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Sigurd Skogestad and Manfred Morari

Ind. Eng. Chem. Res.

**27** (10),
pp 1848 - 1862, (1988)

**Abstract**

The dynamic behavior of a distillation column is approximated with a two time constant model. The response to changes in the external flows is approximately first order with time constant tau1. This dominant time constant can be estimated by using a simple mixing tank model for the column. The response to changes in the internal flows is also first order, but its time constant T~ is generally significantly smaller than tau1. The condition number and the RGA are smaller a t high frequency than a t steady state. Most models presented in the literature do not take this into account. The two time constant model does predict this behavior, and tau2 can be estimated by matching the RGA at high frequency. Finally, it is shown that the effect of nonlinearity is almost eliminated if logarithmic compositions ln xB and ln (1 - yD) are used. In particular, this applies to the initial response which is of primary importance for feedback control.