Burkert Type 8635 - Manual (Page 149)

8635 - 147
G
ENERAL
R
ULES
(A
PPENDIX
)
Step response and rise response of the PID controller
Nachstellzeit Tn
t
P-Anteil
I-Anteil
D-Anteil
Y
t
Xd
X
Kp•Xd
Vorhaltzeit Tv
t
P-Anteil
I-Anteil
D-Anteil
Y
t
X
Step response of the PID controller Rise response of the PID controller
I component
P component
D component
Reset time Tn
D component
I component
P component
Rate time Tv
1
Ti
Superimposing the P, I and D components
Function: Y = Kp Xd + ∫∫∫∫∫ Xd dt + d Xd/dt
Substituting Kp · Ti = Tn and Kd/Kp = Tv, we obtain for the function of the PID controller:
Y = Kp (Xd + ∫∫∫∫∫ Xd dt + Tv dXd/dt)
Kp is the proportional action factor / amplification factor
Tn Reset time
(the time required to obtain the same change in correcting variable by the I component as was
caused by the P component)
Tv is the rate time
(the time by which a certain change in correcting variable is obtained earlier with the D
component than if would have been with a pure P controller)
1
Tn