78 ◾  Distillation Control, Optimization, and Tuning
8.6 Summary
This chapter presented a flow diagram of a PID feedback
control loop with the process streams and instrument lines
labeled. The proportional, integral, and derivative actions of
the controller were defined mathematically and described for
the example in the diagram.
Exercises
8.1 How much does the controller output change if a
proportional-only controller gain is 5 and the process
variable changes by 5% of its span?
8.2 With a proportional-only temperature controller in
Figure 8.1 using a controller gain of 12.5, the process
water flow increased and the steam valve position
increased by 7% at steady state. What is the offset in
outlet temperature in degrees in centigrade if the span
of the temperature transmitter is linear from 0°C to
200°C? Was the new steady-state temperature of the
process water out too low or too high?
8.3 For a PI controller with a proportional band of 25% and
a reset rate of 0.05 repeats per minute, what is the proportional gain of the controller and how many minutes
will it take to change the controller output the same
amount as the gain for a fixed amount of error?
Reference
1. Corripio, A. B., Tuning of Industrial Control Systems, 2nd ed.,
ISA, Research Triangle Park, North Carolina, 2001.