Superposition.of.p,.I.and.d.portions - Burkert 8692 Operating Instructions Manual

Type 8692, 8693
Additional technical information
39.4 Superposition of P, I and D Portions
Function:
1
∫
= ⋅ +
Y K p X d X
i T
Where Kp · Ti = Tn and Kd/Kp = Tv the function of the PID controller is calculated according to the following
equation:
1
∫
= ⋅ +
Y K p ( X d
T n
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
X
Xd
Y
D-portion
Kp⋅Xd
Reset time Tn
Step response of the PID controller
Figure 143: Characteristic of step response and ramp response of PID controller
d X d
+
d t d K d (7)
t d
d X d
+
X d t d T v ) (8)
t d
t
I-portion
P-portion
t
X
Y
Hold-back time Tv
Ramp response of the PID controller
english
t
I-portion
D-portion
P-portion
t
241