Approximate observability and back and forth observer of a PDE model of crystallisation process

In this paper, we are interested in the estimation of Particle Size Distributions (PSDs) during a batch crystallization process in which particles of two different shapes coexist and evolve simultaneously. The PSDs are estimated thanks to a measurement of an apparent Chord Length Distribution (CLD),...

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Bibliographic Details
Published in:arXiv.org 2021-03
Main Authors: Lucas Brivadis, Sacchelli, Ludovic
Format: Article
Language:English
Subjects:
Algorithms
Crystallization
Online Access:Get full text
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Summary:In this paper, we are interested in the estimation of Particle Size Distributions (PSDs) during a batch crystallization process in which particles of two different shapes coexist and evolve simultaneously. The PSDs are estimated thanks to a measurement of an apparent Chord Length Distribution (CLD), a measure that we model for crystals of spheroidal shape. Our main result is to prove the approximate observability of the infinite-dimensional system in any positive time. Under this observability condition, we are able to apply a Back and Forth Nudging (BFN) algorithm to reconstruct the PSD.
ISSN:2331-8422