Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T20:38:49.574Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust Feedback Control Designfor a Nonlinear Wastewater Treatment Model

Published online by Cambridge University Press:  02 October 2009

M. Serhani ,
N. Raissi  and
P. Cartigny
M. Serhani*
Affiliation:
FSJES, University My Ismail, B.P. 3102, Toulal, Meknes, Morocco
N. Raissi
Affiliation:
EIMA, FS, University Ibn Tofail, B.P. 133, Kénitra, Morocco
P. Cartigny
Affiliation:
GREQAM, University la Méditerranée, 2 rue de la Charité, 13002 Marseille, France
*
mserhani@hotmail.com
Get access

Abstract

In this work we deal with the design of the robust feedback control ofwastewater treatmentsystem, namely the activated sludge process. This problem is formulated by anonlinearordinary differential system. On one hand, we develop a robust analysis when thespecific growthfunction of the bacterium μ is not well known. On the other hand, when alsothe substrate concentrationin the feed stream s in is unknown, we provide an observer of system andpropose a designof robust feedback control in term of recycle rate, in order to keep thepollutant concentration lowerthan an allowed maximum level s d .

Keywords

wastewater treatmentdynamical systemsstabilityrobustnessfeedback controlactivated sludge
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 5: Modelling of geographical processes and natural resources , 2009 , pp. 128 - 143
Copyright
© EDP Sciences, 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

V. Alcaraz-Gonzalez, J. Harmand, A. Rapaport, J.-P. Steyer, V. Gonzalez Alvarez, C. Pelayo Ortiz. Application of a robust interval observer to an anaerobic digestion process. Developments in Chemical Engineering Mineral Processing, 13 (2005), No. 3/4, 267–278.
V. Alcaraz-Gonzalez, J. Harmand, A. Rapaport, J.-P. Steyer, V. Gonzalez Alvarez, C. Pelayo Ortiz. Robust interval-based regulation for anaerobic digestion processes. Water Science and Technology, 52 (2005), No. 1-2, 449–456.
Andrews, J.F.. Kinetic models of biological waste treatment process. Biotech. Bioeng. Symp., 2 (1971), 5–34.
J.F. Andrews. Dynamics and control of wastewater systems. Water quality management library, vol. 6, 1998.
Busb, J.F., Andrews, J.F.. Dynamic modelling and control strategies for the activated sludge process. J. of Wat. Pollut. Control Fed., 47 (1975), 1055–1080.
C.R. Curds. Computer simulation of microbial population dynamics in the activated sludge process. Water Research 5 (1971), 1049–1066.
D. Dochain, M. Perrier. Control design for nonlinear wastewater treatment processes. Wat. Sci. Tech. 11-12 (1993), 283–293.
D. Dochain, M. Perrier. Dynamical modelling, analysis, monitoring and control design for nonlinear bioprocess. T. Scheper (Ed.), Advances in Biochemical and Biotechnology, 56 (1997), Spring Verlag, Berlin, 147–197.
C. Gómez-Quintero, I. Queinnec. Robust estimation for an uncertain linear model of an activated sludge process. Proc. of the IEEE Conference on Control Applications (CCA), Glasgow (UK), (2002), 18-20 december.
Hadj-Sadok, M.Z., Gouzé, J.L.. Estimation of uncertain models of activated sludge processes with interval observers. J. of Process Control, 11 (2001), 299–310. CrossRef
B. Haegeman, C. Lobry, J. Harmand. Modeling bacteria flocculation as density-dependent growth. Aiche Journal, 53 (2007), No.2, 535–539.
Marsili-Libelli, S.. Optimal control of the activated sludge process. Trans. Inst. Meas. Control, 6 (1984), 146–152. CrossRef
A. Martínez, C. Rodríguez, M.E. Vázquez-Méndez. Theoretical and numerical analysis of an optimal control problem related to wastewater treatment. SIAM J. CONTROL OPTIM., Vol. 38 (2000), No. 5, 1534–1553.
M.K. Rangla, K.J. Burnham, L. Coyle, R.I. Stephens. Simulation of activated sludge process control strategies. Simulation '98. International Conference on (Conf. Publ. No. 457), 30 Sep - 2 Oct (1998), 152–157.
A. Rapaport, J. Harmand. Robust regulation of a class of partially observed nonlinear continuous bioreactors. J. of Process Control, 12 (2002), No. 2, 291–302.
M. Serhani, J.L. Gouzé, N. Raïssi. Dynamical study and robustness for a nonlinear wastewater treatment model. Proceeding book “Systems Theory: Modeling, Analysis & Control, FES2009”, Eds A. EL Jaï, L. Afifi & E. Zerrik, PUP, ISBN 978-2-35412-043-6, pp. 571-578.
H.L. Smith. Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. American Matheatical society, 1995.
H.L. Smith, P. Waltman. The theory of the chemostat. Cambridge University Press, Cambridge, 1995.