New dynamical observer for a batch crystallization process based on solute concentration

Brivadis, Lucas; Andrieu, Vincent; Chabanon, Élodie; Gagnière, Émilie; Lebaz, Noureddine; Serres, Ulysse

doi:10.1016/j.jprocont.2019.12.012

“…Here G is supposed to be known, contrary to u and n. In practice, G can be estimated via a simple model based on the solute concentration and the solubility thanks to solute concentration and temperature sensors (see, e.g., [10,30], or [22,23] for more detailed models). We reformulate (6.11) in order to match our theoretical results.…”

Section: Modeling the Batch Crystallization Processmentioning

confidence: 99%

Luenberger Observers for Infinite-Dimensional Systems, Back and Forth Nudging, and Application to a Crystallization Process

Brivadis¹,

Andrieu²,

Serres³

et al. 2021

SIAM J. Control Optim.

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This paper deals with the observer design problem for time-varying linear infinitedimensional systems. We address both the problem of online estimation of the state of the system from the output via an asymptotic observer, and the problem of offline estimation of the initial state via a Back and Forth Nudging (BFN) algorithm. In both contexts, we show under a weak detectability assumption that a Luenberger-like observer may reconstruct the so-called observable subspace of the system. However, since no exact observability hypothesis is required, only a weak convergence of the observer holds in general. Additional conditions on the system are required to show the strong convergence. We provide an application of our results to a batch crystallization process modeled by a one-dimensional transport equation with periodic boundary conditions, in which we try to estimate the Crystal Size Distribution from the Chord Length Distribution.

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“…Here G is supposed to be known, contrary to u and n. In practice, G can be estimated via a simple model based on the solute concentration and the solubility thanks to solute concentration and temperature sensors (see, e.g., [9,29], or [21,22] for more detailed models). We reformulate (6.10) in order to match our theoretical results.…”

Section: Modeling the Batch Crystallization Processmentioning

confidence: 99%

Luenberger observers for infinite-dimensional systems, Back and Forth Nudging and application to a crystallization process

Brivadis,

Andrieu,

Serres

et al. 2020

Preprint

Self Cite

0

View full text Add to dashboard Cite

This paper deals with the observer design problem for time-varying linear infinitedimensional systems. We address both the problem of online estimation of the state of the system from the output via an asymptotic observer, and the problem of offline estimation of the initial state via a Back and Forth Nudging (BFN) algorithm. In both contexts, we show under a weak detectability assumption that a Luenberger-like observer may reconstruct the so-called observable subspace of the system. However, since no exact observability hypothesis is required, only a weak convergence of the observer holds in general. Additional conditions on the system are required to show the strong convergence. We provide an application of our results to a batch crystallization process modeled by a one-dimensional transport equation with periodic boundary conditions, in which we try to estimate the Crystal Size Distribution from the Chord Length Distribution.

show abstract

“…The number and quality of sensors being often limited in practice due to cost and physical constraints, such estimation algorithms play a decisive role in a lot of applications. See, as a few examples, the problems of estimating the state of the charge of a battery [59], the position of sensorless permanent magnet synchronous machines [161,49] or the size of the crystals in a crystallization process [68].…”

Section: Introductionmentioning

confidence: 99%

Observer design for continuous-time dynamical systems

Bernard

¹

,

Andrieu

²

,

Astolfi

³

2022

Annual Reviews in Control

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We review the main design techniques of state observer design for continuous-time dynamical systems, namely algorithms which reconstruct online the full information of a dynamical process on the basis of partially measured data. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show how each class of observer relies on transforming the system dynamics in a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Finally, some implementation aspects and open problems are briefly discussed.

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New dynamical observer for a batch crystallization process based on solute concentration

Cited by 9 publications

References 29 publications

Luenberger Observers for Infinite-Dimensional Systems, Back and Forth Nudging, and Application to a Crystallization Process

Luenberger Observers for Infinite-Dimensional Systems, Back and Forth Nudging, and Application to a Crystallization Process

Luenberger observers for infinite-dimensional systems, Back and Forth Nudging and application to a crystallization process

Observer design for continuous-time dynamical systems

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