Control of distillation columns with sharp temperature profiles

Temperature control problems are frequently encountered in distillation columns that, as a result of high purity products and an easy separation, have large temperature changes over a few trays. The describing function technique is used in this paper to analyze the stability of this type of column in which a nonlinear feedback control loop for column temperature control manipulates vapor boilup. The cycling usually experienced in these systems is shown to be unavoidable in many cases because the process transfer function has such a high gain that it acts like an on-off switch. The process also displays nonlinear dynamics: system time constants vary with the magnitude of change in vapor boilup. To overcome these difficulties an adaptive, nonlinear feedback controller is proposed that keeps the loop in a small-amplitude limit cycle by adaptively changing controller gain. The system is evaluated by digital simulation of a nonlinear model of the column.