Automatic Control and Computer Sciences

, Volume 52, Issue 1, pp 13–24 | Cite as

A New Approach for Nonlinear Multivariable Fed-Batch Bioprocess Trajectory Tracking Control

  • M. Cecilia Fernández
  • Santiago Rómoli
  • M. Nadia Pantano
  • Oscar A. Ortiz
  • Daniel Patiño
  • Gustavo J. E. Scaglia


This paper proposes a new control law based on linear algebra. This technique allows nonlinear path tracking in multivariable and complex systems. This new methodology consists in finding the control action to make the system follow predefined concentration profiles solving a system of linear equations. The controller parameters are selected with a Monte Carlo algorithm so as to minimize a previously defined cost index. The control scheme is applied to a fed-batch penicillin production process. Different tests are shown to prove the controller effectiveness, such as adding parametric uncertainty, perturbations in the control action and in the initial conditions. Moreover, a comparison with other controllers from the literature is made, showing the better performance of the present approach.


nonlinear control fed-batch fermentation penicillin production profiles tracking control 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Petre, E. and Selisteanu, D., A multivariable robust-adaptive control strategy for a recycled wastewater treatment bioprocess, Chem. Eng. Sci., 2013, vol. 90, pp. 40–50.CrossRefGoogle Scholar
  2. 2.
    Chung, H., Yang, J.E., Ha, J.Y., Chae, T.U., Shin, J.H., Gustavsson, M., et al., Bio-based production of monomers and polymers by metabolically engineered microorganisms, Curr. Opin. Biotechnol., 2015, vol. 36, pp. 73–84.CrossRefGoogle Scholar
  3. 3.
    Mohammadi, M., Najafpour, G.D., Younesi, H., Lahijani, P., Uzir, M.H., and Mohamed, A.R., Bioconversion of synthesis gas to second generation biofuels: A review, Renewable Sustainable Energy Rev., 2011, vol. 15, pp. 4255–4273.CrossRefGoogle Scholar
  4. 4.
    Ashoori, A., Moshiri, B., Khaki-Sedigh, A., and Bakhtiari, M.R., Optimal control of a nonlinear fed-batch fermentation process using model predictive approach, J. Process Control, 2009, vol. 19, pp. 1162–1173.CrossRefzbMATHGoogle Scholar
  5. 5.
    Liang, J. and Chen, Y., Optimization of a fed-batch fermentation process control competition problem using the NEOS server, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2003, vol. 217, pp. 427–432.Google Scholar
  6. 6.
    Wang, L., Ridgway, D., Gu, T., and Moo-Young, M., Bioprocessing strategies to improve heterologous protein production in filamentous fungal fermentations, Biotechnol. Adv., 2010, vol. 23, pp. 115–129.CrossRefGoogle Scholar
  7. 7.
    Hecklau, C., Pering, S., Seibel, R., Schnellbaecher, A., Wehsling, M., Eichhorn, T., et al., S-sulfocysteine simplifies fed-batch processes and increases the CHO specific productivity via anti-oxidant activity, J. Biotechnol., 2016, vol. 218, pp. 53–63.CrossRefGoogle Scholar
  8. 8.
    Jin, H., Chen, X., Yang, J., Wu, L., and Wang, L., Hybrid intelligent control of substrate feeding for industrial fed-batch chlortetracycline fermentation process, ISA Trans., 2014, vol. 53, pp. 1822–1837.CrossRefGoogle Scholar
  9. 9.
    De Battista, H., Picó, J., and Picó-Marco, E., Nonlinear PI control of fed-batch processes for growth rate regulation, J. Process Control, 2012, vol. 22, pp. 789–797.CrossRefzbMATHGoogle Scholar
  10. 10.
    Arpornwichanop, A. and Shomchoam, N., Control of fed-batch bioreactors by a hybrid on-line optimal control strategy and neural network estimator, Neurocomputing, 2009, vol. 72, pp. 2297–2302.CrossRefGoogle Scholar
  11. 11.
    Chen, J. and Lin, Y.-H., Multibatch model predictive control for repetitive batch operation with input-output linearization, Ind. Eng. Chem. Res., 2012, vol. 51, pp. 9598–9608.CrossRefGoogle Scholar
  12. 12.
    Honda, H. and Kobayashi, T., Fuzzy control of bioprocess, J. Biosci. Bioeng., 2000, vol. 89, pp. 401–408.CrossRefGoogle Scholar
  13. 13.
    Pantano, M.N., Serrano, M.E., Fernandez, M.C., Rossomando, F.G., Ortiz, O.A., and Scaglia, G.J.E., Multivariable control for tracking optimal profiles in a nonlinear fed-batch bioprocess integrated with state estimation, Ind. Eng. Chem. Res., 2017, vol. 56, no. 2, pp. 6043–6056.CrossRefGoogle Scholar
  14. 14.
    Rómoli, S., Serrano, M.E., Ortiz, O.A., Vega, J.R., and Scaglia, G.J.E., Tracking control of concentration profiles in a fed-batch bioreactor using a linear algebra methodology, ISA Trans., 2015, vol. 57, pp. 162–171.CrossRefGoogle Scholar
  15. 15.
    Imtiaz, U., Jamuar, S.S., Sahu, J., and Ganesan, P., Bioreactor profile control by a nonlinear auto regressive moving average neuro and two degree of freedom PID controllers, J. Process Control, 2014, vol. 24, pp. 1761–1777.CrossRefGoogle Scholar
  16. 16.
    Aiba, S., Review of process control and optimization in fermentation, Biotechnology and Bioengineering, No. 9 Computer Applications in Fermentation Technology; 2nd International Conference, Philadelphia, PA, August 28–30, 1978, New York, 1979, pp. 269–281.Google Scholar
  17. 17.
    Cuthrell, J.E. and Biegler, L.T., Simultaneous optimization and solution methods for batch reactor control profiles, Comput. Chem. Eng., 1989, vol. 13, pp. 49–62.CrossRefGoogle Scholar
  18. 18.
    Wang, L. and Feng, Q., Application of fuzzy control simulation human intelligence controller in ferment process of supplying sugar, Appl. Mech. Mater., 2014, vols. 668–669, pp. 441–444.Google Scholar
  19. 19.
    Klebanov, N. and Georgakis, C., Dynamic response surface models: A data-driven approach for the analysis of time-varying process outputs, Ind. Eng. Chem. Res., 2016, vol. 55, pp. 4022–4034.CrossRefGoogle Scholar
  20. 20.
    Georgakis, C., Design of dynamic experiments: A data-driven methodology for the optimization of time-varying processes, Ind. Eng. Chem. Res., 2013, vol. 52, pp. 12369–12382.CrossRefGoogle Scholar
  21. 21.
    Ochoa, S., A new approach for finding smooth optimal feeding profiles in fed-batch fermentations, Biochem. Eng. J., 2016, vol. 105, pp. 177–188.CrossRefGoogle Scholar
  22. 22.
    Martinez, E.C., Cristaldi, M.D., and Grau, R.J., Dynamic optimization of bioreactors using probabilistic tendency models and Bayesian active learning, Comput. Chem. Eng., 2013, vol. 49, pp. 37–49.CrossRefGoogle Scholar
  23. 23.
    Riaskos, C.A. and Pinto, J.M., Optimal control of bioreactors: A simultaneous approach for complex systems, Chem. Eng. J., 2004, vol. 99, pp. 23–34.CrossRefGoogle Scholar
  24. 24.
    Balsa-Canto, E., Banga, J.R., Alonso, A.A., and Vassiliadis, V.S., Efficient optimal control of bioprocesses using second-order information, Ind. Eng. Chem. Res., 2000, vol. 39, pp. 4287–4295.CrossRefGoogle Scholar
  25. 25.
    Luus, R., On the application of iterative dynamic programming to singular optimal control problems, IEEE Trans. Autom. Control, 1992, p. 1802.Google Scholar
  26. 26.
    Zhou, K., Doyle, J.C., and Glover, K., Robust and Optimal Control, Upper Saddle River, NJ: Prentice-Hall, Inc., 1996.zbMATHGoogle Scholar
  27. 27.
    Tokat, S., Sliding mode controlled bioreactor using a time-varying sliding surface, Trans. Inst. Measur. Control, 2009, vol. 31, no.5.Google Scholar
  28. 28.
    Strang, G., Linear Algebra and Its Applications, 2006, 4th ed.zbMATHGoogle Scholar
  29. 29.
    Scaglia, G., Rosales, A., Quintero, L., Mut, V., and Agarwal, R., A linear-interpolation-based controller design for trajectory tracking of mobile robots, Control Eng. Practice, 2010, vol. 18, pp. 318–329.CrossRefGoogle Scholar
  30. 30.
    Scaglia, G., Quintero, O., Mut, V., and di Sciascio, F., Numerical methods based controller design for mobile robots, IFAC World Congress, 2008.Google Scholar
  31. 31.
    Scaglia, G., Montoya, L.Q., Mut, V., and di Sciascio, F., Numerical methods based controller design for mobile robots, Robotica, 2009, vol. 27, pp. 269–279.CrossRefGoogle Scholar
  32. 32.
    Wang, C.-J. and Kao, M.-Y., Optimal search for parameters in Monte Carlo simulation for derivative pricing, Proceedings of the 2014 IEEE Conference on Computational Intelligence for Financial Engineering and Economics (CIFEr), 2014, pp. 384–390.CrossRefGoogle Scholar
  33. 33.
    Morzfeld, M., Implicit sampling for path integral control, Monte Carlo localization, and SLAM, J. Dyn. Syst., Measur. Control, 2015, vol. 137, p. 051016.CrossRefGoogle Scholar
  34. 34.
    Heyvaert, M. and Onghena, P., Randomization tests for single-case experiments: State of the art, state of the science, and state of the application, J. Contextual Behav. Sci., 2014, vol. 3, pp. 51–64.CrossRefGoogle Scholar
  35. 35.
    Tempo, R. and Ishii, H., Monte Carlo and Las Vegas randomized algorithms for systems and control: An introduction, Eur. J. Control, 2007, vol. 13, pp. 189–203.CrossRefzbMATHGoogle Scholar
  36. 36.
    Calafiore, G.C., Distributed randomized algorithms for probabilistic performance analysis, Syst. Control Lett., 2009, vol. 58, pp. 202–212.MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Dimov, I., Maire, S., and Sellier, J.M., A new Walk on Equations Monte Carlo method for solving systems of linear algebraic equations, Appl. Math. Modell., 2015, vol. 39, no. 15, pp. 4494–4510.MathSciNetCrossRefGoogle Scholar
  38. 38.
    Mohammadi, Y., Pakdel, A.S., Saeb, M.R., and Boodhoo, K., Monte Carlo simulation of free radical polymerization of styrene in a spinning disc reactor, Chem. Eng. J., 2014, vol. 247, pp. 231–240.CrossRefGoogle Scholar
  39. 39.
    de Oliveira, L.P., Verstraete, J.J., and Kolb, M., A Monte Carlo modeling methodology for the simulation of hydrotreating processes, Chem. Eng. J., 2012, vol. 207, pp. 94–102.CrossRefGoogle Scholar
  40. 40.
    Cheein, F.A. and Scaglia, G., Trajectory tracking controller design for unmanned vehicles: A new methodology, J. Field Rob., 2014, vol. 31, pp. 861–887.CrossRefGoogle Scholar
  41. 41.
    Wechselberger, P., Seifert, A., and Herwig, C., PAT method to gather bioprocess parameters in real-time using simple input variables and first principle relationships, Chem. Eng. Sci., 2010, vol. 65, pp. 5734–5746.CrossRefGoogle Scholar
  42. 42.
    George, J., On adaptive loop transfer recovery using Kalman filter-based disturbance accommodating control, IET Control Theory Appl., 2014, vol. 8, no. 4, pp. 267–276.MathSciNetCrossRefGoogle Scholar
  43. 43.
    Müller, M.M. and Hausmann, R., Regulatory and metabolic network of rhamnolipid biosynthesis: Traditional and advanced engineering towards biotechnological production, Appl. Microbiol. Biotechnol., 2011, vol. 91, pp. 251–264.CrossRefGoogle Scholar
  44. 44.
    Åström, K.J. and Hägglund, T., Control PID Avanzado, Madrid: Pearson, 2009.Google Scholar
  45. 45.
    Alford, J.S., Bioprocess control: Advances and challenges, Comput. Chem. Eng., 2006, vol. 30, pp. 1464–1475.CrossRefGoogle Scholar
  46. 46.
    Rivadeneira, P.S. and Adam, E.J., Suboptimal control strategies for finite-time nonlinear processes with input constraints, J. Nonlinear Dyn., 2013, vol. 2013.Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  • M. Cecilia Fernández
    • 1
  • Santiago Rómoli
    • 1
  • M. Nadia Pantano
    • 1
  • Oscar A. Ortiz
    • 1
  • Daniel Patiño
    • 2
  • Gustavo J. E. Scaglia
    • 1
  1. 1.Instituto de Ingeniería QuímicaUniversidad Nacional de San Juan (UNSJ), CONICETSan JuanArgentina
  2. 2.Instituto de AutomáticaUniversidad Nacional de San Juan (UNSJ), CONICETSan JuanArgentina

Personalised recommendations