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
Time
PV
nf-1
= the previous Process Value T
I
= the Inte
ral Time Constant
PV
nf-2
= the second previous Process Value T
D
= the Time Derivative Constant
∆
MV = the chan
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
re
ister the
must be set.
Forward and Reverse operation (S
3
+1, b0)
The Forward operation is the condition where the Process Value, PV
nf
, is
reater than the Set
Point, SV. An example is a buildin
that requires air conditionin
. Without air conditionin
, the
temperature of the room will be hi
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
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
element is turned On.
The assumption is made with PID control that some work will need to be performed to brin
the s
stem into balance. Therefore,
∆
MV will alwa
s have a value. Ideall
, a s
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
∆
∑
=
