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192 • Chapter 10 Theory of Operation DMC-1700/1800
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 D(z) =
KZ A
Z
CZ
Z
()
−
+
− 1
Low-pass L(z) =
1
−
−
B
ZB
Notch N(z) =
))((
))((
pZpZ
zZzZ
−−
−−
The filter parameters, K, A, C and B are selected by the instructions KP, KD, KI and PL, respectively. The
relationship between the filter coefficients and the instructions are:
K = (KP + KD)⋅ 4
A = KD/(KP + KD)
C = KI/2
B = PL
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 = 4KP
D = 4T
⋅
KD
I = KI/2T
a =
⎟
⎠
⎞
⎜
⎝
⎛
B
n
T
1
1
1
where T is the sampling period, and B is the pole setting
For example, if the filter parameters of the DMC-1700 or DMC-1800 are
KP = 4
KD = 36
KI = 2
PL = 0.75
T = 0.001 s
the digital filter coefficients are
K = 160
A = 0.9
C = 1
a = 250 rad/s
and the equivalent continuous filter, G(s), is