Chapter 6 Usage of Various Functions
6-13
3) Realization of PID control on the PLC option card
In this chapter, it will describe how to get the digitized formula of the P, I, and D terms.
(a) P control
The digitized formula of P control is as following;
[
]
)
(
)
(
)
(
n
PV
n
SV
K
n
P
−
=
n : sampling number
K : proportional gain constant
b : reference value
SV : set value
PV : present value
(b) I control
The continuous formula of I control is as following;
∫
=
t
i
ds
s
e
T
K
t
I
0
)
(
)
(
: integral term
K : proportional gain constant
Ti : integral time
e(s) : deviation value
By derivation about t, we can obtain;
e
Ti
K
dt
dI
=
where, e = (SV – PV) : deviation value
The digitized formula is as following;
)
(
)
(
)
1
(
n
e
Ti
K
h
n
I
n
I
=
−
+
where,
h : sampling period
)
(
)
(
)
1
(
n
e
Ti
Kh
n
I
n
I
+
=
+
(c) D control
The continuous formula of derivative term is as following;
dt
dy
KTd
D
D
dt
d
N
Td
−
=
+
×
N : high frequency noise depression ration
y : the object to be controlled (PV)
