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Motor-Amplifier
The current drive generates a current I, which is proportional to the input voltage, V, with a gain of Ka.
The resulting transfer function in this case is
where Kt and J are as defined previously. For example, a current amplifier with K a = 2 A/V with the
motor described by the previous example will have the transfer function:
If the motor is a DC brushless motor, it is driven by an amplifier that performs the commutation. The
combined transfer function of motor amplifier combination is the same as that of a similar brush
motor, as described by the previous equations.
CURRENT SOURCE
V
Figure 10.6 - Mathematical model of the motor and amplifier
Encoder
The encoder generates N pulses per revolution. It outputs two signals, Channel A and B, which are in
quadrature. Due to the quadrature relationship between the encoder channels, the position resolution is
increased to 4N quadrature counts/rev.
The model of the encoder can be represented by a gain of
For example, a 1000 lines/rev encoder is modelled as
DAC
The DAC or D-to-A converter converts a 16-bit number to an analog voltage. The input range of the
numbers is 65536 and the output voltage range is +/-10V or 20V. Therefore, the effective gain of the
DAC is
Digital Filter
The digital filter has three element in series: PID, low-pass and a notch filter. The transfer function of
the filter. The transfer function of the filter elements are:
70 • Chapter 10 Theory of Operation
P/V = K a K t / Js 2
P/V = 1000/s 2
[rad/V]
I
K
a
K f = 4N/2π
[count/rad]
K f = 638
K= 20/65536 = 0.0003
K
t
JS
[V/count]
W
1
S
CDS-3310
P
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