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

Publication date: 22 March 2021

Abstract: 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.

Has companion code repository: https://github.com/sacchelli/BFNCrist

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