# (667b) A Decomposition Approach for the Integration of Scheduling and Model Predictive Control in Fast Changing Market Conditions

- Conference: AIChE Annual Meeting
- Year: 2017
- Proceeding: 2017 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Thursday, November 2, 2017 - 8:17am-8:34am

Such frequent operational changes may result in processes operating in transient regimes, rather than in steady state conditions. This fact is contrary to the premise of most current scheduling methodologies, and emphasizes the necessity to account for the dynamic behavior of the system while making decisions at the scheduling level. Although the integrated scheduling and dynamic optimization problem has been addressed in the literature (Nystrom, Franke et al. 2005, Flores-Tlacuahuac and Grossmann 2006), few works considered the operation in transient regimes (Pattison, Touretzky et al. 2016), and even fewer take advantage of advanced control techniques in such integrated scheduling and control frameworks.

In this work, we propose a framework for the integration of scheduling and control for continuous processes operating in fast changing market conditions. The framework is based on an iterative procedure where problems at scheduling and control level are solved in each iteration. The first step is to identify the dynamic dependent variables and obtain algebraic approximations in terms of key decision variables (for example, production rate is dependent on production rate set points). The second step is to model the scheduling problem using the identified algebraic expressions. We use a discrete time representation of the system, and the number of slots is defined according to the frequency of change in parameters driving the costs of the system (for example, utility prices drive the costs of energy intensive industries). The problem is formulated as a mixed integer nonlinear problem. The scheduling problem defines the key decision variables (for example, production rate set points over time) in order to minimize costs. Since the scheduling problem is just an approximation of the real system, the costs predicted by the scheduling problem will provide a lower bound solution for the integrated problem.

The third step is to transfer the scheduling solution to the control level. At this level, we propose to use model predictive control in order to track the different set points over time while ensuring stability, robustness, safety and fast tracking. A closed loop simulation of the system is performed throughout the entire scheduling horizon, using the set points provided by the scheduling problem. The feasibility of the scheduling solution is verified and the actual cost of the system is calculated and compared to the scheduling cost. If the solution is infeasible, the sequence of set points defined in this iteration is cut from the scheduling problem, and the problem is resolved. If the solution is feasible, the scheduling cost associated to this sequence of set points is updated with the actual (simulated) cost, and the scheduling problem is resolved in the next iteration. The control problem sets an upper bound solution for the integrated problem, which is chosen at every iteration as the minimum simulated cost so far. The iterations proceed until the difference between upper and lower bounds are within a threshold. To illustrate the proposed approach, a case study involving the production of gaseous nitrogen in an air separation unit is presented.

Flores-Tlacuahuac, A. and I. E. Grossmann (2006). "Simultaneous cyclic scheduling and control of a multiproduct CSTR." Ind Eng Chem Res **45**(20): 15.

Nystrom, R. H., et al. (2005). "Production campaign planning including grade transition sequencing and dynamic optimization." Comput Chem Eng **29**: 17.

Pattison, R. C., et al. (2016). "Optimal Process Operations in Fast-Changing Electricity Markets: Framework for Scheduling with Low-Order Dynamic Models and an Air Separation Application." Ind Eng Chem Res **55**: 4562-4584.