Off line computation of optimum controls for a plate distillation column

Abstract

The work reported was undertaken with a view to developing efficient numerical techniques for the study of optimum time-varying operation of non-linear systems. A very simple model of a binary distillation column was used as an example, and two problems concerning start-up of the column were studied, requiring transition between two specified states either in minimum time or for minimum cost. The related problem of optimum operation over a fixed period is also discussed. The approach adopted was to improve an arbitrary initial control policy using gradient methods, with the derivatives determined from the adjoint equations. A good first approximation to the optimum policy was obtained using a version of the steepest descent method applied to the control values. However switching policies with a small number of switches usually gave a significant improvement over this result, and these were successfully determined by applying Fletcher and Powell's conjugate direction method to the switching times.