The Extended Kalman Filter for Nonlinear State Estimation in a U-loop Bioreactor

In this paper, we consider nonlinear state estimation in the U-loop reactor for single-cell protein (SCP) production. The model of the U-loop reactor is a mixture of stochastic partial differential equations and stochastic differential equations which are stiff. By a typical finite-volume spatial discretization, the resulting system of stochastic differential equations for numerical simulation and state estimation has 83 states. We investigate and discuss the continuous-discrete EKF for state estimation in this high-dimensional and stiff continuous-discrete-time system.

[1]  A. M. Al Taweel,et al.  Effect of Mixing on Microorganism Growth in Loop Bioreactors , 2012 .

[2]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[3]  W. Marsden.  I and J , 2012 .

[4]  A. Fraser.  Hidden Markov Models and Dynamical Systems , 2011 .

[5]  Krist V. Gernaey,et al.  Modelling and simulation of a U-loop Reactor for Single Cell Protein Production , 2016 .

[6]  James B. Rawlings,et al.  Particle filtering and moving horizon estimation , 2006, Comput. Chem. Eng..

[7]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[8]  Sten Bay Jørgensen,et al.  Modeling and Simulation of Single Cell Protein Production , 2010 .

[9]  Niels Kjølstad Poulsen,et al.  New developments in state estimation for nonlinear systems , 2000, Autom..

[10]  Bjarne A. Foss,et al.  Noise modeling concepts in nonlinear state estimation , 2009 .

[11]  Tianhai Tian,et al.  The composite Euler method for stiff stochastic differential equations , 2001 .

[12]  D. Bernstein,et al.  What is the ensemble Kalman filter and how well does it work? , 2006, 2006 American Control Conference.

[13]  John Villadsen,et al.  Mixing and mass transfer in a pilot scale U‐loop bioreactor , 2017, Biotechnology and bioengineering.

[14]  Sten Bay Jørgensen,et al.  Single-Cell Protein Production in a U-Loop Reactor , 2010 .

[15]  John Bagterp Jørgensen,et al.  Real-time economic optimization for a fermentation process using Model Predictive Control , 2014, 2014 European Control Conference (ECC).

[16]  Sten Bay Jørgensen,et al.  Systematic Model Analysis for Single Cell Protein (SCP) Production in a U-Loop Reactor , 2010 .

[17]  Tor Steinar Schei,et al.  ON-LINE ESTIMATION FOR PROCESS CONTROL AND OPTIMIZATION APPLICATIONS , 2008 .

[18]  Denis Dochain,et al.  State and parameter estimation in chemical and biochemical processes: a tutorial , 2003 .

[19]  Ali H. Sayed,et al.  Linear Estimation (Information and System Sciences Series) , 2000 .

[20]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[21]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[22]  T. Schei.  A finite-difference method for linearization in nonlinear estimation algorithms , 1998 .