Batch process optimal scheduling using Dynamic Programming

GUILLERMO A. DURAND; DENNIS BONNÉ; STEPHEN BRIDGES; STEN BAY JØRGENSEN

Turku (Finlandia)

Congreso; Nordisk Processes Control Workshop 10; 2001

Nordic Working Group on Process Control

Batch processing is most important since half the chemical products are produced in batch processes. Batch processing consists of a sequence of processing steps, which also may take place between continuous processes in a production line. A special problem in bath processing is the possible variation in task performance. The performance of a task depends, for example, on the equipment used, the chosen operating conditions, the state and the quantity of the feed and the selected external agents. Time varying conditions can make the throughput vary widely. If the processing capabilities of upstream and downstream units do not match those of the batch stage(s) then accumulation problems may arise. The most common solution is to use more than one batch unit and schedule their operation to make the overall production of the batch process as similar as possible to that of the upstream and downstream continuous stages. The scheduling has also to be planned considering the optimization of the operation in order to reach the maximum utilization of the total process plant, constrained by the batch stage and intermediate storage sizes. Thus, batch process design and batch operation design are tightly interrelated. The scheduling basically consists of a series of decisions of whether to start or not a specified batch unit at a determined moment. The discrete time control problem and the dynamic batch-to-batch behavior of the units make the dynamic programming approach a suitable methodology for optimizing scheduling. The objective of this paper is to develop a scheduling algorithm based on dynamic programming, applied to a particular batch process: sugar crystallization from the thick juice obtained in the production of sugar. The goal of the scheduling algorithm is to maximize the production respecting the constraints of available resources and market demand. Including securing stable syrup quality, low sugar loss and low energy consumption due to a smoother operation. The existence of an optimal static periodic solution (OSPS) to the scheduling problem has been shown. An inherent problem of dynamic programming (DP) is exponential growth in computing load. The outrolling technique is used to avoid that problem. The outrolling technique consists in the rollout of the states resulting from the DP at a specified point in time until the final time. Outrolling is initiated when DP has reached a specified number of possible states. The rollout is carried out using the OSPS. This produces one outrolling final state per DP state. Comparing the final objective function values, a given number of the best final states are selected. The DP algorithm continues from the starting outrolling time, but analyzing only the selected best states, until the final time or until the outrolling technique is needed again. The action of selecting states limits the number of states to be analyzed, thereby avoiding exponential growth. Once the algorithm reaches the final time, the control sequence leading to the optimal final state is constructed as normally in dynamic programming. However, a number of the DP states will not be in the OSPS at the start of the outrolling and the OSPS cannot be applied to those states without creating an in-feasible situation. Therefore, an additional objective of this paper is to find a transition method from the dynamic behavior to the OSPS, in order to be able to correctly apply the OSPS. A first principles model is also being developed in order to test the solutions given by the dynamic scheduling for several operation scenarios, including starting and stopping. A preliminary dynamic programming solution has been developed for a simple model with a limited time horizon.