Optimization of a semi-batch reaction system under safety constraints

Maximizing the yield of a second-order reaction by manipulating the inlet flow rate is considered in both the isoperibolic and isothermal modes. For safety considerations, constraints on (i) the amount of heat produced, and (ii) the temperature under cooling failure are imposed. The optimal solution is discontinuous and is first obtained numerically. Analytical expressions for (i) the evolution of the input between the discontinuities, and (ii) the switching times are obtained. Using the analytical characterization of the optimal solution, an efficient feedback implementation strategy is designed.