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Chapter 10 Theory of Operation
y 139
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
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 elements in series: PID, low-pass and a notch filter. The transfer function of
the filter. The transfer function of the filter elements are:
the filter. The transfer function of the filter elements are:
PID
D(z)
=
K Z
A
Z
CZ
Z
(
)
−
+
− 1
Low-pass L(z)
=
1
−
−
B
Z
B
Notch
N(z)
=
(
)(
)
(
)(
)
Z
z Z
z
Z
p Z
p
−
−
−
−
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:
The relationship between the filter coefficients and the instructions are:
K = (KP + KD)
⋅
4
A = KD/(KP + KD)
C = KI/2
B = PL
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)
P = 4KP
D
=
4T
⋅
KD
I = KI/2T
a = 1/T ln (1/B)
where T is the sampling period.