Optimal Operation of Batch Processes with Multiple Inputs and Constraints

Optimal Operation of Batch Processes with Multiple Inputs and Constraints B. Srinivasan, S. Palanki, and D. Bonvin Optimal operation of batch processes has become increasingly important in recent years in the face of increased competition and also due to the trend towards building small, flexible plants n e a r the markets of consumption. Traditionally, batch processes have been operated with rudimentary control loops, which hinders the implementation of best operating policies in t h e face of uncertainty. This results in substantial losses in both quality and productivity. In this paper, a theoretical framework for on-line optimization o f batch processes with multiple inputs and constraints is developed. It is shown that the optimal solution consists o f several discontinuous input intervals; however, the inputs are a n a l y t i c in between discontinuities. Some combinations the i n p u t s push the system towards the constraints of the p r o b l e m , while other combinations exploit the intrinsic compromises present in the system. A procedure is developed t o separate these two combinations of inputs. This c h a r a c t e r i z a t i o n of the optimal solution can be utilized t o develop an efficient numerical procedure for computing the n o m i n a l optimal solution. Furthermore, the characterization also helps develop a measurement-based optimization scheme t h a t is highly efficient in the presence of uncertainties. The benefits of this scheme are illustrated via the simulation of a non-isothermal semi-batch reactor.