Monitoring of chlorine concentration in drinking water distribution systems using an interval estimator

• Autorzy: Rafał Łangowski , Mietek A. Brdys
• Języki publikacji: EN

Abstrakty

EN

This paper describes the design of an interval observer for the estimation of unmeasured quality state variables in drinking water distribution systems. The estimator utilizes a set bounded model of uncertainty to produce robust interval bounds on the estimated state variables of the water quality. The bounds are generated by solving two differential equations. Hence the numerical efficiency is sufficient for on-line monitoring of the water quality. The observer is applied to an exemplary water network and its performance is validated by simulations.

Słowa kluczowe

EN

modelling dynamics; bounding methods; water quality; estimators

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: 17
• Numer: 2
• Strony: 199-216

Daty

wydano

2007

otrzymano

2006-10-11

poprawiono

2007-05-15

Twórcy

autor

Rafał Łangowski

• Department of Automatic Control, Gdańsk University of Technology, ul. G. Narutowicza 11/12, 80–952 Gdańsk, Poland

autor

Mietek A. Brdys

• Department of Electronic, Electrical and Computer Engineering, School of Engineering, University of Birmingham, Birmingham B15 2TT, UK

Bibliografia

• Al-Omari A.S. and Chaudhry M.H. (2001): Unsteady-state inverse chlorine modeling in pipe networks. - J. Hydr. Eng., Vol.127, No.8, pp.669-677.
• Alcaraz-Gonzalez V., Harmand J., Rapaport A., Steyer J.P., Gonzalez-Alvarez V. and Pelayo Ortiz C. (2004): Application of a robust interval observer to an anaerobic digestion process. - Proc. 10th IWA World Congress Anaerobic Digestion, AD10, Montreal, Canada, Vol.1, pp.337-342.
• Boccelli D.L., Tryby M.E., Uber J.G. and Summers R.S. (2003): A reactive species model for chlorine decay and THM formation under rechlorination conditions. - Water Res., Vol.37, No.11, pp.2654-2666.
• Boulos P.F., Lansey K.E. and Karney K.E. (2004): Comprehensive Water Distribution Systems Analysis Handbook. - Pasadena, CA: MWH Soft Inc.
• Brdys M.A. and Ulanicki B. (1994): Operational Control of Water Systems: Structures, Algorithms and Applications. - New York: Prentice Hall.
• Brdys M.A. and Kang C.Y. (1994): Algorithms for state bounding in large-scale systems. - Int. J. Adapt. Contr. Signal Process., Vol.8, No.1, pp.103-118.
• Brdys M.A. and Chen K. (1995): Joint estimation of state and parameters in quantity models of water supply and distribution systems. - Automatisierungstechnik, Vol.43, No.2, pp.77-84.
• Brdys M.A. and Chen K. (1996): Joint estimation of states and parameters of integrated quantity and quality models of dynamic water supply and distribution systems. - Proc. 13th IFAC World Congress, San Francisco, Vol.1, pp.73-78.
• Chen K. (1997): Set membership estimation of state and parameters and operational control of integrated quantity and quality models of water supply and distribution systems. - Ph.D. thesis, University of Birmingham, Birmingham, UK.
• Clark R.M., Rossman L.A. and Wymer L.J. (1995): Modeling distribution system water quality: Regulatory implications. - J. Water Res. Plann.Manag., Vol.121, No.6, pp.423-428.
• Duzinkiewicz K., Brdys M.A. and Chang T. (2005): Hierarchical model predictive control of integrated quality and quantity in drinking water distribution systems. - Urban Water J., Vol.2, No.2, pp.125-137.
• Duzinkiewicz K. (2006): Set membership estimation of parameters and variables in dynamic networks by recursive algorithms with a moving measurement window. - Int. J. Appl. Math. Comput. Sci., Vol.16, No.2, pp.209-217.
• Gouze J.L., Rapaport A. and Hadj-Sadok M.Z. (2000): Interval observers for uncertain biological systems. - Ecol. Modell., Vol.13, No.1, pp.45-56.
• Grewal M.S. and Andrews A.P. (2001): Kalman Filtering: Theory and Practice, 2nd Ed.. - New York: Wiley.
• Hadj-Sadok M.Z. and Gouze J.L. (2001): Estimating of uncertain models of activated sludge process with interval observers. - J. Process Contr., Vol.11, No.3, pp.299-310.
• Harmand J. and Rapaport A. (2002): Interval observers for interconnected biotechnological systems. - Proc. 15th IFAC World Congress, Barcelona, Spain, (on CD-ROM).
• Luenberger D.G. (1979): Introduction to Dynamic Systems: Theory, Models and Applications. - New York: Wiley.
• Łangowski R. and Brdys M.A. (2006): Interval asymptotic estimator for chlorine monitoring in drinking water distribution systems. - Proc. 1st IFAC Workshop Applications of Large Scale Industrial Systems, Helsinki, Stockholm, (on CD-ROM).
• Males R.M., Clark R.M., Wehrman P.J. and Gates W.E. (1985): Algorithm for mixing problems in water systems. - J. Hydr. Eng., Vol.111, No.2, pp.206-219.
• Males R.M., Grayman W.M. and Clark R.M. (1988): Modeling water quality in distribution systems. - J. Water Res. Plann. Manag.,Vol.114, No.2, pp.197-209.
• Milanese M., Norton J., Piet-Lahanier H. and Walter E. (1996): Bounding Approaches to System Identification. - New York: Plenum Press.
• Mitchel A.R. and Griffiths D.F. (1980): The Finite Difference Method in Partial Differential Equations. - New York: Wiley.
• Park K. and Kuo A.Y. (1999): A multi-step computation scheme: decoupling kinetic processes from physical transport in water quality models. - Water Res., Vol.30, No.10, pp.2255-2264.
• Rapaport A. and Dochain D. (2005): Interval observers for biochemical processes with uncertain kinetics and inputs. - Math. Biosci., Vol.193, No.2, pp.235-253.
• Rossman L.A., Boulos P.F. and Altman T. (1993): Discrete volume element method for network water-quality models. - J. Water Res. Plann.Manag., Vol.119, No.5, pp.505-517.
• Rossman L.A., Clark R.M. and Grayman W.M. (1994): Modeling chlorine residuals in drinking water distribution systems. - J. Env. Eng., Vol.120, No.4, pp.803-820.
• Rossman L.A. and Boulos P.F. (1996): Numerical methods for modeling water quality in distribution systems: a Comparison. - J. Water Res. Plann. Manag., Vol.122, No.2, pp.137-146.
• Smith H.L. (1995): Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems. - Providence, Rhode Iand: AMS