(647d) Closed-Loop Properties of a Mixed Scheduling and Control Problem
Closed-Loop Properties of a Mixed Scheduling and Control Problem
Douglas Allan, James B. Rawlings, and Thomas Badgwell
Integration of production scheduling and process control is a subject rich with research opportunities. The high level, low-detail models often used by schedulers can result in suboptimal process economics because they do not take into account detailed process dynamics, and sometimes the resulting schedules are found to be infeasible at the control level. In recent years, advances have been made in combining scheduling and control. One major approach formulates one large problem containing all the aspects of both scheduling and control into a mixed-integer dynamic optimization (MIDO). The MIDO is then discretized into a mixed-integer nonlinear program (MINLP), which is in turn decomposed into a mixed-integer linear program (MILP) and nonlinear program (NLP), which can be solved iteratively to a solution [1,2,3].
This approach can result in great improvements in process economics, but is fundamentally an open-loop control strategy. Process disturbances or unplanned changes in schedule can disrupt the control sequence calculated offline, which then can result in poor performance. Several feedback strategies have been proposed. Instead of calculating control moves offline, Chu and You calculated the optimal tuning parameters of many multiloop PI controllers . Unfortunately, this control structure precludes more advanced control strategies, such as model predictive control (MPC) which limits the system performance. Chu and You have also proposed a method of repairing a schedule calculated offline in a structured way in order to reduce the online computational burden . Finally, Zhuge and Ierapetritou (2014) implemented a control strategy to resolve the optimization problem if the process deviates farenough from the target trajectory .
Simply running the open-loop strategies online (when computationally tractable) does not necessarily provide good performance. It is well known in the control community that optimality doesn't necessarily guarantee even closed-loop stability. The concept of stability is new to the scheduling community, but recent efforts to apply the methods of MPC directly to a scheduling problem have shown that stability is indeed meaningful in a scheduling context, and that when neglected, inventory can increase without bound . Therefore, we propose to analyze the closed-loop behavior of a mixed scheduling and control problem. Economic MPC provides a good framework to solve this problem and analyze stability and closed-loop behavior.
In this work we develop a simplified blending process example in which one product is delivered continuously into a pipeline and another is fed to a product tank. The tank is drained periodically by customers who have signed contracts for delivery of a full tank with a given composition at a specified time. As is typical in such contracts, there is a severe economic penalty if the product tank is not full with the correct product composition when the customer arrives to take delivery. Therefore the most important goal of the scheduling/control system is to create a full tank of the product with the correct composition when the customer arrives. In addition, the scheduling/control system must be flexible enough to handle disturbances in the delivery schedule, such as when a customer signals that they will be late picking up the product. In this case the combination of a delayed order and rush order must be accounted for by the dynamic controller. We propose to present a solution and closed-loop analysis of a class of problems displaying these features.
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