Rockwell Automation 1772-L8_LW_LWP_LX_LXP,D17726.5.8 User Manual - Manual (Page 215)

EAF
Process Control Instructions
Chapter 16
16-4
Independent Gains
Using the independent gain equation you adjust the proportional, integral
and derivative terms separately.
CO
+ K
P
E
) K
I
ŕ
Edt
)
KD[E
* E(n * 1)]
dt
) Bias
t
o
CO
+ K
P
E
) K
I
ŕ
Edt
)
KD[PV
* PV(n * 1]
dt
) Bias
t
o
or
where: C= control output
K
P
= proportional gain constant (unitless)
K
I
= integral gain constant (1/sec)
K
D
= derivative gain constant (sec)
dt = time between samples
Bias = feedforward or output bias
E = error equal to (PV – SP) or (SP – PV)
E(n-1) = error from last sample
PV = process variable
PV(n-1) = process variable from last sample
You can convert dependent gain constants to independent gain constants by
using the following formulas:
K
P
= K
C
K
I
= K
C
/(Ti(60 sec/min))
K
D
= K
C
(TD)(60 sec/min)
For more information about PID control, see the Fundamentals of Process
Control Theory by Paul W. Murrill (Instrument Society of America).