Optimal Operation of Batch Processes via the Tracking of Active Constraints Dominique Bonvin and Bala Srinivasan Institut d’Automatique Ecole Polytechnique F´ ed´ erale de Lausanne CH-1015 Lausanne, Switzerland dominique.bonvin@epfl.ch November 15, 2001 Abstract: This paper presents a new measurement-based optimization framework for batch processes, whereby optimal operation is achieved via the tracking of active constraints. It is shown that, under mild assumptions and to a first-order approximation, tracking the necessary conditions of optimality is equivalent to tracking active constraints (both during the batch and at the end of the batch). Thus, the optimal input trajectories can be adjusted using measurements without the use of a model of the process. When only batch- end measurements are available, the proposed method leads itself to an efficient batch-to-batch optimization scheme. The approach is illustrated via the simulation of a semi-batch reactor under uncertainty. Keywords: Batch chemical industry, Batch process, Dynamic optimization, Optimal control, On-line opti- mization, Batch-to-batch optimization, Run-to-run optimization. 1 Introduction Batch and semi-batch processes are of considerable importance in the chemical industry. This paper considers batch and semi-batch processes in the same manner and, thus herein, the term ‘batch processes’ includes semi-batch processes as well. A wide variety of specialty chemicals, pharmaceutical products, and certain types of polymers are manufactured in batch operations. Batch processes are typically used when the production volumes are low, when isolation is required for reasons of sterility or safety, and when frequent changeovers are necessary. With the recent trend in building small flexible plants that are close to the markets of consumption, there has been a renewed interest in batch processing (Macchietto 1998, Wiederkehr 1988). Batch chemical processing includes the important steps of capacity planning, tasks scheduling, and operation of individual units (Rippin 1989). This paper considers only the last step which is important for reducing production costs, improving product quality, and meeting safety requirements and environmental regula- tions. The operation of batch processes typically involves following recipes that have been developed in the laboratory in such a way that they can be implemented safely in production (Friedrich and Perne 1995). However, since there are constraints related to both the operation (equipment limitations, limits on key vari- ables such as temperature or pressure) and the final quality, the operators will naturally introduce a certain conservatism to guarantee feasibility in the presence of process disturbances and differences in equipment and scale. 1