Superposition of p, i and d portions, . superposition.of.p,.i.and.d.portions – Burkert Type 8793 User Manual
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243
Additional technical information
40.4. Superposition of P, I and D Portions
Function:
∫
+
+
⋅
=
(7)
t
d
d
X
d
d
K
t
d
d
X
i
T
1
d
X
p
K
Y
Where Kp · Ti = Tn and Kd/Kp = Tv the function of the PID controller is calculated according to the following
equation:
∫
+
+
⋅
=
(8)
)
t
d
d
X
d
v
T
t
d
d
X
n
T
1
d
X
(
p
K
Y
Kp Proportional coefficient / proportional gain
Tn Reset time
(Time which is required to obtain an equally large change in the actuating variable by the I portion, as
occurs due to the P portion)
Tv Derivative time
(Time by which a certain actuating variable is reached earlier on account of the D portion than with a
pure P-controller)
Step.response.and.ramp.response.of.the.PID.controller
Step response of the PID controller
Ramp response of the PID controller
Xd
X
D-portion
X
Y
I-portion
P-portion
I-portion
P-portion
D-portion
Y
Reset time Tn
Hold-back time Tv
Kp⋅Xd
t
t
t
t
Figure 137: Characteristic of step response and ramp response of PID controller
english
Type 8792, 8793