Nonlinear Model Reduction Methods for Real-Time Nonlinear Model Predictive Control of Process Systems

RWTH Publications (RWTH Aachen)

Abstract

Enabling industrial processes to make rapid operational adjustments in the context of energy demand flexibility represents a fundamental paradigm shift within the ongoing energy transformation. Advanced automation strategies are a key technology for implementing short-term load changes in process plants. Nonlinear model predictive control (NMPC) in particular is considered a promising automation technology. An NMPC uses a nonlinear mathematical prediction model and numerical optimization to continuously determine suitable process parameters in real time, ensuring operating requirements are met. Adequate prediction models can be provided in the form of “digital twins”, based on detailed physical/mechanistic process modeling. While advantageous in terms of model accuracy and validity, detailed process models are very computationally expensive for many industrial processes and are therefore not directly suitable for control purposes. With the aim of enabling real-time NMPC, this dissertation deals with model simplification, specifically with “model reduction methods”. The thesis investigates methods based on model insight as well as purely data-driven approaches using machine learning. Alongside a systematic literature review, as well as the theoretical and a numerical comparison of existing reduction methods, this dissertation proposes two model reduction methods. The first method extends manifold learning, a machine learning approach, to account for input variables in non-autonomous systems. The second method applies Koopman theory to reduce models of input-affine systems, which is the primary focus of this thesis.Koopman theory is an abstract mathematical framework based on operator and systems theory, and is used herein to derive suitable model structures that can be applied effectively in the context of data-driven model reduction. Specifically, this thesis develops Koopman models with generic “Wiener” block structure, which is particularly well-suited for this purpose. These models are not only mathematically simple but can also be exploited very effectively in NMPC optimization problems. Thereby, real-time optimization for process control becomes feasible. The developed Koopman method is implemented in a machine learning framework, enabling the data-driven identification of reduced models via artificial neural networks. Moreover, the data-driven nature of this reduction method requires only little process insight, facilitating the complete reduction of entire process models in a single step and making the method user-friendly. Finally, reduced prediction models are applied in three NMPC case studies. In addition to the data-driven Koopman models developed in this dissertation, the so-called “nonlinear wave propagation model”, a low-order mechanistic model, is also considered. Cryogenic air separation processes, which are classical candidates for energy demand flexibility, are used as case studies. We demonstrate that both types of reduced models facilitate real-time NMPC. However, the Koopman models are easier to handle numerically and provide a more drastic reduction in CPU time of up to 99 %.

Authors 1

1. Jan C. Schulze corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen