(733h) Linear Surrogate Dynamical Models for Embedding Process Dynamics in Optimal Production Scheduling Calculations

On-demand manufacturing and fast changing electricity markets have created a need for production schedule changes to occur over time scales (hours or minutes) comparable to the process time constants. For these production schedules to be feasible for plant operation, the dynamics of the plant must be accounted for in scheduling calculations. Embedding dynamic information in scheduling calculations is challenging due to the multiple time-scales involved—short term setpoint execution must be balanced with long term scheduling decisions.

Detailed models describing the dynamics of industrial processes are almost invariably nonlinear and highly dimensional, making it challenging to solve the associated optimal scheduling problems (which are in a mixed-integer nonlinear program form) in a practical amount of time. Motivated by this, in this paper we present a novel approach to formulating and solving optimal scheduling problems under dynamic constraints, predicated on developing a Mixed Integer Linear Program (MILP) formulation amenable to real-time solution.

Specifically, in our previous work[1], we have shown that (nonlinear) scheduling-relevant low-order models of the process dynamic can be derived [2] using routine operating data. In this work, we focus on two classes of such models (Hammerstein-Wiener (HW) and Finite Step Response (FSR)). We propose a novel framework for reformulating HW models as a set of linear equations comprising both continuous and integer variables. Further, we demonstrate that for specific choices of the model nonlinearity, this linearization is exact. We compare various linearization techniques and discuss scaling and computational cost. In addition, comparisons between linearized and discretized HW models and inherently linear and discrete FSR models are drawn.

On this basis, we study the formulation and solution strategies for the production scheduling problem, including adaptive sampling, relaxation, and decomposition. A polymerization reactor and an air separation unit are utilized to demonstrate the theoretical concepts developed, showing considerable improvements in computation time compared to previous works [1].

[1] R. C. Pattison, C. R. Touretzky, T. Johansson, I. Harjunkoski, and M. Baldea, “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., vol. 55, no. 16, pp. 4562–4584, Apr. 2016.

[2] S. A. Billings, Nonlinear system identification : NARMAX methods in the time, frequency, and spatio-temporal domains. Chichester, West Sussex: John Wiley & Sons, 2013.