Real-Time Optimization of Batch Processes by Tracking the Necessary Conditions of Optimality

The use of measurements to compensate for the effect of uncertainty has recently gained attention in the context of real-time optimization of dynamic systems. The commonly used approach consists of updating a process model and performing numerical optimization using the refined model. In contrast, this paper presents a two-level approach that does not require repeating the optimization: At the upper level, the constraints that are active in the optimal solution are identified from optimization of a nominal process model; at the lower level, feedback control is used to enforce the necessary conditions of optimality, i.e., meet the identified active constraints and push selected gradients to zero. A key feature of this self-optimizing control scheme is the use of an input parametrization that is tailored to the identified active constraints. Another feature that is specific to batch processes is the possibility to meet the control objectives either online or on a run-to-run basis. The self-optimizing control approach is illustrated on a semibatch reactor example.