Optimisation Optimal Control of Batch Distillation

Dynamic Optimisation (Optimal Control) of Batch Distillation 

Batch distillation is inherently a dynamic process and thus results to optimal control or dynamic optimisation problems (unless batch distillation task is carried out in a continuous distillation column). 

The optimal control of a process can be defined as a control sequence in time, which when applied to the process over a specified control interval, will cause it to operate in some optimal manner. The criterion for optimality is defined in terms of an objective function and constraints and the process is characterised by a dynamic model. The optimality criterion in batch distillation may have a number of forms, maximising a profit function, maximising the amount of product, minimising the batch time, etc. subject to any constraints on the system. The most common constraints in batch distillation are on the amount and on the purity of the product at the end of the process or at some intermediate point in time. The most common control variable of the process is the reflux ratio for a conventional column and reboil ratio for an inverted column and both for an MVC column. 

The optimal operation of a batch column depends of course on the objectives one wishes to achieve at the end of the process. Depending on the objective function and any associated constraints, a variety of dynamic optimisation problems were defined in the past for conventional batch distillation column. Brief formulations of these optimisation problems are presented in the following subsections. Situations in which each formulation can be applied are discussed. 

The batch time for the operation is given by t = tlp —tg, where t F is the end time of distillation task i. Note that if tg = 0, (Bw, Jtg1) becomes (B0, jc q) and 

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