period and counting the number of pulses during
that period to estimate the velocity, we measure the time period between two consecutive
pulses using a high resolution timer, that is using a μs resolution timer/counter. Then, the
estimated velocity is
V = 1[count]∕T (6.89)
period
Since the time period measurement is very accurate, the velocity estimation is more
accurate than the first case. Let us assume that we have an encoder with a resolution of
10 000 cnt∕rev (including a ×4 quadrature count multiplication), and that it is connected to
a shaft which rotates at 6.0rev∕min. Assume that the sampling rate is T sampling = 1.0ms.
This results in 60 000 counts∕min or equivalently 1 cnt∕ms.
Let us assume that due to small variations in the velocity, there were two count
changes within one sampling period instead of the normal one pulse, one at the beginning
of the sampling period, and one at the 900 μs mark. The velocity estimation using the fixed
sampling period approach would give
V = 2 cnt∕1.0 ms (6.90)
= 2 cnt∕1.0 ms(60 000 ms∕1 min)(1 rev∕10 000 cnt) (6.91)
= 12 rev∕min. (6.92)
If the second pulse transition did not happen at the 900 μs mark, but beyond the 1.0ms
sampling period, that is at 1.001 ms, the estimated velocity would have been,

V = 1 cnt∕1.0 ms (6.93)
= 1 cnt∕1.0 ms(60 000 ms∕1min)(1rev∕10 000 cnt) (6.94)
= 6rev∕min. (6.95)
If the velocity was estimated by the time period measurement method, then the instantenous
velocity would be accurately estimated. Let us assume that we measure the time period
between two consecutive pulses using a 1 μs resolution timer/counter. Let us assume that
in one case the measured time period between two pulses is 900 μs and in another case it is
901 μs due to timer/counter resolution. The estimated velocity from both of these cases is

V = 1 cnt∕0.9ms = 6∕0.9rpm = 6.6667 rpm (6.96)
1
and the second estimated velocity is
V = 1 cnt∕0.901 ms = 6∕0.901 rpm = 6.6593 rpm (6.97)
2
Clearly, using the time period measurement between two consecutive pulses using a 1 μs
resolution timer/counter results in 0.11% error in velocity measurement. Whereas, counting
the number of pulses during a fixed sampling period can result in velocity measurement
errors as high as 100%.

6.6 ACCELERATION SENSORS

Three different types of acceleration sensors, also called accelerometers, each based on a
different transduction principle, are discussed as follows.

1. An inertial motion based accelerometer, where the sensor consists of a small mass-
damper-spring in an enclosure and mounted on the surface of an object whose accel-
eration is to be measured. The displacement (x) of the sensor inertia is proportional