Galil DMC-4040, User Manual

Page: 199 / 284

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) =
K Z A
Z
CZ
Z
( )
−
+
−
1
Low-pass L(z) =
1
−
−
B
Z B
Notch N(z) =
) )( (
) )( (
p Z p Z
z Z z Z
− −
− −
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)
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 = KP
D = T
⋅
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-40x0 are
KP = 16
KD = 144
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
G(s) = [16 + 0.144s + 1000/s]
∗
250/ (s+250)
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 damping. It is best to select
DMC-40x0 User Manual Chapter 10 Theory of Operation
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