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FX Series Programmable Controlers Applied Instructions 5
5-103
PID Equations
PV
nf
= PV
n
+
α(
PV
nf-1
- PV
n
)
EV
n
= the current Error Value D
n
= the Derivative Value
EV
n-1
= the previous Error Value D
n-1
= the previous Derivative Value
SV = the Set Point Value (S
1
) K
P
= the Proportion Constant
PV
n
= the current Process Value (S
2
)
α =
the Input Filter
PV
nf
= the calculated Process Value T
S
= the Samplin
g
Time
PV
nf-1
= the previous Process Value T
I
= the Inte
g
ral Time Constant
PV
nf-2
= the second previous Process Value T
D
= the Time Derivative Constant
∆
MV = the chan
g
e in the Output K
D
=
the Derivative Filter Constant
Manipulation Values
MV
n
= the current Output Manipulation Value (D)
Please see the Parameter setup section for a more detailed description of the variable
parameters and in which memor
y
re
g
ister the
y
must be set.
Forward and Reverse operation (S
3
+1, b0)
The Forward operation is the condition where the Process Value, PV
nf
, is
g
reater than the Set
Point, SV. An example is a buildin
g
that requires air conditionin
g
. Without air conditionin
g
, the
temperature of the room will be hi
g
her than the Set Point so work is required to lower PV
nf
.
The Reverse operation is the condition where the Set Point is hi
g
her than the Process Value.
An example of this is an oven. The temperature of the oven will be too low unless some work
is done to raise it, i.e. - the heatin
g
element is turned On.
The assumption is made with PID control that some work will need to be performed to brin
g
the s
y
stem into balance. Therefore,
∆
MV will alwa
y
s have a value. Ideall
y
, a s
y
stem that is
stable will require a constant amount of work to keep the Set Point and Process Value equal.
Forward
PV
nf
> SV
Reverse
SV > PV
nf
∆
MV K
P
EV
n
(
EV
n1–
()
–
)
T
S
T
I
------
EV
n
D
n
++
=
EV
n
PV
nf
SV–=
D
n
T
D
T
S
K
D
T
D
⋅
+
-------------------------------
2PV–
nf 1–
PV
nf
PV
nf 2–
++
()
K
D
T
D
⋅
T
S
K
D
T
D
⋅
+
-------------------------------
D
n1–
⋅
+=
MV
n
∆
MV
∑
=
∆
MV K
P
EV
n
EV
n1–
–
()
T
S
T
I
------
EV
n
+D
n
+
=
EV
n
SV PV
nf
–=
D
n
T
D
T
S
K
D
+T
D
⋅
-------------------------------
=2PV
nf 1–
PV
nf
–PV
nf 2–
–
()
K
D
T
D
⋅
T
S
K
D
+T
D
⋅
-------------------------------
+D
n1–
⋅
MV
n
∆
MV
∆
∑
=