Estudo comparativo entre o filtro de partículas e o filtro de kalman estendido para monitoramento on-line da síntese de galactooligossacarídeos

Abstract

Galactooligosaccharides (GOS) are nondigestible oligosaccharides composed of chains of 2 to 8 units of galactose and glucose. Their production starts with lactose, an abundant byproduct of the dairy industry, via an enzymatic reaction known as β-galactosidase-catalyzed lactose transgalactosylation, generating a complex mixture of di-, tri-, and tetrasaccharides. Key benefits of GOS include the stimulation of the intestinal microbiota, the blocking of pathogen adhesion in the digestive tract, and the enhancement of mineral absorption. In addition to their physiological effects, GOS are widely applied in food formulations due to their high water solubility, thermal stability, and resistance to pH variations. These characteristics make GOS highly attractive to the food industry and motivate the development of optimized processes for their production. Such processes, when operated at scale, require effective reactor control to minimize product losses from hydrolysis and determine a satisfactory stopping point for batch processes. This highlights the need for robust and precise monitoring methods capable of providing real-time process information. Direct online measurement techniques, such as spectrometric methods, can provide real-time measurements of some process variables. However, these techniques have limitations both in terms of the variables they can measure and the noise present in their measurements, which can restrict their usefulness for control purposes. By combining a fundamental model of the system with online measurements, it is possible to leverage more system information, thereby achieving improved monitoring and control performance. This combination is enabled through state estimators which, in general, first perform a prior estimate of the state based on the model and then receive a system measurement and apply a correction, providing a posterior estimate. The present study seeks to explore the capabilities of two types of state estimators - the Particle Filter (PF) and the Extended Kalman Filter (EKF) - for performing real-time monitoring of a GOS synthesis, described mathematically by a kinetic model and measured using a UVVis probe. Despite the greater complexity and computational cost of the PF, the results showed that, when starting from well-defined initial conditions with low uncertainty, the performance of both estimators was similar. However, when using an initial condition far from reality and with higher uncertainty, the PF showed superior performance compared to the EKF, converging more rapidly to the experimental data and achieving errors approximately half those obtained by the EKF for most of the estimated species.