116 ◾  Distillation Control, Optimization, and Tuning
valve position or less. For example, if the average valve position is moving up and down erratically between 58% and
60% with a proportional gain of 3, then the gain could be cut
in half to 1.5 to reduce the band of valve movement to run
between 58.5% and 59.5%. Also, the liquid level signal could
be filtered to reduce the noise level.
An open-loop step test on a level controller would start
with the liquid level and controller output at steady-state values with a constant flow rate of liquid into the vessel. Then,
increase the controller output by a step change, and observe
the rate of change in the liquid level. For example, with the
initial liquid level at 50% and the controller output at 70%,
put the controller in manual output mode and increase the
controller output to 80%. Observe the rate of change of the
process variable, say, a decline of 1.0%/min. This can be used
as the maximum process response rate, MPRR, for calculating
a controller gain, K c , by the Z-N equation in Table 10.2. K c =
(0.9)(10)(1)(1) = 9 for an apparent dead time, ADT, of 1 min or
K c = 18 for an ADT of 0.5 min. This would be expected to give
very tight level control compared to using a gain of K c = 1.25
for level averaging described earlier in this chapter and also in
Chapter 9, Section 9.8.
10.7 Summary
This chapter described the characterization of a process
response by introducing a step change in the controller output with a controller in manual output mode. The values of
apparent dead time, first-order time constant, and process gain
were used to characterize an open-loop self-regulating process
response. The values of apparent dead time and percentage
change in accumulator level per minute were used to characterize the open-loop integrating process response. Calculations
for controller PID settings were provided by several different
tuning rules.