Superimposing The P, I And D Components - Burkert 8630 Operating Instructions Manual

Superimposing the P, I and D components

Function: Y = Kp Xd +
Substituting Kp · Ti = Tn and Kd/Kp = Tv we obtain for the function on the PID controller:
1
∫ ∫ ∫ ∫ ∫ Xd dt + Tv dXd/dt)
Y = Kp (Xd +
Tn
Kp is the proportional action factor/amplification factor
Tn is the reset time
(the time required to obtain the same change in correcting variable as was caused by the P
component) and
Tv is the rate time
(the time by which a certain change in correcting variable is obtained earlier with the D
component than t would have been with a pure P controller).
Step response and rise response of the PID controller
X
Xd
Y
D-Component
D-Anteil
Kp•Xd
Nachstellzeit Tn
Reset time Tn
Step response of the PID controller
1
∫ ∫ ∫ ∫ ∫ Xd dt + d Xd/dt
Ti
t
I-Anteil I-Component
P-Anteil P-Component
t
G
ENERAL
X
Y
I-Anteil
D-Anteil
P-Anteil
Vorhaltzeit Tv
Derivative action time Tv
Rise response of the PID controller
R (A
ULES PPENDIX
t
I-Component
D-Component
P-Component
t
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)