(753h) Parameterizations of Data-Driven Process Models for Integrated Stochastic Scheduling and Process Control

Modern chemical manufacturing plants increasingly seek to integrate decision-making processes in real time (“enterprise-wide optimization”, “Industry 4.0”, “smart manufacturing”), in response to competitive global market conditions and aided by advances in hardware and algorithms. Process scheduling, which is concerned with setting production amounts/sequences and allocating plant resources, is a natural target for (real-time) optimization. For example, under demand response programs, processes which consume electricity as a primary feedstock can modulate their production schedule in response to electricity prices; these decisions are generally made hourly or daily, and looking several days into the future. The optimal production schedules are then implemented in the plant by a process control system, which operates at a higher frequency and over a shorter prediction horizon than the scheduling layer.

As production schedules are adjusted more frequently under paradigms like demand response, it is no longer possible to assume that the process operates primarily at steady-state when solving the scheduling optimization problem; the dynamic response of the closed-loop process should be explicitly considered. However, integrating scheduling and control results in a computationally challenging optimization problem, especially for large, multivariable industrial processes. Computational complexity increases further if (inevitable) uncertainty in problem parameters is to be considered. As a result, parsimonious models that capture scheduling-relevant process dynamics (which we refer to as “scale-bridging models”) are needed [1].

In this work, we build on prior developments to introduce a framework for computationally efficient integrated scheduling and control under uncertainty. As in [1], we build scale-bridging models, which represent the closed-loop dynamic response to of a process changes in setpoints/targets imposed by the scheduling layer, noting that closed-loop data of the type required for this effort are readily available at most chemical plants. The models are in Hammerstein-Wiener (HW) [2] form, consisting of static nonlinear input and output blocks flanking a linear dynamic block. The novel aspect of the current contribution is that we exploit features of the HW model structure to parameterize the scale-bridging models, and therefore to significantly reduce the dimension of the integrated scheduling and control problem. We show that dimensionality reduction is possible due to the linear nature of the HW dynamic block, and depends on the form of the static input/output nonlinear blocks, which are assumed to be piecewise linear (PWL) in this work. Our framework considers parameterizations of path constraints, accumulative (integrated) terms, and constraints relating to transition times. We demonstrate its efficacy on a case study considering demand-response scheduling of a chlor-alkali process; the reduced problem size enables order-of-magnitude reduction in solution time compared to a reference problem [3], and enables the formulation and solution of (previously intractable) stochastic formulations that account for uncertainty.

[1] Du, J., Park, J., Harjunkoski, I., & Baldea, M. (2015). A time scale-bridging approach for integrating production scheduling and process control. Computers & Chemical Engineering, 79, 59-69.

[2] Zhu, Y. (2002). Estimation of an N–L–N Hammerstein–Wiener model. Automatica, 38(9), 1607-1614.

[3] Otashu, J. I., & Baldea, M. (2019). Demand response-oriented dynamic modeling and operational optimization of membrane-based chlor-alkali plants. Computers & Chemical Engineering, 121, 396-408.