# Integrating production scheduling and process control using latent variable dynamic models

## TL;DR

This paper presents a novel approach that combines process scheduling and control by learning low-dimensional latent models of process dynamics, enabling more efficient and detailed scheduling in chemical processes.

## Contribution

It introduces a data-driven method to identify low-dimensional latent manifolds for process dynamics, simplifying scheduling and control calculations in complex chemical systems.

## Key findings

- Reduces computational effort in scheduling tasks.
- Provides more detailed dynamic information than previous methods.
- Successfully applied to air separation unit scheduling.

## Abstract

Given their increasing participation in fast-changing markets, the integration of scheduling and control is an important consideration in chemical process operations. This generally involves computing optimal production schedules using dynamic models, which is challenging due to the nonlinearity and high-dimensionality of the models of chemical processes. In this paper, we begin by observing that the intrinsic dimensionality of process dynamics (as relevant to scheduling) is often much lower than the number of model state and/or algebraic variables. We introduce a data mining approach to "learn" closed-loop process dynamics on a low-dimensional, latent manifold. The manifold dimensionality is selected based on a tradeoff between model accuracy and complexity. After projecting process data, system identification and optimal scheduling calculations can be performed in the low-dimensional, latent-variable space. We apply these concepts to schedule an air separation unit under time-varying electricity prices. We show that our approach reduces the computational effort, while offering more detailed dynamic information compared to previous related works.