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DMC-2X00 Chapter 10 Theory of Operation y 145
The function G is equivalent to a digital filter of the form:
D(z) = 4KP + 4KD(1-z
-1
)
where
P = 4 ∗ KP
D = 4 ∗ KD ∗ T
and
4 ∗ KD = D/T
Assuming a sampling period of T=1ms, the parameters of the digital filter are:
KP = 20.6
KD = 68.6
The DMC-2x00 can be programmed with the instruction:
KP 20.6
KD 68.6
In a similar manner, other filters can be programmed. The procedure is simplified by the following
table, which summarizes the relationship between the various filters.
Equivalent Filter Form
DMC-2x00
Digital D(z) =[K(z-A/z) + Cz/(z-1)]∗ (1-B)/(Z-B)
Digital D(z) = [4 KP + 4 KD(1-z
-1
) + KI/2(1-z
-1
)] ∗(1-B)/(Z-B)
KP, KD, KI, PL K = (KP + KD)
⋅
4
A = KD/(KP+KD)
C = KI/2
B = PL
Continuous G(s) = (P + Ds + I/s) ∗ a/S+a
PID, T P = 4 KP
D = 4 T*KD
I = KI/2T
a = 1/T ln (1/PL)