100 ◾  Distillation Control, Optimization, and Tuning
7. Set the integral (reset) time constant in the controller to
be equal to the response time.
A reflux drum is sized and purchased to retain some inventory of liquid and dampen the response in the flow rates
leaving the drum, namely, the reflux and distillate. So, there is
no financial incentive for controlling the liquid level within a
narrow band. On the contrary, there is a penalty for tight level
control by moving the flow rates to overshoot the final flow
rate and create high variability. Another issue is that a level
controller does not actually need any integral (reset) action. A
proportional-only controller could be used with a proportional
gain, K c , of 1.25 and a controller output bias of 50%, so that
the outlet liquid valve could be wide open when the drum
was 90% full and completely closed when the drum was 10%
full. This is equivalent to a proportional band of 80%, that is,
100%/K c . A proportional gain, K c , of 2.0 could be used so that
the valve would be wide open when the drum was 75% full
and completely closed when the drum was 25% full.
The dead time for a level control loop is usually very small,
so the loop has very little tendency to cycle until the proportional gain is quite high. As a result of all these considerations,
the recommended procedure for tuning the level controller for
the reflux drum is to simply use a proportional gain in the controller of 1.25 to 2.00 and start with an integral time constant,
T i , of 30 min. Introduce a step change in level setpoint, and
observe the response time reach 95% of the step change. The
level may only approach the new setpoint and may not overshoot as shown in Figure 9.9 for a constant liquid flow rate into
the drum of 40% of the maximum flow rate and a step change
in level setpoint from 50% to 60%. Then set the integral time
constant equal to the response time. The response to a load
change, that is, a step change in liquid flow rate into a reflux
drum from 40% to 70%, is shown in a simulation in Figure 9.10.
Tuning the control loop for the liquid level in the bottom of
a distillation column can be similar to a reflux drum. However,