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In this paper, we are interested in the estimation of Particle SizeDistributions (PSDs) during a batch crystallization process in which particlesof two different shapes coexist and evolve simultaneously. The PSDs areestimated thanks to a measurement of an apparent Chord Length Distribution(CLD), a measure that we model for crystals of spheroidal shape. Our mainresult is to prove the approximate observability of the infinite-dimensionalsystem in any positive time. Under this observability condition, we are able toapply a Back and Forth Nudging (BFN) algorithm to reconstruct the PSD.

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