CHAPTER 5: SETTINGS
where
y is the process signal
r is the setpoint signal
w is the tracking signal
u is the regulator output
K is the proportional gain
b is the setpoint weighting
T
is the derivative time constant
d
N is the derivative limit
T
is the integral time constant
i
T
is the anti-windup time constant
t
s is the domain
In discrete form, the equations for the regulator are
e k
p k
d k
u k
i k 1
where
T
is the sampling time
S
AW is a flag which enables anti-windup
The incremental form of this equation is:
C30 CONTROLLER SYSTEM – INSTRUCTION MANUAL
Figure 5-68: PID block diagram
r k y k
=
–
K br k y k
=
–
T
d
------------------ -
------------------ -
=
d k 1
–
–
T
+
NT
T
d
S
p k i k d k
=
+
+
e k
T
KT
S
S
i k
+
=
+
------------------
+
----
T
T
t
i
Du k
u k u k 1
=
–
Dp k Di k Dd k
=
+
kT
N
d
y k y k 1
–
–
+
NT
d
S
w k u k
AW
–
–
+
CONTROL ELEMENTS
5
Eq. 5-1
Eq. 5-2
5-147