Feasibility of decoupling in conventionally controlled distillation columns. Reply to comments

Abstract

Sir:In his correspondence, Treiber questions the use of decouplers with constant grains in the work of Weischedel and McAvoy (1980). He seems to contend that decoupling can be achieved through the use of nonlinear compensators. In principle, Treiber is correct and it should be possible to use nonlinear decouplers to compensate for the nonlinear process gains. In practice, we feel that his approach would also fail because of inevitable errors in the nonlinear decouplers.A nonlinear decoupling approach would require models for the various process gains. If a simple steady-state model is used (McAvoy, 1981), these gains can be shown to depend on distillate flow and composition, bottoms flow and composition, number of ideal stages, relative volatility, and feed conditions. It would be essentially impossible to develop and implement a multivariable model for these gains that was completely error free. In the linear region near steady state the relative gain sensitivity analysis is valid for the nonlinear decoupling scheme. If the relative gain for the nondecoupled system is large, e.g., 50, then the sensitivity analysis indicates that small decoupler errors (-1%) would lead to loop interaction.Treiber is correct in pointing out that our results are clouded by the fact that they not only involve decoupler sensitivity but nonlinear effects as well. We could have eliminated the nonlinear effects by making very small step tests both in determining our transfer functions and in testing our control schemes. However, our goal was to emulate the type of approach that would be taken industrially and this determined the size of the forcing functions that we used.In summary, it is our contention that Treiber's conclusion about the relative gain being inappropriate is incorrect. We also strongly contend that in a practical application one would not be able to decouple a high-sensitivity column or indeed any other high-sensitivity system and that Treiber's conclusion on this point is wrong.