Low-pass L(z) =
Notch N(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
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/T
a =
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 = 2
a = 250 rad/s
and the equivalent continuous filter, G(s), is
G(s) = [16 + 0.144s + 2000/s] ∙ 250/ (s+250)
The notch filter has two complex zeros, z and , and two complex poles, p and .
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
the notch parameters by the frequency terms. The poles and zeros have a frequency in Hz, selected by the
command NF. The real part of the poles is set by NB and the real part of the zeros is set by NZ.
The most simple procedure for setting the notch filter, identify the resonance frequency and set NF to the same
value. Set NB to about one half of NF and set NZ to a low value between zero and 5.
Chapter 10 Theory of Operation ▫ 176 DMC-40x0 User Manual
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