Feedforward control of binary distillation

The open-loop transfer functions relating distillate and bottoms composition to feed composition, reflux rate and boilup rate were determined from pulse tests of a binary distillation column. Similar transfer functions were determined by mathematical solution of the linearized differential equations describing the column. Comparison of these two sets of functions showed that the simple feedforward controller transfer functions based upon the linear model should provide adequate control for binary distillation columns in the low frequency range (below a frequency of 1.6 radians per dimensionless time -- dimensionless time is defined to be the tray holdup divided by the stripping section liquid rate).

The experimental data were determined for the benzene-n-heptane system at atmospheric pressure. The column was 8 inches in diameter and contained 18 sieve trays spaced 12 inches apart. A total condenser provided the reflux, and a thermosiphon reboiler provided the stripping vapor. Analyses were made by refractive index measurements.

The transient distillate and bottoms compositions were determined as responses to pulsed variations of feed composition, reflux rate and boilup rate. These tests were performed at each of two different steady state conditions. Fourier transform analysis was used to convert the pulse data to frequency response data, and Bode diagrams were prepared.

The mathematical solution used the techniques of Lamb and Pigford for linearization and solution of the equations describing the column. This technique involves step-wise tray-to-tray calculations in the frequency domain.

The transfer functions developed by the two approaches were compared. They were in close agreement up to frequencies of about 1.6 radians per dimensionless time. Above this frequency the nonlinear and higher order effects have an appreciable effect on the dynamics of the distillation column. Use of the linear model at frequencies above 1.6 radians per dimensionless time is not recommended.