. superposition.of.p,.i.and.d.portions, Superposition of p, i and d portions – Burkert Type 8693 User Manual
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General Rules (Appendix)
57.4. 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 / amplification factor
Tn Reset time
(Time which is required to obtain an equally large change in the actuating variable by the I portion as
occurs with 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 136: Characteristic of step response and ramp response of PID controller
english
Type 8692,8693