An algorithmic approach to constructing the on‐line estimation system for the specific growth rate

Abstract

The objective of this article is to propose an algorithm for the on-line estimation of the specific growth rate in a batch or a fed-batch fermentation process. The algorithm shows the practical procedure for the estimation method utilizing the macroscopic balance and the extended Kalman filter. A number of studies of the on line estimation have been presented. However, there are few studies discussing about the selection of the observed variables and for the tuning of some parameters of the extended Kalman filter, such as covariance matrix and initial values of the state.The beginning of this article is devoted to explain the selection of the observed variable. This information is very important in terms of the practical know-how for using technique. It is discovered that the condition number is a practically useful and valid criterion for number is a practically useful and valid criterion for choosing the variable to be observed.Next, when the extended Kalman filter in applied to the online estimation of the specific growth rate, which is directly unmeasurable, criteria for judging the validity of the estimated value from the observed data are proposed. Based on the proposed criteria, the system equation of the specific growth rate is selected and initial value of the state variable and covariance matrix of the system noises are adjusted. From many experiments, it is certified that the specific growth rate in the batch or fed -batch fermentation can be estimated accurately by means of the algorithm proposed here. In these experiments, that is, when the cell concentration is measured directly, the extended Kalman filter using the covariance matrix with a constant element can estimate more accurately values of the specific growth rate than the adaptive extended Kalman filter does.

State observation of a nonlinear system: Application to (bio)chemical processes

“…In order to overcome these difficulties, we propose nonlinear observers for the on-line estimation of these variables. The approach to design estimators for the Ž reaction rates is not new and has often been exploited Wang and Stephanopoulos, 1984;Shimizu et al, 1989;Bastin and . Dochain, 1990 : it consists of augmenting the state vector to include, in addition to the state variables, those of the process parameters that it is not desirable for models to express, that is, the reaction rates.…”

Model parameter tracking in microbial growth processes

“…Several researchers have suggested model-independent estimation of specific growth rate as a time-varying parameter. The extended Kalman filter (EKF) is widely applied to this effect (Stephanopoulos and San, 1984;Shimizu et al, 1989). The EKF is derived from the application of a Kalman filter to the linearized model of a nonlinear system.…”

Time-varying system identification using modulating functions and spline models with application to bio-processes

“…Motivated by the need to find estimation schemes that are independent of kinetic rate models, several researchers proposed non linear adaptive schemes for estimating the kinetic rates themselves as time-varying parameters. The extended Kalman filter (EKF) is widely applied to this effect (Stephanopoulos & San, 1984;Shimizu, Takamatsu, Shioya & Suga, 1989). The EKF is derived from the application of Kalman filter to the linearized model of a nonlinear system.…”