Chemical Engineering Journal, Vol.75, No.1, 1-9, 1999
Towards practical optimal control of batch reactors
Instead of finding only the optimal temperature profile, the optimal flow rates of heating and cooling fluids are determined, so that the yield of a desired product in a batch reactor is maximized. The two additional differential equations that are introduced to handle the heat balances make the optimization more difficult, especially when constraints are placed on the reactor temperature. However, by using iterative dynamic programming (IDP) in multi-pass fashion, the optimal policy can be readily obtained. Optimization as carried out on two typical batch reactor problems shows that if the heat transfer coefficient is reasonably chosen, then the optimal yield can be significantly larger than what can be expected from the best isothermal operation. To prevent simultaneous flows of heating and cooling streams, we used for optimization a single heat flow term as a control variable. When positive, this heat flow term is equal to the heating stream flow rate; when negative, the magnitude of the heat dow term is equal to the coolant flow rate. An augmented performance index was used to handle state constraints resulting from the bounds on the reactor temperature in the second example. In both the examples, it was clear that significantly better yields than those possible from the best isothermal temperature profile can be obtained, even if the heat transfer coefficient is not known accurately at the start of the batch time.