Hybrid Koopman model predictive control of nonlinear systems using multiple EDMD models: An application to a batch pulp digester with feed fluctuation

Abstract

In the pulping process, feed fluctuations often occur due to the supply of raw materials from various and unconventional sources, such as recycle to meet the increasing market demand for paper, and strict environmental regulations. However, such feed fluctuation can significantly extend the operating range of the process, which may cause differing local dynamics that degrade the performance of a single model-based controller. Motivated by these concerns, in this work, a hybrid Koopman model predictive control (KMPC) framework for a batch pulping process is developed to regulate the Kappa number and the cell wall thickness (CWT) of fibers to produce pulp with desired properties in the presence of feed fluctuations. Specifically, multiple local models are constructed by clustering the time-series operation data from the pulping process and identifying lifted state–space models for each cluster using extended dynamic mode decomposition (EDMD). Subsequently, a local EDMD model-based controller for each cluster is developed. In the closed-loop system, one local controller is selected based on the current system state at every time step. Consequently, in the numerical experiments, the derived multiple EDMD models successfully predicted the local behavior of the batch pulping process, and the developed hybrid KMPC system was able to obtain the desired Kappa number and CWT values in the presence of feed fluctuations.