NB1 Demo
20-tray binary distillation column
W. L. Luyben describes a mathematical model of an ideal 20-tray binary distillation column in the classic text Process Modeling, Simulation, and Control for Chemical Engineers 1. There are two inputs and two outputs: one controller manipulates the reflux flowrate to control the overhead composition, and another manipulates the vapor boilup to control the bottoms composition.
The following figure shows a schematic of the process.
20-tray binary distillation column
Reproduced from Fig. 3.12 of Luyben's text
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The system is characterized by over 80 dynamic equations, which are given at the bottom of this page.
Luyben's text also provides two PI controllers.
We don't know how long it took to tune these PIs,
but we do know that configuring multiple PID controllers
for multivariable processes usually involves things like
log modulus criteria and frequency response plots in the
complex number plane. It would be nice to have something easier.
We simply plugged two NB1s into this problem, and without any tuning, training,
or modification of any kind, the NB1s dramatically outperformed the PIs.
Two NB1s compared to two PIs controlling the 20-tray binary distillation column
The objective is to hold the overhead composition xD and the bottoms composition xB at their respective setpoints while the process undergoes a series of disturbances, including a 10% change in feed composition at 1.25 minutes, a spike in xD at 25 minutes, and a drop in xB at 50 minutes. Both the NB1s' and PIs' reactions to the disturbances in xD and xB illustrate the strong dynamic interactions between the controlled variables.
The NB1s are much more successful at maintaining the controlled variables at their setpoints.
Disturbances that cause the PIs to go haywire barely make the NB1s flinch.
The following figure shows the controller outputs required to maintain the
performance seen above.
The controller outputs of the NB1s compared to the PIs controlling the 20-tray binary distillation column
These results are typical. In case after case the NB1s and NB2s have provided plug-and-play control
for all sorts of different single- and multivariable systems,
and they have proven extraordinarily robust every time.
* * * *
Below are the system equations for the binary distillation column, with tray number n ∈ {1,2,...Nt=20}, and the following variable definitions.
xB: liquid composition in the column base (controlled variable)
xD: liquid composition in the reflux drum (controlled variable)
xn: liquid composition in the nth tray
yn: vapor composition in the nth tray
Ln: liquid flow leaving the nth tray
Mn: liquid holdup of the nth tray
F: feed rate
z: feed composition
R: reflux flowrate (manipulated variable)
V: vapor boilup (manipulated variable)
Top tray
Feed tray
Bottom tray
All other trays
Column base, liquid flows and vapor compositions
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W.L. Luyben, Process Modeling, Simulation, and Control for Chemical Engineers, 2nd edition, McGraw-Hill, New York, 1990.
