5.6 CONTROL ELEMENTS
A general form of a PID regulator in the s domain is shown below.
y
r
w
The following terms apply to the block diagram:
•
y is the process signal
•
r is the setpoint signal
•
w is the tracking signal
5
•
u is the regulator output
•
K is the proportional gain
•
b is the setpoint weighting
•
Td is the derivative time constant
•
N is the derivative limit
•
Ti is the integral time constant
•
Tt is the anti-windup time constant
In discrete form, the equations for the regulator are:
Where T
is the sampling time and AW is a flag which enables anti-windup. The incremental form of the above equation is:
S
Where:
5-116
b
-1
-
e
+
K
Ti
Figure 5–43: PID BLOCK DIAGRAM
e k
r k y k
=
–
p k
K br k y k
=
–
T
d
d k
----------------------- -
d k 1
=
–
T
NT
+
d
S
u k
p k
i k
d k
=
+
+
e k
KT
S
i k
i k
1
---------------------- -
+
=
+
T
i
Du k
u k u k 1
=
Dp k
=
C30 Controller System
+
K
+
sKTd
1+sTd/N
+
1
s
+
1
Tt
+
-
kT
N
d
----------------------- -
y k y k 1
–
–
T
NT
+
d
S
T
S
w k u k
------
AW
+
–
T
t
–
–
Di k
Dd k
+
+
5 SETTINGS
p
+
d
+
u
+
i
–
(EQ 5.1)
(EQ 5.2)
GE Multilin