(457d) Integrated Scheduling and Control Formulation for Processes Controlled By Nonlinear MPC Systems

Operating flexibility is a key factor in ensuring viability of the participation of electricity intensive industries in demand-side management programs [1]. The reason is that manufacturers should rapidly adjust their electricity consumption to compensate for variations in the power grid load, easing the incorporation of intermittent energy sources (e.g. renewables) to the electric grid [2]. From a process control system perspective, this operating flexibility often translates into more frequent scheduling changes (e.g. changes in production targets, product types, operating set-points). In a context where these scheduling changes happen on a time scale in which the control dynamics are relevant, it makes sense to account for the process dynamics when solving the scheduling problem [3, 4]. This has fueled efforts for the integration of scheduling and control,

A number of integrated scheduling and control formulations have been proposed in recent years [5, 6, 7]. They focus particularly on processes controlled by linear model predictive control (LMPC) due to its popularity [8] in the chemical industry. Processes controlled by nonlinear model predictive control (NMPC) within the context of integrated scheduling and control have, until now, received scant attention, making them the focus of this study. NMPC finds application in highly nonlinear processes, or mildly nonlinear but with a large operating region [9].

In this work, we propose a closed-loop integrated scheduling and control framework for processes controlled by NMPC. The integrated problem is solved at the dynamic-real time optimization (DRTO) level to compute set-points to the underlying NMPC control layer, which then computes the inputs applied to the plant. One of the main advantages of the proposed approach is that it maintains the NMPC architecture currently in place intact (i.e. no changes to the NMPC formulation are required). Another advantage is that the DRTO is aware of the NMPC controller. This prevents the DRTO from computing set-points that are unreachable and/or infeasible for the NMPC. A schematic diagram is presented in Figure 1. For this study, the DRTO is solved online at a pre-specified time-interval which is an integer multiple of the NMPC sampling time.

At the DRTO level, we use the NMPC first-order Karush-Kuhn-Tucker (KKT) conditions to compute the input action applied to the process model at every prediction time-step. This is represented in Figure 1 by the NMPC-KKT subproblems constraints. The Linking constraints ensure that the first piece of the input trajectory computed by NMPC-KKT subproblems is applied to the Process model, where the Process model is a mathematical representation of the plant dynamics (e.g. state-space model). The Scheduling constraints capture grade transitions, production sequencing, quality targets, and it also includes an inventory model. The quality targets are defined with respect to (a subset) of the (measured) outputs of the Process model (e.g. different product grades have different concentrations). The amount produced of each grade is determined as part of the solution of the DRTO problem. Note that the main degrees of freedom of the DRTO problem are the set-points to the NMPC-KKT subproblems, which impacts the Process model, and hence the Scheduling constraints, via the inputs. The DRTO receives output and inventory measurements from the plant, as well as market information regarding the demand and utilities cost. We use complementarity constraints to model discrete scheduling decisions. The scheduling and NMPC-KKT complementarities are addressed via a regularization approach [10] as part of the solution of the DRTO problem.

We demonstrate the performance of the proposed integrated scheduling and control framework on two nonlinear processes operated by an NMPC, a SIMO (single-input multiple-output) CSTR and a MIMO (multiple-input multiple-output) polymerization reactor. For both case studies, the proposed framework successfully drives the plant to meet the product demands, even under detuned controller conditions. Of note is that the DRTO utilizes the set-point trajectories to compensate for the detuned conditions. Additionally, for the case studies considered, we show that the NMPC-KKT conditions always yield a local minimum, and that the proposed complementarity formulation successfully approximates the discrete scheduling decisions.

REFERENCES

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