Closed-Loop Tuning of Controllers ◾  97
The integral time constant can be adjusted to about 4 times
longer than the response time, and this will reduce any effect
from the integral (automatic reset) action. The response time
is the time that elapses between the introduction of a step
change in setpoint and the first peak in the response of the
process variable. With T i = 52 min, the response time was 13.2
min for the process variable to reach a peak height of 60.3
and a valley height of 58.7 in Figure 9.8. Since the reset was so
slow, the first peak did not overshoot the setpoint very far, and
there was a significant offset between the process variable and
the setpoint for a long period of time.
Next, the integral time constant, T i , can be set equal to
the response time for excellent response to a load change or
twice the response time for minimum variability from a setpoint change.
The value of T i can be set to about 2 times the response
time of 13.0 min, that is, 26 min, for minimum variability to a
setpoint change. For many combinations of K p , K c , DT, T 1 , and
T 2 for self-regulating control loops, a correlation was observed
for minimum IAE, as shown in Equation 9.1. In this case, the
optimum value of K c was found to be 4.08, and K p was 1.0,
so the calculated T i , was 1.75 times the response time of 13.0
min, that is, 22.7 min.
T i = [0.24 + (0.37 K c K p )] response time
(9.1)
where:
T i = integral time constant for controller (in
minutes) for minimum IAE for setpoint
changes
K c = controller proportional gain
K p = process gain
Response time = elapsed time between step change in
setpoint and first peak (in minutes)