Nonlinear observer of crystal‐size distribution during batch crystallization

Abstract

A high-gain observer was designed to estimate the crystal-size distribution (CSD) in batch crystallization processes. The observer is based on the discretization of population balance equations describing the evolution of the CSD using finite difference method. Due to process impurities and other batch-to-batch variations, the kinetic parameters involved in the dynamic model of the crystallization, relating primary and secondary nucleation in particular, are subject to significant variations. In order to avoid any estimation divergence, an on-line parameter identification algorithm was added to the observer.Assuming that measurements of the nuclei particles are available, the observer is shown to provide a discretized reconstruction of the entire CSD which can be used for control purposes or process supervision.

A stochastic formulation for the description of the crystal size distribution in antisolvent crystallization processes

“…A great deal of effort for understanding the main factors that affect the MCS and the CSD has been reported in the literature. [1][2][3][4][5][6] Traditionally, mathematical modeling of particulate systems (e.g., crystallization) is based-on Structured Population Balances (SPB) [7][8][9][10] taking into account the effect of formation, growth, and coagulation of the CSD. However, detailed structured population models demand a comprehensive knowledge of the thermodynamic properties of all the components involved in the system under consideration.…”

On the stability of a differential Riccati equation for continuous-discrete observers

“…Continuous-discrete systems are used in order to model processes having continuous state dynamics and a discrete measurement procedure, which reflects many practical situations. This approach is meaningful when the measurements sampling time is not constant, or when state estimates are needed between updates (Ahmed-Ali, Postoyan, & Lamnabhi-Lagarrigue, 2009;Astorga, Othman, Othman, Hammouri, & McKenna, 2002;Andrieu, Nadri, Serres, & Vivalda, 2013;Bakir, Othman, Fevotte, & Hammouri, 2006;Bristeau, Dorveaux, Vissière, & Petit, 2010;Dymkov, Gaishun, Rogers, Galkowski, & Owens, 2004;Jazwinski, 1970;Karafyllis & Kravaris, 2009;Nadri & Hammouri, 2003;Nicolao & Strada, 1998;Sebesta & Boizot, 2014;Sebesta, Boizot, Busvelle, & Sachau, 2010;Song & Shin, 2010).…”

Two state estimators for the barium sulfate precipitation in a semi-batch reactor

“…Aguilar-López and Maya-Yescas (2005) developed a sliding mode observer for a polymerisation process. Bakir et al (2006) suggested a high gain observer for a batch crystalliser, which is applicable, when the nuclei are measurable, because then the model equations are given directly in observability normal form. For this work, two modern state estimation techniques have been chosen, which to our knowledge have not yet been applied to population balance models before.…”