Dynamic self-optimizing control for unconstrained batch processes

In this paper, we consider near-optimal operation for a class of unconstrained batch processes using the self-optimizing control (SOC) methodology. The existing static SOC approach is extended to the dynamic case by means of a static reformulation of the dynamic optimization problem. However, the dynamic SOC problem is posed as a structure-constrained controlled variable (CV) selection problem, which is different from the static cases. A lower-block triangular structure is specified for the combination matrix, H, to allow for optimal operation whilst respecting causality. A new result is that the structure-constrained SOC problem still results in a convex formulation, which has an analytic solution where the optimal CVs associated with discrete time instants are solved separately. In addition, the inputs are directly determined based on current CV functions for on-line utilization. A fed-batch reactor and a batch distillation column are used to demonstrate the usefulness of the proposed approach.