An interacting control system may be internally decoupled through the use of noninteracting manipulative variables.Application of this concept to dual composition control of a binary column (9 = 1) leads to the unexpected result that the conditions for half-decoupling of either loop are effectively the same. This degeneracy very closely approximates the column material balance and makes lt impossible to completely decouple the system. The findings appear to be of general validity and afford insight into the success of the Shinskey material balance control scheme.In recent years, an increasing significance has been attached to the steady-state control of industrial processes (Ellingsen, 1976; Lee and Weekman, 1976). Several tools are now available which aid in determining steady-state control strategies for multivariable systems. These concepts have found a natural application in the design and implementation of control algorithms for distillation. The most successful of the syntheses has been the material 0019-7882/78/ 11 17-0485$01 .OO/O

In this paper new, more accurate analytical expressions for the relative gain array (RGA) for dual composition control of binary columns are presented. Both material balance control and conventional control achieved through manipulation of reflux and boilup are examined. The new expressions, which can be derived from the rigorous Smoker equation, compare very well with published numerical results. A consistency relationship for material balance and conventional RGA's is presented.

An approximate analytical solution of Smoker's equation can be used to develop simple models for predicting the design and control of distillation columns. The design equationgives predictions that are usually within two or three trays of the exact solution, which exceeds the accuracy associated with plate efficiency calculations.

An approximate analytical solution for binary distillation columns combined with order of magnitude arguments can be used to develop simple models for predicting the effect of disturbances on the column performance, the economic penalties associated with overrefluxing a column, and steady-state control algorithms for both binary and multicomponent systems. For predictions of column operability the simplest model derived appears to be superior to existing empirical correlations, while for column control systems the results agree with Shinskey's prediction that the boil-up to feed ratio should be maintained constant.

Using the Eduljee equation (19754, approximate steady-state decoupling algorithms for dual composition control are developed analytically for binary columns. Use of the algorithms in multicomponent columns is also discussed. These algorithms agree very well with exact decoupling results. The fact that complete decoupling probably cannot be realized in dual composition control of high purity columns is shown analytically. The relationships presented should be useful in future studies and applications of decoupling control to distillation columns.