Continuous ‐ discrete interval observers for monitoring microalgae cultures

Algorithms estimating unmeasured component concentrations play a key role in bioprocess applications where only a few on‐line measurements are usually available. In this article, interval observers are designed to provide guaranteed intervals for the key components involved in cultures of microalgae. In contrast with most of the published studies focusing on continuous‐time measurements, this study considers discrete‐time measurements with possibly long and irregular sampling and defines predictors based on model equations and state transformations to ensure the enclosure of the state variables between two measurement times. The methods are validated with experimental data where the remaining inorganic nitrogen and the microalgal internal quota are estimated. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009

[1]  O. Bernard,et al.  INTERVAL OBSERVERS FOR NON MONOTONE SYSTEMS. APPLICATION TO BIOPROCESS MODELS , 2005 .

[2]  O. Pulz,et al.  Photobioreactors: production systems for phototrophic microorganisms , 2001, Applied Microbiology and Biotechnology.

[3]  Manuel Berenguel,et al.  Model predictive control of pH in tubular photobioreactors , 2004 .

[4]  A. Sciandra,et al.  An automatic device for in vivo absorption spectra acquisition and chlorophyll estimation in phytoplankton cultures , 2002, Journal of Applied Phycology.

[5]  K. Davidson,et al.  Carbon-nitrogen relations at whole-cell and free-amino-acid levels during batch growth of Isochrysis galbana (Prymnesiophyceae) under conditions of alternating light and dark , 1994 .

[6]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[7]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[8]  Miguel Olaizola,et al.  Commercial development of microalgal biotechnology: from the test tube to the marketplace. , 2003, Biomolecular engineering.

[9]  M. R. Droop,et al.  Vitamin B12 and Marine Ecology. IV. The Kinetics of Uptake, Growth and Inhibition in Monochrysis Lutheri , 1968, Journal of the Marine Biological Association of the United Kingdom.

[10]  Eric Walter,et al.  Guaranteed Nonlinear State Estimator for Cooperative Systems , 2004, Numerical Algorithms.

[11]  John R. Benemann,et al.  CO2 mitigation with microalgae systems , 1997 .

[12]  F B Metting,et al.  Biodiversity and application of microalgae , 1996, Journal of Industrial Microbiology.

[13]  Y. Candau,et al.  Bounded error moving horizon state estimator for non-linear continuous-time systems: application to a bioprocess system , 2005 .

[14]  Chris Cosner,et al.  Book Review: Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems , 1996 .

[15]  Ph Bogaerts,et al.  Software sensors for bioprocesses. , 2003, ISA transactions.

[16]  Olivier Bernard,et al.  Near optimal interval observers bundle for uncertain bioreactors , 2007, 2007 European Control Conference (ECC).

[17]  L. Mailleret,et al.  Nonlinear control for algae growth models in the chemostat , 2003, 2003 European Control Conference (ECC).

[18]  Jean-Luc Gouzé,et al.  Closed loop observers bundle for uncertain biotechnological models , 2004 .

[19]  M. Huntley,et al.  CO2 Mitigation and Renewable Oil from Photosynthetic Microbes: A New Appraisal , 2007 .

[20]  Jean-Luc Gouzé,et al.  Estimation of uncertain models of activated sludge processes with interval observers , 2001 .

[21]  Olivier Bernard,et al.  Nonlinear observers for a class of biological systems: application to validation of a phytoplanktonic growth model , 1998, IEEE Trans. Autom. Control..

[22]  Olivier Bernard,et al.  A non-linear software sensor to monitor the internal nitrogen quota of phytoplanktonic cells , 2001 .

[23]  Y. Chisti.  Biodiesel from microalgae. , 2007, Biotechnology advances.

[24]  O. Bernard,et al.  The effects of a controlled fluctuating nutrient environment on continuous cultures of phytoplankton monitored by computers , 1996 .

[25]  A. Carvalho,et al.  Microalgal Reactors: A Review of Enclosed System Designs and Performances , 2006, Biotechnology progress.

[26]  J. Monod,et al.  Recherches sur la croissance des cultures bactériennes , 1942 .

[27]  J. Gauthier,et al.  Observability and observers for non-linear systems , 1986, 1986 25th IEEE Conference on Decision and Control.

[28]  David E. Burmaster,et al.  The unsteady continuous culture of phosphate-limited Monochrysis lutheri droop: Experimental and theoretical analysis , 1979 .