(769h) Integration of Scheduling and Control within a Dynamic Real-Time Optimization (DRTO) Framework

Large chemical plants and petroleum refineries typically employ a hierarchical process automation architecture, with low-level controllers (PID’s) coordinated by a higher level Model Predictive Controller (MPC), which may in turn receive set-points from a Real-Time Optimization (RTO) system. The RTO system may compute these trajectories based on scheduling and planning information such as product qualities and demand [1]. As such, these different levels of the plant hierarchy are typically posed as optimization problems and solved separately, with information being sent down from one level to the next. The RTO system typically employs a steady-state process model for calculating set-point trajectories. However, for plants with slow transitions, the RTO system would benefit from having knowledge of the process dynamics. This presents an opportunity to solve these three problems simultaneously, where the optimizer would choose the sequence of operating points and when to transition.

Several attempts have already been made to integrate scheduling and control as a single optimization problem. Chu and You [2] consider PI control and solve a scheduling problem where the process and controller equations are included as constraints and the controller parameters are chosen by the optimizer. Chu and You [3] subsequently introduce surrogate models used as constraints in the scheduling problem, which are low-order representations of the process dynamics. Du et al. [4] also introduce a low-order representation of the process dynamics, referred to as a time-scale bridging model, that is utilized in the scheduling problem. Zhuge and Ierapetritou [5] integrate control and scheduling by utilizing explicit control laws through a multi-parametric MPC formulation.

In previous work [6], a closed-loop DRTO formulation was used to provide set-point trajectories to an underlying MPC system. The DRTO optimization is based on the predicted closed-loop response generated through a sequence of MPC calculations along the DRTO prediction horizon. This was implemented by embedding the first-order KKT optimality conditions of each MPC sub-problem as equality constraints in the DRTO optimization problem, resulting in a single mathematical program with complementarity constraints (MPCC). The DRTO algorithm was subsequently applied to coordination of distributed MPC systems by accounting for interaction effects between subsystems, and adjusting the set-point trajectories accordingly [7].

This work aims to incorporate scheduling decisions into the DRTO framework. A common theme that was seen in the prior work was combining scheduling and control, omitting the RTO layer. The result of this showed that the output set-point trajectories are the same as the output targets, and that each target is given a slot in a sequence. Key features of this work’s formulation are to introduce binary decision variables to specify which product target is active at a given time point and specify if the output quality is within the target band, that is, the process will only accumulate revenue if within the band. The DRTO allows the output set-points to deviate from the output targets should it facilitate faster or smoother transitions. An additional feature is to decouple the complementarity constraints by introducing another binary variable. The result is a single level optimization problem formulated as a mixed-integer linear or quadratic program if the process dynamics are linearized. The performance of the proposed scheme is demonstrated through application to case studies.

References

[1] T. E. Marlin and A. N. Hrymak, “Real-time operations optimization of continuous processes,” In: Kantor, J.C., Garcia, C.E., Carnahan, B. (eds.) AIChE Symposium Series: Proceedings of the 5^th International Conference on Chemical Process Control, pp. 156–164, 1997.

[2] Y. Chu and F. You, “Integration of scheduling and control with online closed-loop implementation : Fast computational strategy and large-scale global optimization algorithm,” Comput. Chem. Eng., vol. 47, pp. 248–268, 2012.

[3] Y. Chu and F. You, “Integrated Planning , Scheduling , and Dynamic Optimization for Batch Processes : MINLP Model Formulation and Efficient Solution Methods via Surrogate Modeling,” Ind. Eng. Chem. Res., 53, 13391-13411, 2014.

[4] J. Du, J. Park, I. Harjunkoski, and M. Baldea, “A time scale-bridging approach for integrating production scheduling and process control,” Comput. Chem. Eng., vol. 79, pp. 59–69, 2015.

[5] J. Zhuge and M. G. Ierapetritou, “Integration of Scheduling and Control for Batch Processes Using Multi-Parametric Model Predictive Control,” AIChE. J., vol. 60, no. 9, 3169-3183, 2014.

[6] M. Z. Jamaludin and C. L. E. Swartz, “Dynamic Real-Time Optimization with Closed-Loop Prediction,” AIChE J., vol. 63, no. 9, 3896-3911, 2017.

[7] H. Li, “Dynamic real-time optimization of distributed MPC systems using riogorous closed-loop prediction,” In press, Comput. Chem. Eng., 2018