LS Industrial Systems GLOFA G7M-DT60U(N)/DC - Page 132

Chapter 7. Usage of Various Functions
7-25
(2) Realization of PID control on the PLC
In this chapter, it will described that 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;
Kp: proportional gain constant, SV: set value, PV: present value
(b) I control
The continuous formula of I control is as following;
Kp: proportional gain constant Ti: integral time
E(s): deviation value
By derivation about t, we can obtain;
where, e = (SV – PV): deviation value
The digitized formula is as following;
where, h: sampling period
(c) D control
The continuous formula of derivative term is as following;
N: high frequency noise depression ratio
y: the object to be controlled (PV)
)()( PVSVKnP
P
−=
∫
=
t
i
P
dssE
T
K
tI
0
)()(
E
T
K
dt
dI
i
P
=
)(
)()1(
nE
T
K
h
nInI
i
P
=
−+
)()()1( nE
T
hK
nInI
i
P
+=+
dt
dy
TKnD
dt
ndD
N
T
dP
D
−=+ )(
)(