Free-Time Optimal Control of a Batch Distillation Column through Genetic Algorithms

Free-Time Optimal Control of a Batch Distillation Column through Genetic Algorithms

Abstract:

Finding the optimal control of a highly nonlinear system is not trivial, even when the final time is fixed; when this is free, a supplemental variable to be optimized appears. For batch distillation processes, free-time optimal control means to compute both the minimum working time and the best control profile to achieve a given performance index, such as the mean product concentration in the distillate. From several popular choices when it comes to batch distillations, the reflux was used as control parameter. If the free-time optimal problem is considered as optimization over a set of stages, dynamic programming could be used with proven success. According to this method, both time and control variables are discretized to a predefined number of values, particular to a stage. A systematic backward search method in combination with the simulation of the system model equations is used to find the optimal path through the defined grid. Applied iteratively, dramatic reduction of computational load occurs, but convergence to the global minimum is no longer guaranteed. To overcome these drawbacks, an evolutionary optimization strategy could be used, based on Genetic Algorithms (GAs), which became a reliable optimization method of strong nonlinear systems with many variables. GAs are based on natural evolution processes, where selection results in species that fit the best. Variation in the population is achieved by genetic crossover and mutation. Because of the non-linear structure of a batch distillation, given by the thermodynamic vapour-liquid equilibrium, the use of GAs to calculate a piece-wise step-like trajectory of the control variable is appealing. A stage is defined as a period of constant reflux. The reflux indirectly influences the duration of this stage, which is computed using the reboiler heat flow also. All the stages are encoded in the chromosome. The population, formed by individuals with different chromosomes, is restricted naturally to the feasible region through the mechanisms of reproduction or mutation. A balance between the convergence to the global minimum and the calculation efforts by choosing the population size and selection mechanism was sought. Keywords: batch distillation, genetic algorithms, free-time optimal control, piece-wise optimal control profile

Issue: 2005, Volume 56, Issue 11

Pages:

This article is published under the Creative Commons Attribution 4.0 International License

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