Galil Motion Control DMC-18 2 Series User Manual page 173

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
K= 20/65536 = 0.0003
Digital Filter
The digital filter has a transfer function of D(z) = [K(z-A)/z + Cz/z-1] ∗ (1-B)/(Z-B) and a sampling
time of T.
The filter parameters, K, A, C and P 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
This filter includes a lead compensation, an integrator and a low pass filter. It is equivalent to a
continuous PID filter with a transfer function G(s).
G(s) = (P + sD + I/s) ∗ a/(S+a)
P = 4KP
D = 4T
I = KI/2T
a = (1-B)/T
For example, if the filter parameters of the DMC-18x2 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)
162 ● Chapter 10 Theory of Operation
Artisan Technology Group - Quality Instrumentation ... Guaranteed | (888) 88-SOURCE | www.artisantg.com
[V/count]
⋅
4
⋅
KD
DMC-18x2