Application of iterative dynamic programming to optimal control of a distiltation column

Abstract

Iterative Dynamic Programming (IDP) is proven to be a useful technique for solving constrained dynamic optimisation problems. A high purity binary distillation column model has been chosen to investigate some of the IDP properties as well as its applicability. The investigated problems cover transitions from one steady state to another with the minimization of a quadratic cost function with associated terminal constraints.Dans cet article, nous avons demontre que la programmation dynamique iterative est une methode adaptee a la resolution des problemes d'optimisation dynamique sous contraintes. Une colonne de distillation binaire de grande purete est utilisee pour etudier I'applicabilite et certaines proprietes de cette technique. Le probleme etudie conceme la transition d'un point de fonctionnement stationnaire a un autre par minimisation d'un critere quadratique sous contraintes terminales.

Handling Inequality Constraints in Optimal Control by Problem Reformulation

“…To get to the vicinity of the global optimum, however, more than one grid point at each time step was required for both of the systems considered. As noted by Fikar et al and by Rusnak et al, here we also found that faster convergence resulted if the grid points are generated by assigning control values at random rather than uniformly. Computations showed that for this problem no more than 7 grid points are required at each time stage if the initial control policy is far from the optimum.…”

“…The clipping technique is used to handle the control constraints given in eq 15. In step 2, in generating the grid points, the suggestion of Fikar et al 18 is used where the values to control are generated at random inside the region. This method of generating grid points has been found to be especially useful for the optimal control of fed-batch reactors.…”

Multistage dynamic optimization of a copolymerization reactor using differential evolution

“…To avoid this difficulty, Luss proposed a technique known as iterative dynamic programming (IDP) that uses accessible state grids and region contraction to reduce dimension expansion. This method attempts to generate a number of random control policies about the current best rather than maintaining a high dimensional lattice, and it has been applied to solve different optimal control problems . In recent years, various stochastic optimization algorithms such as genetic algorithm (GA), simulated annealing, and ant colony optimization derived from the principles of natural phenomena are increasingly used to solve complex optimization problems due to their flexibility, ease of operation, and global perspective.…”

Time-Optimal Control of Startup Distillation Columns by Iterative Dynamic Programming

“…TOC of startup distillation columns involves a large number of state variables, being a very high-dimensional problem. Fikar et al 10 have studied the application of IDP on optimal control of a distillation column for separation of the binary mixture methanol-isopropanol. They have used the top product molar flow rate and the reflux molar flow rate as control variables.…”