(491e) A Closed-Loop Integrated Scheduling and Control Formulation for Processes Controlled By Distributed MPC Systems

Historically, scheduling and control have evolved largely independently from one another. However, chemical industries are currently required to operate in an increasingly dynamic market environment and are expected to respond to market changes ever more efficiently and rapidly [1]. This includes rapid adjustments of operating set-points and production targets, as well as utilities and raw material consumption. The adjustment of electricity consumption based on the power grid load falls within this category. Providing energy intensive plants with the operating flexibility required to rapidly and safely adjust their electricity consumption would enable their participation in demand-side management programs [2] and potentially ease the integration of intermittent energy sources (e.g. renewables) to the power grid. In this context, the integration of scheduling and control has often been suggested as a pathway to improve the operating flexibility of chemical processes [3,4].

In recent years, open [5] and closed-loop [6,7,8] formulations have been proposed for the integrated scheduling and control problem. Closed-loop formulations either use a dynamic process model that is representative of the closed-loop plant behavior, or account for the controller action via an explicit or implicit control law. Open-loop formulations neglect the presence of the controller and consider the open-loop process response. Because of the popularity of model predictive control (MPC) [9], a number of studies have proposed integrated scheduling and control formulations for processes controlled by centralized MPC [7,8]. PI controllers have also been considered in some studies [6]. Distributed MPC systems, however, have received very little attention from the perspective of integration of scheduling and control. Nevertheless, distributed MPC is sometimes favored over a centralized MPC approach for reliability, maintenance, and computational purposes [10, 11].

In this study, we propose an integrated scheduling and control formulation that accounts for the action of distributed MPC systems. Given that the integrated problem is an optimization problem and the MPC problem is also an optimization problem, this results in a multilevel optimization formulation with multiple MPC problems in the constraints. To solve this problem, we replace the MPC subproblems by their first-order Karush-Kuhn-Tucker (KKT) conditions which, for convex problems (e.g. linear MPC), are necessary and sufficient for optimality. This approach has been successfully adopted in a number of studies with [7,8,14] and without [12,13] scheduling considerations. In the present work, we use binary variables to capture discrete scheduling decisions, and to linearize the KKT-complementarity conditions. This leads to a mixed-integer linear programming (MILP) problem. The MPC-KKT reformulation, and scheduling constraints are linear, and we assume that a linear model coupled with a bias update mechanism is able to capture the true process dynamics sufficiently well. This closed-loop integrated scheduling and control problem is solved in real-time at the dynamic real-time optimization (DRTO) level to compute the input and output set-points assigned to the lower-level MPC systems. Production sequencing is also communicated to the plant via the set-points assigned to the MPCs. Due to that, one of the advantages of the proposed approach is that no changes are required to the existing control architecture (i.e. the MPC formulation is kept intact). A schematic representation of the integrated scheduling and control framework proposed in this study is presented in Figure 1.

We consider application of the proposed closed-loop integrated scheduling and control formulation to a process where two CSTRs are operated in parallel to meet the demand of distinct product grades. Each production line is assumed to be controlled by a distinct MPC subsystem. We investigate the economic gains and computational burden derived from accounting for the control action in the proposed formulation under closed-loop operation. Our results suggest that beyond a certain horizon, much shorter than the scheduling horizon, there is little economic benefit in rigorously accounting for the control action. We also observe a large variation in the time taken to solve the integrated scheduling and control problem, likely due to changes in the demand profile. However, the maximum observed solution times decrease sharply with the number of time-steps for which a rigorous approach is used to model the distributed MPC system action. In a second case study, we consider a nonlinear process. We show that the proposed formulation with a linear process model (i.e. there is plant-model mismatch) is able to drive the nonlinear plant to meet the quality specifications of three different product grades even before steady-state operation is reached. The proposed framework also adjusts the operating conditions based on the raw material costs.

In conclusion, we propose a closed-loop integrated scheduling and control formulation for plants operated by distributed MPC systems, and demonstrate its performance under conditions of perfect model knowledge and plant-model mismatch. We show that the proposed framework can coordinate the MPC subsystems and also drive the plant to produce product that meets the quality specifications before steady-state operation is reached. The ability to produce valuable product during transient periods has the potential to largely decrease operating costs, and may be essential for efficient market driven operation of processes with large time constants.

REFERENCES

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