Burkert Type 8793 - Manual (Page 244)

244
Additional technical information
40.5. Implemented PID controller
40.5.1. D Portion with delay
In the process controller Type 8793 the D portion is implemented with a delay T.
Function:
(9)
t d
d X d
d K Y
t d
Y d
T ⋅ = + ⋅
Superposition.of.P,.I.and.DT.Portions
X
Xd
Y
t
t
Xd
T
T
Figure 138: Characteristic of superposition of P, I and DT Portions
40.5.2. Function of the real PID controller
(10)
t d
d X d
v T t d d X
n T
1
d X ( p K Y
t d
Y d
T
∫ + + = + ⋅
Superposition.of.P,.I.and.DT.Portions
X
Xd
Y
t
t
Tn
Kp⋅Xd
Xd
T
Kp
Figure 139: Characteristic of step response of the real PID controller; adjustment rules for PID controllers
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Type 8792, 8793