Advertisement

Bioprocess and Biosystems Engineering

, Volume 35, Issue 9, pp 1615–1625 | Cite as

Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms

  • Hernán De Battista
  • Jesús Picó
  • Fabricio GarelliEmail author
  • José Luis Navarro
Original Paper

Abstract

This paper deals with the estimation of unknown signals in bioreactors using sliding observers. Particular attention is drawn to estimate the specific growth rate of microorganisms from measurement of biomass concentration. In a recent article, notions of high-order sliding modes have been used to derive a growth rate observer for batch processes. In this paper we generalize and refine these preliminary results. We develop a new observer with a different error structure to cope with other types of processes. Furthermore, we show that these observers are equivalent, under coordinate transformations and time scaling, to the classical super-twisting differentiator algorithm, thus inheriting all its distinctive features. The new observers' family achieves convergence to time-varying unknown signals in finite time, and presents the best attainable estimation error order in the presence of noise. In addition, the observers are robust to modeling and parameter uncertainties since they are based on minimal assumptions on bioprocess dynamics. In addition, they have interesting applications in fault detection and monitoring. The observers performance in batch, fed-batch and continuous bioreactors is assessed by experimental data obtained from the fermentation of Saccharomyces Cerevisiae on glucose.

Keywords

Bioreactors Bioprocess control Bioprocess observers Sliding modes 

Notes

Acknowledgments

This work was supported by the National University of La Plata (Project 2012-2015), the Agency for the Promotion of Science and Technology ANPCyT (PICT2007-00535) and the National Research Council CONICET (PIP112-200801-01052) of Argentina; the Technical University of Valencia (PAID-02-09), the CICYT (DPI2005-01180) and AECID (A/024186/09) of Spain; and by the project FEDER of the European Union.

References

  1. 1.
    Aborhey S, Williamson D (1978) State amd parameter estimation of microbial growth process. Automatica 14:493–498CrossRefGoogle Scholar
  2. 2.
    Bastin G, Dochain D (1986) On-line estimation of microbial specific growth rates. Automatica 22:705–709CrossRefGoogle Scholar
  3. 3.
    Bastin G, Dochain D (1990) On-line estimation and adaptive control of bioreactors. Elsevier, AmsterdamGoogle Scholar
  4. 4.
    Bejarano F, Fridman L (2009) Unbounded unknown inputs estimation based on high-order sliding mode differentiator. In: Proceedings of the 48th IEEE conference on decision and control, pp 8393–8398Google Scholar
  5. 5.
    Corless M, Tu J (1998) State and input estimation for a class of uncertain systems. Automatica 34(6):757–764Google Scholar
  6. 6.
    Dabros M, Schler M, Marison I (2010) Simple control of specific growth rate in biotechnological fed-batch processes based on enhanced online measurements of biomass. Bioprocess Biosyst Eng 33:1109–1118CrossRefGoogle Scholar
  7. 7.
    Davila A, Moreno J, Fridman L (2010) Variable gains super-twisting algorithm: a lyapunov based design. In: American control conference (ACC), 2010, pp 968–973Google Scholar
  8. 8.
    Dávila J, Fridman L, Levant A (2005) Second-order sliding-mode observer for mechanical systems. IEEE Transact Automatic Control 50(11):1785–1789CrossRefGoogle Scholar
  9. 9.
    De Battista H, Picó J, Garelli F, Vignoni A (2011) Specific growth rate estimation in (fed-)batch bioreactors using second-order sliding observers. J Process Control 21:1049–1055CrossRefGoogle Scholar
  10. 10.
    Dochain D (2001) Bioprocess control. Wiley, HobokenGoogle Scholar
  11. 11.
    Dochain D (2003) State and parameter estimation in chemical and biochemical processes: a tutorial. J Process Control 13(8):801–818CrossRefGoogle Scholar
  12. 12.
    Edwards C, Spurgeon S, Patton R (2000) Sliding mode observers for fault detection and isolation. Automatica 36(2):541–553CrossRefGoogle Scholar
  13. 13.
    Evangelista C, Puleston P, Valenciaga F, Fridman L (2012) Lyapunov designed super-twisting sliding mode control for wind energy conversion optimization. Indus Electron IEEE Transact. doi: 10.1109/TIE.2012.2188256
  14. 14.
    Farza M, Busawon K, Hammouri H (1998) Simple nonlinear observers for on-line estimation of kinetic rates in bioreactors. Automatica 34(3):301–318CrossRefGoogle Scholar
  15. 15.
    Fridman L, Davila J, Levant A (2008) High-order sliding modes observation. In: International workshop on variable structure systems, pp 203–208Google Scholar
  16. 16.
    Fridman L, Levant A (2002) Sliding mode control in engineering, higher-order sliding modes. Marcel Dekker, Inc., New York, pp 53–101Google Scholar
  17. 17.
    Fridman L, Shtessel Y, Edwards C, Yan X (2008) Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems. Int J Robust Nonlinear Control 18(3–4):399–412CrossRefGoogle Scholar
  18. 18.
    Gauthier J, Hammouri H, Othman S (1992) A simple observer for nonlinear systems: applications to bioreactors. IEEE Transact Automatic Control 37(6):875–880CrossRefGoogle Scholar
  19. 19.
    Gnoth S, Jenzsch M, Simutis R, Lubbert A (2008) Control of cultivation processes for recombinant protein production: a review. Bioprocess Biosyst Eng 31(1):21–39CrossRefGoogle Scholar
  20. 20.
    Hitzmann B, Broxtermann O, Cha Y, Sobieh O, Stärk E, Scheper T (2000) The control of glucose concentration during yeast fed-batch cultivation using a fast measurement complemented by an extended kalman filter. Bioprocess Eng 23(4):337–341CrossRefGoogle Scholar
  21. 21.
    Kiviharju K, Salonen K, Moilanen U, Eerikainen T (2008) Biomass measurement online: the performance of in situ measurements and software sensors. J Indus Microbiol Biotechnol 35(7):657–665CrossRefGoogle Scholar
  22. 22.
    Levant A (1998) Robust exact differentiation via sliding mode technique. Automatica 34(3):379–384CrossRefGoogle Scholar
  23. 23.
    Levant A (2003) Higher-order sliding modes, differentiation and output-feedback control. Int J Control 76(9/10):924–941CrossRefGoogle Scholar
  24. 24.
    Lubenova V, Rocha I, Ferreira E (2003) Estimation of multiple biomass growth rates and biomass concentration in a class of bioprocesses. Bioprocess Biosyst Eng 25:395–406CrossRefGoogle Scholar
  25. 25.
    Moreno J, Alvarez J, Rocha-Cozatl E, Diaz-Salgado J (2010) Super-twisting observer-based output feedback control of a class of continuous exothermic chemical reactors. In: Proceedings of the 9th IFAC international symposium on dynamics and control of process systems, pp 719–724. Leuven, BelgiumGoogle Scholar
  26. 26.
    Moreno J, Osorio M (2008) A Lyapunov approach to second-order sliding mode controllers and observers. In: Proceedings of the 47th IEEE conference on decision and control. Cancún, México, pp 2856–2861Google Scholar
  27. 27.
    Moreno J, Osorio M (2012) Strict Lyapunov functions for the super-twisting algorithm. IEEE Transact Automatic Control 57:1035–1040CrossRefGoogle Scholar
  28. 28.
    Navarro J, Picó J, Bruno J, Picó-Marco E, Vallés S (2001) On-line method and equipment for detecting, determining the evolution and quantifying a microbial biomass and other substances that absorb light along the spectrum during the development of biotechnological processes. Patent ES20010001757, EP20020751179Google Scholar
  29. 29.
    Neeleman Boxtel (2001) Estimation of specific growth rate from cell density measurements. Bioprocess Biosyst Eng 24(3):179–185CrossRefGoogle Scholar
  30. 30.
    November E, van Impe J (2002) The tuning of a model-based estimator for the specific growth rate of Candidautilis. Bioprocess Biosyst Eng 25:1–12CrossRefGoogle Scholar
  31. 31.
    Park Y, Stein J (1988) Closed-loop, state and input observer for systems with unknown inputs. Int J Control 48(3):1121–1136CrossRefGoogle Scholar
  32. 32.
    Perrier M, de Azevedo SF, Ferreira E, Dochain D (2000) Tuning of observer-based estimators: theory and application to the on-line estimation of kinetic parameters. Control Eng Pract 8:377–388CrossRefGoogle Scholar
  33. 33.
    Picó J, De Battista H, Garelli F (2009) Smooth sliding-mode observers for specific growth rate and substrate from biomass measurement. J Process Control 19(8):1314–1323. Special section on hybrid systems: modeling, simulation and optimizationGoogle Scholar
  34. 34.
    Schenk J, Balaszs K, Jungo C, Urfer J, Wegmann C, Zocchi A, Marison I, von Stockar U (2008) Influence of specific growth rate on specific productivity and glycosylation of a recombinant avidin produced by a Pichia pastoris Mut + strain. Biotecnol Bioeng 99(2):368–377CrossRefGoogle Scholar
  35. 35.
    Shtessel Y, Taleb M, Plestan F (2012) A novel adaptive-gain supertwisting sliding mode controller: Methodol Appl Automatica (in press)Google Scholar
  36. 36.
    Soons Z, van Straten G, van der Pol L, van Boxtel A (2008) On line automatic tuning and control for fed-batch cultivation. Bioprocess Biosyst Eng 31(5):453–467CrossRefGoogle Scholar
  37. 37.
    Utkin V, Poznyak A, Ordaz P (2011) Adaptive super-twist control with minimal chattering effect. In: Proceedings of 50th IEEE conference on decision and control and European control conference. Orlando, pp 7009–7014Google Scholar
  38. 38.
    Veloso A, Rocha I, Ferreira E (2009) Monitoring of fed-batch E. coli fermentations with software sensors. Bioprocess Biosyst Eng 32(3):381–388CrossRefGoogle Scholar
  39. 39.
    Venkateswarlu C (2004) Advances in monitoring and state estimation of bioreactors. J Sci Indus Res 63:491–498Google Scholar
  40. 40.
    Zamboni N, Fendt S, Rühl M, Sauer U (2009) 13c-based metabolic flux analysis. Nat Protocols 4:878–892CrossRefGoogle Scholar
  41. 41.
    Zorzetto LFM, Wilson JA (1996) Monitoring bioprocesses using hybrid models and an extended kalman filter. Comput Chem Eng 20(Suppl 1):S689–S694CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Hernán De Battista
    • 1
  • Jesús Picó
    • 2
  • Fabricio Garelli
    • 1
    Email author
  • José Luis Navarro
    • 2
  1. 1.LEICI, Facultad de IngenieríaUniversidad Nacional de La PlataLa PlataArgentina
  2. 2.Institut d’Automàtica i Informàtica IndustrialUniversitat Politècnica de ValènciaValenciaSpain

Personalised recommendations