(644g) Integration of Scheduling and Optimal Control for Multi-Product Processes Using a Switched Dynamic System Formulation

In the process industry, decision making involves supply chain management, planning, scheduling and process control. Traditionally, these layers have been addressed individually and solved sequentially. This strategy may lead to sub-optimal or even infeasible solutions when decisions made at upper (long-term) levels do not take into consideration information from lower (short-term) levels [1]. There are well known benefits from integration of scheduling and control, e.g., sequences that prevent costly changeovers and reduce transition times and off-spec products; scheduling programs that minimize operational problems (e.g., aggressive control actions); and the use of more precise and timely information in scheduling [2]. As a result, there is an increasing interest in a tighter coordination and collaboration across multiple decision-making scales. Studies have proposed strategies to integrate a dynamic model of the continuous system into the scheduling framework following a so called top-down approach [3,4,5]. Despite these efforts, most of the integrated methods face difficulties introduced by the presence of binary/logic variables, differential algebraic equations, multiple time scales and performance criteria [6,7]. Typical integrated formulations involving scheduling and control layers consist of Mixed-Integer Dynamic Optimization (MIDO) models that pose computational challenges [8]. Often, these models describe process scheduling as a static system whereas the production process is considered dynamic over certain time periods (e.g., transition periods). Several initialization, reformulation and decomposition techniques have been developed to overcome the computational burden [9,10,11]. However, alternatives to MIDO formulations have not been thoroughly explored in the open literature.

In this work, we propose a novel integrated model that circumvents the need to deal with integer decision variables. The key idea is to formulate an optimal control problem of a switched system [12], which is obtained by coupling the dynamic models of both scheduling and production decisions along the entire horizon. We focus on multi-product continuous processes where one product is manufactured at a time following a cyclic production time. Multiple products can be obtained by manipulating one or more variables to switch between different operating conditions associated with each product. Time-scaling transformation is used to handle variable switching times [13]. A binary function with an associated penalty term is added and transformed into a set of parameters to model the sequencing of the multi-product unit. Due dates are also considered in the present framework. Unlike previous works, the proposed formulation does not assume that once a desired value is attained, the transition is complete and the system remains at that steady state until the next transition. Instead, the framework enforces this behavior by parameterizing the control variables and applying interior constraints preventing potential instabilities. The optimal control problem is then converted into a Nonlinear Programming (NLP) model by applying an efficient discretization scheme that allows to find transitions for stable and unstable systems. An iterative procedure to improve transition times and computational costs is provided.

Multiple case studies involving multi-product continuous processes have been used to test the performance of the proposed framework. The goal was to find an optimal switching sequence and manipulated variables profiles such that the total profit is maximized with and without due dates. The solutions obtained by the present approach are similar to those obtained with Mixed-Integer Nonlinear Programing (MINLP) problems that come from the classical MIDO formulations, but with more compact models and less computational effort. Unlike previous works, solutions provide a simultaneous dynamic description of the integrated scheduling and production, and due dates are readily accommodated. The proposed framework can be considered as an efficient alternative to mixed-integer models involving scheduling and control decisions. Motivated by the performance of the proposed switched system formulation, future works in this research aims to extend the framework to a closed-loop implementation using Model Predictive Control (MPC) and more complex scenarios emerging in chemical manufacturing plants.

References

1. L. S. Dias, M. G. Ierapetritou, From process control to supply chain management: An overview of integrated decision making strategies, Computers & Chemical Engineering 106 (2017) 826–835.
2. S. Engell, I. Harjunkoski, Optimal operation: Scheduling, advanced control and their integration, Computers & Chemical Engineering 47 (2012) 121–133.
3. A. Flores-Tlacuahuac, I. E. Grossmann, Simultaneous cyclic scheduling and control of a multiproduct cstr, Industrial & Engineering Chemistry Research 45 (2006) 6698–6712.
4. M. Baldea, I. Harjunkoski, Integrated production scheduling and process control: A systematic review, Computers & Chemical Engineering 71 (2014) 377 – 390.
5. M. A. Gutirrez-Limn, A. Flores-Tlacuahuac, I. E. Grossmann, Minlp formulation for simultaneous planning, scheduling, and control of short-period single-unit processing systems, Industrial & Engineering Chemistry Research 53 (2014) 14679–14694.
6. Y. Chu, F. You, Model-based integration of control and operations: Overview, challenges, advances, and opportunities, Computers & Chemical Engineering 83 (2015) 2–20.
7. M. Rafiei, L. A. Ricardez-Sandoval, New frontiers, challenges, and opportunities in integration of design and control for enterprise-wide sustainability, Computers & Chemical Engineering 132 (2020) 106610.
8. R. W. Koller, L. A. Ricardez-Sandoval, A dynamic optimization framework for integration of design, control and scheduling of multi-product chemical processes under disturbance and uncertainty, Computers & Chemical Engineering 106 (2017) 147–159.
9. J. Zhuge, M. G. Ierapetritou, A decomposition approach for the solution of scheduling including process dynamics of continuous processes, Industrial & Engineering Chemistry Research 55 (2016) 1266–1280.
10. Y. Chu, F. You, Integration of production scheduling and dynamic optimization for multi-product cstrs: Generalized benders decomposition coupled with global mixed-integer fractional programming, Computers & Chemical Engineering 58 (2013) 315–333.
11. I. Mitrai, P. Daoutidis, Decomposition of integrated scheduling and dynamic optimization problems using community detection, Journal of Process Control 90 (2020) 63 – 74.
12. S. C. Bengea, R. A. DeCarlo, Optimal control of switching systems, Automatica 41 (2005) 11 – 27.
13. K. L. Teo, L. S. Jennings, H. W. J. Lee, V. Rehbock, The control parameterization enhancing transform for constrained optimal control problems, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40 (1999) 314335.