Modeling the different dynamics in parallel flow regenerative kilns for the production of quicklime is one of the steps towards obtaining the digital twins of the kilns. This paper shows a data-driven modeling approach based on the dynamic mode decomposition algorithm leveraged with a maximum likelihood method that gives linear and discrete-time models of the system. This allows capturing the transient dynamics of the process for the design of subsequent observers of the unknown dynamics, for the implementation of anomaly detection algorithms and eventual control and optimization of the manufacturing process.

This study shows how to combine the concepts of extended dynamic mode decomposition and model predictive control in a decentralized approach to drive interconnected oscillators. To achieve this goal, the predictive power of the decomposition algorithm is used to make an approximation of the state of the system, but also to predict the behavior of the interconnection input that affects a particular subsystem. As the prediction of the extended system captures the dynamics linearly, this approach is suitable for the design of local model predictive controllers such that each subsystem can be driven to a desired state despite not having complete knowledge of the other subsystems.