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S. Skogestad, ``Modelling and Control of Distillation Columns as a 5 x 5 System'', DECHEMA Monographs, 116, R. Eckermann (Ed.), 403-411 (1989) (From 20th Europ. Symp. on Computer Applications in the Chemical Industry (CACHI 89), Erlangen, Germany, April 1989).

Abstract. Distillation columns may be viewed as a 5 x 5 plant. The optimal controller should, based on all available information (measurements, process model with expected uncertainty, expected disturbances), manipulate all 5 inputs (L; V; V_T; D;B) in order to keep the 5 outputs (levels in top and bottom, pressure, top and bottom compositions) as close as possible to their desired values. However, in order to obtain a simpler control system, single loops are usually used (Fig. 1).

In the paper the design of both simpler (denoted 2 x 2 control since there are only two inputs used for composition control) and more complex (5 x 5) control systems are adressed. Simpler control systems are desirable provided their performance loss compared to the optimal `full' controller is acceptable. It is therefore of interest to find the upper limit on performance provided by the optimal controller (eg., optimality in terms of robust performance), even though it may never be implemented. To derive the optimal controller a general model of the 5 x 5 plant is needed. Such a model was not found in the literature, and a considerable part of this paper is devoted at deriving a linear model of the overall system which also takes into account variations in pressure and holdup.