Koopman-based model predictive control for continuous crystallization process

Crystallization is a complex process with highly interrelated kinetic mechanisms. The population balance equation (PBE) framework is the most widely accepted modeling approach of crystallization processes. When designing a model predictive controller (MPC) for crystallization based on the commonly used moment based PBE solution, this can lead to a non-convex optimization problem. A novel approach to solve the problem of controlling nonlinear systems is based on the so-called Koopman operator. The Koopman operator is a linear operator that governs the evolution of scalar functions along the trajectories of a given nonlinear dynamical system. The main idea is to lift the nonlinear dynamics to a higher dimensional space where its evolution can be described with a linear system model. In this paper, we use the extended dynamic mode decomposition (EDMD) method to find the Koopman operator of the continuous crystallization process. Then a MPC controller based on Koopman model is developed to control the whole continuous crystallization process, so that the final crystal size distribution (CSD) can match the expected value. Both model identification and predictive controller design are validated using simulation.