Inadequacy of steady-state analysis for feedback control: distillate-bottom control of distillation columns

Abstract

It is often claimed that for distillation columns the steady-state description is much more important than the dynamic description for control purposes. The ultimate counterexample to this misconception is the recently proposed distillate-bottom (DB) configuration that involves using distillate and bottom flow to control compositions. This control scheme has previously been labeled "impossible" by most distillation control experts because D and B are not independent at steady state (since D + B = F) and the gain matrix is singular. Yet, as shown by Finco et al. for a propane-propylene splitter, both with simulations and with implementation, the scheme does actually work. Finco et al. do not provide any explanations for this, but as shown in this paper, the main reason is the flow dynamics (liquid lag from the top to the bottom of the column), which decouples the responses at high frequency (initial response) and makes the system quite easy to control. The results in this paper demonstrate that steady-state data may be entirely misleading for evaluating control performance. This is of course well-known, for example, from the Ziegler-Nichols tuning rules, which are based on high-frequency behavior only, but often seems to be forgotten when analyzing multivariable systems.