(647a) An Integrated Framework for Scheduling and Control Using Fast Model Predictive Control

Authors: 
Zhuge, J., Rutgers - The State University of New Jersey
Ierapetritou, M. G., Rutgers, The State University of New Jersey

An integrated approach that models the scheduling and control simultaneously addresses the information sharing between scheduling and control levels, leading to the integrated decision making that is overall optimal (Terrazas-Moreno, et al., 2008). Meanwhile, the integration increases the complexity of modeling and thus the computational requirements of the solution approaches (Engell and Harjunkoski, 2012). In online applications where disturbance is non-negligible, the integration of scheduling and control requires a repetitive solution of the integrated problem at real time in order to handle the state deviation caused by disturbance (Zhuge and Ierapetritou, 2012).

In this study we propose an integrated framework that involves two control loops for the online integration of scheduling and control. In the outer loop we approximate the original process dynamics using a piece-wise affine (PWA) model and incorporate it with the scheduling level. This leads to an integrated problem that is subject to linear constraints. The integrated problem at the outer loop generates both the production scheduling and the state reference for control problem. The scheduling solution and state reference are provided to the inner loop where fast Model Predictive Control (MPC) is used to track the state reference and to compute the exact control solution online. Note that these two loops correspond to different models and different time scales. The outer loop uses the integrated model and solves it in the period of days or weeks while the inner loop uses the process dynamic model and updates the solution in seconds. Essentially the inner loop is solved much more frequently than the outer loop does. Following this approach the outer loop is able to achieve an overall optimality for both scheduling and control levels efficiently, and the inner loop fast MPC is able to respond quickly to the local disturbance. Note that the proposed approach is applicable in a dynamic market environment as the outer loop incorporates the market information such as demand and price. The proposed framework solves an integrated model to guarantee the overall optimality and employes fast MPC to respond timely to process disturbances. While solving the integrated problem the latest market information such as material price and product demands are incorporated into the integrated problem, and the scheduling solutions are updated accordingly.

When disturbance is detected which means that a state deviation from the referece is measured, the state information is feedback to the inner fast MPC or outer integrated problem. A threshold is introduced to determine the feedback. If the state deviation is less than the threshold, the state is feedback to inner fast MPC and locally treated by fast MPC. Otherwise if the state deviation is large (higher than the threshold) it is feedback to the integrated problem and the scheduling solution is updated accordingly. The threshold is an empirical value and it is determined to avoid unecessary changes of the scheduling solution when disturbances are small enough that can be handled efficiently in the control level, whereas updates in the scheduling solution are considered if significant disturbance occurs. Results of case studies show the feasibility and efficiency of the proposed approach.

Reference:

Terrazas-Moreno, S.; Flores-Tlacuahuac, A.; Grossmann, I. E. Simultaneous design, scheduling, and optimal control of a methyl-methacrylate continuous polymerization reactor. AIChE Journal 2008, 54, (12), 3160-3170.

Engell, S.; Harjunkoski, I. Optimal operation: Scheduling, advanced control and their integration. Computers & Chemical Engineering 2012, 47, 121-133.

Zhuge, J.; Ierapetritou, M. G. Integration of Scheduling and Control with Closed Loop Implementation. Industrial & Engineering Chemistry Research 2012, 51, (25), 8550-8565.