Robust feasible control based on multi-stage eNMPC considering worst-case scenarios

The goal of this work is an efficient control scheme for the robust satisfaction of constraints for batch processes under parametric uncertainties. The multi-stage economic nonlinear model-predictive controller (eNMPC) [S. Lucia, et al. J. Process Control, 2013] is combined with two different methods for robust dynamic optimization. The multi-stage NMPC considers a scenario tree, branching at each sampling interval. In this work, the scenarios for the branches are generated with two previously investigated methods of detecting worst-case scenarios. One method is based on discretization of the uncertain parameter set (J. Puschke, et al. Comput. Chem. Eng., Vol. 98, 2017a). With this approach, all worst-case models are considered, including points not lying at the boundary of the uncertainty set. The other method is a heuristic approach (J. Puschke, et al. Comput. Chem. Eng., 2017b), which considers only values at the boundary with a high sensitivity. These methods for robust control are evaluated on the basis of an illustrative case study. The results show that, in contrast to the nominal eNMPC, less or even no constraint violations occur.