Rockwell Automation 1772-L8_LW_LWP_LX_LXP,D17726.5.8 User Manual - Manual (Page 214)

EAF
Process Control Instructions
Chapter 16
16-3
This is accomplished by evaluating the PID equation whose output goes to
a control device. An additional value may be added to the control output
either as a bias to decrease offset when using proportional control, or as a
feedforward control value. The result of the calculation tends to drive the
quantity that you are trying to control towards the desired value (set point).
The PID Equation = Proportional Term + Integral Term + Derivative Term + Bias Term
Select either of two equations: the Dependent Gains equation or the
Independent Gains equation. Select the equation with which you are most
familiar. There is no difference in the control capabilities; you can achieve
comparable control with either equation. In the Dependent Gains equation,
a change in the proportional term affects the integral and derivative terms.
In the Independent Gains equation, you adjust the proportional, integral
and the derivative terms independently.
Dependent Gains
The Dependent Gains equation is an interactive algorithm that contains
variables dependent upon the controller gain. When you adjust your
controller gain (K
C
), you also change your integral and derivative terms.
CO + K
C
E ) 1Ti
ŕ
Edt ) T
D
[PVćPV(nć1)]
dt
) Bias
CO + K
C
E ) 1Ti
ŕ
Edt ) T
D
[EćE(nć1)]
dt
) Bias
t
0
t
0
or, if derivation of PV is selected:
where: C = control output
K
C
= controller gain constant (unitless)
Ti = integral time constant (minutes)
T
D
= derivative time constant (minutes)
dt = time between samples (minutes)
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