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The model of the encoder can be represented by a gain of
K
= 4N/2π [count/rad]
f
For example, a 1000 lines/rev encoder is modeled as
K
= 638
f
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
K= 20/65536 = 0.0003 [V/count]
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:
PID
Low-pass
Notch
The filter parameters, K, A, C and B are selected by the instructions KP, KD,
relationship between the filter coefficients and the instructions are:
The PID and low-pass elements are equivalent to the continuous transfer function G(s).
G(s) = (P + sD + I/s) · a / (s + a)
where,
P = KP
D = T*KD
I = KI/T
1
a=
T
where T is the sampling period, and B is the pole setting
For example, if the filter parameters of the DMC-21x5 are
KP = 16
KD = 144
KI = 2
PL = 0.75
T = 0.001 s
the digital filter coefficients are
Chapter 10 Theory of Operation ▫ 129
K ( Z −A)
D( z)=
+
Z
1
B
L(z) =
Z
B
( Z − ̄ z )(Z −z)
N (z )=
( Z − p)(Z− ̄ p )
K = (KP + KD)
A = KD/(KP + KD)
C = KI
B = PL
(
)
1
ln
B
CZ
Z −1
and PL, respectively. The
KI
DMC-21x5 User Manual 1.0a1
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