88 ◾  Distillation Control, Optimization, and Tuning
about 20% of the gain. Often, the response is not linear, and
a smaller proportional gain is required to get the 16% peak-tovalley response in one step direction compared to the other,
that is, a step-up versus a step-down. In that case, use the
smaller proportional gain and the longer response time.
Another guideline is that an integral time constant of 4
times the response time will minimize the effect from the integral (reset) action, as indicated in Step 2. Yet another guideline is that an integral time constant significantly less than the
response time will generally destabilize the control loop and
give variability with a long peak-to-peak time period.
The development of the Robbins 2,3 closed-loop tuning methodology was the result of about 11 years of development with
collaboration and feedback of comments from others. A number
of different methods for tuning process control loops were tested
along the way, and this new closed-loop method using pattern
recognition was determined to be the most cost-effective.
Dynamic computer simulations of control loops were run
with thousands of combinations of process models and hundreds of production plant process control loops were tuned
for real plant experience. Most of the plant controllers were on
distillation columns, but control of reactors, furnaces, dryers,
extruders, and other unit operations was also improved by
tuning with these techniques. Most of the computer simulations used a dead time and two capacitance lags, and many
different combinations of those three process parameters were
studied. Initially, the control loop response was tuned for
minimum IAE (integral of absolute error), that is, minimum
deviation of the controlled process variable (controller input)
from the setpoint, after a step change in setpoint was made
in the controller. A pattern was recognized: the minimum IAE
occurred when the overshoot-to-undershoot ratio was about
seven to one. In other words, after a step change of 100%,
the first overshoot was one seventh of that, that is, 14% of
the step change, and the first undershoot was one seventh of
the overshoot, that is, 2% of the step change. This gave an