Towards a framework for the development of control-oriented multiscale models of dynamical systems: semibatch emulsion polymerization case study

Abstract

ABSTRACT: This work develops a framework for the construction of a control-oriented model from a multiscale perspective, using a semibatch emulsion polymerization process as a case study. First, a so-called full multiscale model (considering the macro-, meso-, and micro-scopic scales) was developed which is composed of a set of Partial/Ordinary Differential Equations and a kinetic Monte Carlo simulation (PDE/ODE - kMC). Then, to obtain a reduced-order representation of the multiscale model, Variance Algebra concepts are used as a tool for representing, at the mesoscopic scale, a disperse-phase system from which only statistical information is available. After that, a dataset considering several process operational conditions is built to capture the main dynamics at the microscopic scale. This dataset is used to derive a closed-form model of the microscopic state variables by adopting a statistical modeling approach. The final obtained control-oriented model is composed of a set of ODEs comprising the macroscopic and the mesoscopic scales that can be solved by using standard ODEs integration schemes, whereas the microscopic scale variables are conveniently defined as some of the system outputs, represented by a set of algebraic equations. In order to consistently solve the full multiscale model, a numerical scheme based on the Finite Element Method is developed capturing the nonlinear evolution of the Particle Size Distribution (PSD). The validity of the obtained reduced-order model is verified through several simulations with respect to the system inputs. Finally, the multiscale control-oriented representation is employed to perform a batch output-controllability analysis based on a set-theoretic approach. The proposed framework might be adopted as a tool for the derivation of dynamical multiscale models keeping a good balance between their tractability and predictive capability, which can constitute an advantage when implementing real-time optimization and process control.