Rockwell Automation 1771-PD PID MODULE (+DU) - Manual (Page 124)

Programming
Chapter 3
3Ć81
For example, the sampling of PV values (Figure 3.23) shows a step
change for three samples and then returns to the initial value. Using the
digital filter equation (Figure 3.23) and a filter time constant of 0.3
seconds, calculate the filtered amplitude, Y
n
, of the third sample.
Y
n
-1 = 1.0V
TA = .33
X
n
= 4.0
Y
n
= 1.0 + 010
.33 (4-1.0)
=1.0 + .3(3)
=1.9
Lead/Lag Filter
Lead/lag filtering provides overcompensation or undercompensation of a
feedforward input. The explanation of the lead/lag filter will be based on
a step input.
With no filter, the step change is unaffected. With lead compensation, the
initial step change is overcompensated and then settles out to the step
change based on the value of the lead time constant TB. Lead
compensation is shown as control above the step input value
(Figure 3.25). With lag compensation, the initial step change is
undercompensated and then settles out to the step change based on the
value of the lag time constant TC. Lag compensation is shown as control
below the step input value (Figure 3.26).
When values are entered for both lead and lag, the value with the larger
magnitude will dominate the response. Thus 2/1 is a lead dominated
response and l/2 is a lag dominated response. Lead/lag can be any ratio
but the filter will limit the overcompensation (lead value) to eight times
the step input value.
Also observe that the response time of a lead/lag filter having a given
ratio will depend on the magnitute of the numerator and/or denominator.
For example, a lead/lag filter having a ratio of 6/12 will take longer to
settle out than a filter having a ratio of 1/2.