Computationally efficient NMPC for batch and semi-batch processes using parsimonious input parameterization

Abstract The trend towards high-quality, low-volume chemical production has put more emphasis on batch and semi-batch processing due to its increased operational flexibility. The transient behavior of these processes makes their real-time optimization very challenging. In particular, the large prediction horizons required in shrinking-horizon NMPC increase the real-time computational effort due to expensive matrix factorizations. The computational delay associated with advanced control methods is usually underestimated in theoretical studies. However, this delay may contribute to suboptimal or, worse, infeasible operation in real-life applications. This study proposes to combine a tailored parsimonious input parameterization with shrinking-horizon NMPC to reduce the real-time computational effort. Models of the optimal solution are used to suggest parsimonious parameterizations (especially for sensitivity-seeking arcs) that lead to computationally efficient optimization. The proposed approach is illustrated in simulation on two case studies in the presence of uncertainty, namely a batch binary distillation column and a semi-batch reactor for the hydroformylation of 1-dodecene. The results show that the tailored parsimonious shrinking-horizon NMPC (i) performs very similarly to the standard shrinking-horizon NMPC in terms of cost, (ii) is computationally much more efficient than the standard shrinking-horizon NMPC especially at the beginning of the batch, (iii) is robust to plant-model mismatch.