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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 PID and low-pass elements are equivalent to the continuous transfer function G(s).
where T is the sampling period.
For example, if the filter parameters of the CDS-3310 are
the digital filter coefficients are
and the equivalent continuous filter, G(s), is
The notch filter has two complex zeros, Z and z, and two complex poles, P and p.
The effect of the notch filter is to cancel the resonance affect by placing the complex zeros on top of
the resonance poles. The notch poles, P and p, are programmable and are selected to have sufficient
CDS-3310
PID
D(z) =
1 −
Low-pass
L(z) =
Z
Notch
N(z) =
(
⋅
K = (KP + KD)
4
A = KD/(KP + KD)
C = KI/2
B = PL
G(s) = (P + sD + I/s) ∗ a/(S+a)
P = 4KP
⋅
D = 4T
KD
I = KI/2T
a = 1/T ln (1/B)
KP = 4
KD = 36
KI = 2
PL = 0.75
T = 0.001 s
K = 160
A = 0.9
C = 1
a = 250 rad/s
G(s) = [16 + 0.144s + 1000/s} ∗ 250/ (s+250)
−
(
)
K Z
A
CZ
+
− 1
Z
Z
B
−
B
−
−
(
)(
)
Z
z Z
z
−
−
)(
)
Z
p Z
p
Chapter 10 Theory of Operation
i
71
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