Galil Motion Control CDS-3310, User Manual

Page: 132 / 166

CDS-3310 Chapter 10 Theory of Operation
i
71
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:
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)
P = 4KP
D = 4T
⋅
KD
I = KI/2T
a = 1/T ln (1/B)
where T is the sampling period.
For example, if the filter parameters of the CDS-3310 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
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