Neural Network Model Predictive Control of a Wastewater Treatment Bioprocess

  • Dorin Şendrescu
  • Emil Petre
  • Dan Popescu
  • Monica Roman
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 10)


This paper deals with the design of a nonlinear model predictive control (NMPC) scheme for the regulation of the acetate concentration in a biomethanation process – wastewater biodegradation with production of methane gas that takes place inside a Continuous Stirred Tank Bioreactor. The NMPC control structure is based on a radial basis function neural network used as on-line approximator to learn the nonlinear characteristics of process. Minimization of the cost function is realised using the Levenberg–Marquardt numerical optimisation method. Some simulation results are given to illustrate the efficiency of the proposed control strategy.


Nonlinear systems Neural networks Model predictive control Wastewater treatment bioprocesses 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bastin, G., Dochain, D.: On-line Estimation and Adaptive Control of Bioreactors. Elsevier, Amsterdam (1990)Google Scholar
  2. 2.
    Bastin, G.: Nonlinear and adaptive control in biotechnology: a tutorial. In: Proc. ECC 1991 Conf., Grenoble, pp. 2001–2012 (1991)Google Scholar
  3. 3.
    Selişteanu, D., Petre, E.: Vibrational control of a class of bioprocesses. Contr. Eng. and App. Inf. 3(1), 39–50 (2001)Google Scholar
  4. 4.
    Camacho, E.F., Bordons, C.: Model Predictive Control, 2nd edn. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  5. 5.
    Hayakawa, T., Haddad, W.M., Hovakimyan, N.: Neural network adaptive control for a class of nonlinear uncertain dynamical systems with asymptotic stability guarantees. IEEE Trans. on Neural Networks 19, 80–89 (2008)CrossRefGoogle Scholar
  6. 6.
    Petre, E., Selişteanu, D., Şendrescu, D.: Neural Networks Based Adaptive Control for a Class of Time Varying Nonlinear Processes. In: Int. Conf. on Control, Automation and Systems ICCAS 2008, COEX, Seoul, Korea, October 14-17, pp. 1355–1360 (2008)Google Scholar
  7. 7.
    Funahashi, K.: On the approximate realization of continuous mappings by neural networks. Neural Networks 2, 183–192 (1989)CrossRefGoogle Scholar
  8. 8.
    Yu, W., Li, X.: Some new results on system identification with dynamic neural networks. IEEE Trans. Neural Networks 12(2), 412–417 (2001)CrossRefGoogle Scholar
  9. 9.
    Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, Berlin (1995)zbMATHGoogle Scholar
  10. 10.
    Petre, E.: Nonlinear Control Systems – Applications in Biotechnology, 2nd edn. Universitaria, Craiova (2008) (in Romanian)Google Scholar
  11. 11.
    Dochain, D., Vanrolleghem, P.: Dynamical Modelling and Estimation in Wastewater Treatment Processes. IWA Publishing (2001)Google Scholar
  12. 12.
    Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.: Constrained model predictive control: stability and optimality. Automatica 36, 789–814 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Spooner, J.T., Passino, K.M.: Decentralized adaptive control of nonlinear systems using radial basis neural networks. IEEE Trans. on Autom. Control 44(11), 2050–2057 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Eaton, J.W., Rawlings, J.R.: Feedback control of nonlinear processes using online optimization techniques. Computers and Chemical Engineering 14, 469–479 (1990)CrossRefGoogle Scholar
  15. 15.
    Wang, Y., Boyd, S.: Fast model predictive control using online optimization. In: Proc. of the 17th World Congress of International Federation of Automatic Control, WC-IFAC 2008 (2008)Google Scholar
  16. 16.
    Kouvaritakis, B., Cannon, M.: Nonlinear Predictive Control: Theory and Practice. IEE (2001)Google Scholar
  17. 17.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Heidelberg (1999)zbMATHCrossRefGoogle Scholar
  18. 18.
    Petre, E., Selişteanu, D., Şendrescu, D.: Adaptive control strategies for a class of anaerobic depollution bioprocesses. In: Proc. of Int. Conf. on Automation, Quality and Testing, Robotics, Cluj-Napoca, Romania, Tome II, May 22-25, pp. 159–164 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dorin Şendrescu
    • 1
  • Emil Petre
    • 1
  • Dan Popescu
    • 1
  • Monica Roman
    • 1
  1. 1.Department of Automatic ControlUniversity of CraiovaCraiovaRomania

Personalised recommendations