Null-space method for optimal operation of transient processes

We consider batch process optimization and robust implementation of optimal control policies. The dynamic optimization of such processes is in most cases model based, and therefore subject to uncertainties. This may lead to sub-optimal control trajectories with significant economical losses. In this paper we extended the concept of self-optimizing control for the optimal operation of transient processes. The main idea is to find a function of the measurements whose trajectory is optimally invariant to disturbances, and then track the trajectory using standard feedback controllers. Doing so results in near-optimal economic operation in spite of varying disturbances without the need for re-optimization. We show that the invariant trajectories can be computed as linear combinations of the measurement vector, where the combination matrix is easily obtained from optimal sensitivities. We illustrate the application of the proposed method in a semi-batch reactor case study.