On dealing with measured disturbances in the modifier adaptation method for real-time optimization

In this work, we propose the inclusion of the available information of measured or estimated disturbances in the modifier adaptation methodology for real-time optimization (RTO). The idea is to extend the applicability of this technique to processes wherein the disturbances affect the quantities involved in the necessary optimality conditions of the process. To do so, we include the estimation of process gradients with respect to both the decision variables and disturbances in the methodology. This approach was performed in a laboratory-scale flotation column, where the effects of changes in the feed characteristics on the economic performance of the process were analyzed. The influence of the availability of the disturbance information was also analyzed, considering immediate and delayed availability. In the latter case, the auto regressive integrated moving average model (ARIMA) was used as an estimator in each RTO iteration. The results show that the inclusion of the available disturbance information enables tracking of the optimum of the process under continuously changing feed conditions.