Towards a controllability analysis of multiscale systems: Application of the set-theoretic approach to a semi-batch emulsion polymerization process

摘要

This work presents a framework to evaluating the controllability of multiscale systems based on a set-theoretic approach. Calculation of the Controllable Trajectories Set is the core of the set-theoretic approach. From a multi-scale perspective, such calculation is a computationally- intractable problem. Therefore, to overcome the intrinsic curse of dimensionality of the problem, Variance Algebra concepts and a statistical modeling approach are combined to obtain a closed-form allowing to perform an output-controllability analysis for a multiscale system. A semi-batch emulsion polymerization process is adopted as a case study. Results have shown that both, the final Particle Size Distribution (mesoscopic variable) and the secondary particle nucleation rate (microscopic variable) are output-controllable. Evaluating the controllability of lower-scale variables (i.e. below macroscopic) could mitigate the dependency of the current control strategies of on-line measurements at the lower scales as well as help to better understand the process capabilities of achieving the desired product quality specifications.