188
Supplementary information
Type 8792, 8793 REV.2
26.2.4 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 fol-
lowing 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 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 74:
Characteristic of step response and ramp response of PID controller
english