An active approach to space-reduced NCO tracking and output feedback optimizing control for batch processes with parametric uncertainty

Abstract

Necessary conditions of optimality (NCO) tracking is a promising approach to run-to-run optimization of batch processes, by converting the optimization problem into a feedback control problem. Since batch processes often contain numerous decision variables that hamper input adaptation in a feedback control manner, the directional effect of uncertainty has been utilized to reduce adaptation directions. This paper proposes an active approach that can further simplify the design of NCO tracking controllers for run-ro-run optimization of batch processes. The idea is to actively restrict the plant inputs in an optimal subspace, prior to the separation of constraint- and sensitivity-seeking directions of plant inputs. For this purpose, an extended system is constructed and then the system is operated by the so-called surrogate variables. Depending on the dimensions of active constraints and uncertain parameters, two cases are distinguished and their NCO tracking controllers are designed respectively. In addition, when the number of parameters is greater than the constraints, the neighboring-extremal based output feedback is incorporated into the active approach, such that the time-consuming gradient evaluations are avoided hence convergence is accelerated. In both cases, the number of adapted directions equals to the number of uncertain parameters. A numerical example and a batch distillation column are investigated to show the new methodology.