Uncertainties in parameter estimation and optimal control in batch distillation

Optimal control problems in batch distillation involve finding a trajectory for the reflux ratio so as to maximize a performance index. Then the controller is asked to follow this trajectory in an open loop fashion. It is important to minimize the effect of uncertainties in thermodynamic models on the optimal control profiles to achieve a better operating performance. The non-linear parameter estimation problem in vapor-liquid equilibrium modeling involves determining the values of model parameters, which provide the best fit to experimental data. It was shown previously by Gau et al. [Fluid Phase Equilibria, 168, 1-8, (2000)] that, using a global optimization procedure based on interval-Newton technique combined with interval-branch-and-bound can significantly reduce the error between the predicted and experimental data. Using this method, it was also shown that for some of the data sets published in DECHEMA, the parameters estimated correspond to local minima. The effect of locally and globally optimal parameter estimates on batch distillation optimal control profiles is demonstrated in this work. Since batch distillation is a dynamic process, the static (parametric) uncertainties are translated into time-dependent uncertainties. The time-dependent changes in relative volatility for the two cases are analyzed and represented by Ito processes. Next, the optimal control problem is solved using the maximum principle and NLP approach. Numerical case studies show that using globally optimal parameter estimates versus locally optimal parameter estimates results in a better product yield and the minimum error between the specified purity and the purity that is achieved.