Page 357 - Mechatronics with Experiments

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October 9, 2014 8:1
JWST499-c06
JWST499-Cetinkunt
SENSORS 343 254mm×178mm
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FIGURE 6.14: Excitation voltage for the rotor winding and the induced stator voltages. The
induced voltages are shown as a function of time for a constant rotor speed over a period of
one revolution.

angular position changes beyond one revolution are kept track of through digital counting
circuits. The rotor excitation voltage is (generated by an oscillator circuit),
V (t) = V ⋅ sin(w t) (6.53)
r ref r
The induced voltage on the stator windings are (Figure 6.14)
V (t) = k ⋅ V (t) ⋅ sin( (t)) = k ⋅ V ⋅ sin(w t) ⋅ sin( (t)) (6.54)
s1 0 r 0 ref r
V (t) = k ⋅ V (t) ⋅ cos( (t)) = k ⋅ V ⋅ sin(w t) ⋅ cos( (t)) (6.55)
s2 0 r 0 ref r
Next, the V , V are multiplied by sin and cos functions in the RTDC circuit,
s2
s1
V (t) = k ⋅ V (t) ⋅ sin( (t)) ⋅ cos( (t)) (6.56)
0
r
f1
V (t) = k ⋅ V (t) ⋅ cos( (t)) ⋅ sin( (t)) (6.57)
r
f2
0
Then the output of the error amplifier is
ΔV (t) = k ⋅ V ref ⋅ sin(w t) ⋅ sin( (t) − (t)) (6.58)
0
r
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Then, the signal is demodulated to remove the sin(w t) component by a rectifier and low
r
pass filter. Then, the signal is fed to an integrator which provides input to the voltage
controlled oscillator (VCO). The output of the VCO is fed to an up-down counter to keep
track of the position. This results in making the up-down counter increase or decrease in a
direction so that sin( − ) approaches zero. The value of the up-down counter is converted
to angle by a DAC as an analog signal to feed the sin and cos multiplication circuit. The
iteration on continues until = , at which time the rotor position information is latched
from the up-down counter as digital data. The algorithm finds the angle by iteratively
changing . The iteration stops when ΔV is equal to zero, at which time it means that
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