Bioprocess control from a multivariate process trajectory

Abstract

A multivariate bioprocess control approach, capable of tracking a pre-set process trajectory correlated to the biomass or product concentration in the bioprocess is described. The trajectory was either a latent variable derived from multivariate statistical process monitoring (MSPC) based on partial least squares (PLS) modeling, or the absolute value of the process variable. In the control algorithm the substrate feed pump rate was calculated from on-line analyzer data. The only parameters needed were the substrate feed concentration and the substrate yield of the growth-limiting substrate. On-line near-infrared spectroscopy data were used to demonstrate the performance of the control algorithm on an Escherichia coli fed-batch cultivation for tryptophan production. The controller showed good ability to track a defined biomass trajectory during varying process dynamics. The robustness of the control was high, despite significant external disturbances on the cultivation and control parameters.

Appendix

Simulation model for growth on phosphate, Table1.

Table 1. Model parameters

The bioreactor volume is determined by

$$ {{{dV} \over {dt}} = F_{{phos}} } $$

(19)

with the dilution rate defined as

$$ {D = {{F_{{phos}} } \over V}} $$

(20)

Biomass develops as

$$ {{{dc_{x} } \over {dt}} = (\mu - D)c_{x} } $$

(21)

Substrate usage is described by

$$ \frac{{dc_{{phos}} }} {{dt}} = D\cdot {\left( {c_{{phos,0}} - c_{{phos}} } \right)} - \mu \cdot Y^{{phase}}_{{phos/x}} \cdot c_{x} $$

(22)

The yield coefficient ${Y^{{phase}}_{{phos/x}} }$ during the batch and fed-batch phase changes. Therefore, one yield coefficient during each of the phases was applied.

The specific growth rate follows Monod kinetics for the substrate concentration c _phos .

$$ {\mu = \mu _{{\max }} {{c_{{phos}} } \over {c_{{phos}} + k^{M}_{{phos}} }}} $$

(23)