Optimization of a continuous distillation process under random inflow rate

The paper deals with a continuous distillation process under stochastic rate of inflows collected in a feed tank. The aim of analysis is to find a robust control of extracting feed from the tank over a certain time horizon such that—without knowledge of future realizations of the inflow rate—some level constraints in the feed tank will be met with high probability. This approach relies on formulating and numerically treating probabilistic constraints. The inflow rate is considered as a stochastic process for which two basically different model assumptions are made: the first model assumes a Gaussian process, and thus reflects the superposition of many independent elementary inflows; the second model treats maybe the simplest case of a single elementary inflow profile, namely rectangular inflows with fixed rate and duration but stochastic starting time. Numerical results illustrating both assumptions are presented, and advantages over the simple anticipation of nominal inflow profiles are highlighted.