STATE ESTIMATION FOR WASTEWATER TREATMENT PROCESSES

In this chapter, we provide the key ideas on how to build software sensors (also called observers) for wastewater treatment plants (WWTPs). We give an overview of the existing linear and nonlinear observers and discuss criteria that help to identify which observer is best suited with respect to the amount of information being available for the WWTP. Depending on the model reliability, the available measurements and the level of uncertainties associated to the influent concentrations, different class of observers can be considered. We distinguish between those that rely on a full model description (e.g., the extended Kalman filter), and those based on a mass-balance model wherein the biological kinetics are assimilated to unknown inputs (e.g., the asymptotic observer). Moreover, if bounds are known for the uncertainties, then interval observers can be designed. We discuss the principles of each class of observers and illustrate them through a number of examples.

[1]  F. Fairman.  Introduction to dynamic systems: Theory, models and applications , 1979, Proceedings of the IEEE.

[2]  D. Dochain,et al.  On-Line Estimation and Adaptive Control of Bioreactors , 2013 .

[3]  M. Hou,et al.  Design of observers for linear systems with unknown inputs , 1992 .

[4]  P. Kudva,et al.  Observers for linear systems with unknown inputs , 1980 .

[5]  G. V. Straten,et al.  A recursively identified model for short-term predictions of NH4/NO3 – concentrations in alternating activated sludge processes , 1999 .

[6]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[7]  John F. Andrews,et al.  A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates , 1968 .

[8]  Hong Zhao,et al.  State and parameter estimation for phosphorus removal in an alternating activated sludge process , 1995 .

[9]  Benoît Chachuat,et al.  Probabilistic observers for a class of uncertain biological processes , 2006 .

[10]  W. Gujer,et al.  Activated sludge model No. 3 , 1995 .

[11]  A Genovesi,et al.  Dynamical model development and parameter identification for an anaerobic wastewater treatment process. , 2001, Biotechnology and bioengineering.

[12]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[13]  P Gras,et al.  Evaluation of a four year experience with a fully instrumented anaerobic digestion process. , 2002, Water science and technology : a journal of the International Association on Water Pollution Research.

[14]  Alain Rapaport,et al.  Parallelotopic and practical observers for non-linear uncertain systems , 2003 .

[15]  F. Lewis.  Optimal Estimation: With an Introduction to Stochastic Control Theory , 1986 .

[16]  D. Luenberger.  Observers for multivariable systems , 1966 .

[17]  M. Darouach,et al.  Full-order observers for linear systems with unknown inputs , 1994, IEEE Trans. Autom. Control..

[18]  B. Chachuat,et al.  Reduction of the ASM1 Model for Optimal Control of Small-Size Activated Sludge Treatment Plants , 2003 .

[19]  Jean-Luc Gouzé,et al.  Closed loop observers bundle for uncertain biotechnological models , 2004 .

[20]  J. Gauthier,et al.  Deterministic Observation Theory and Applications , 2001 .

[21]  Sirish L. Shah,et al.  Adaptive multirate state and parameter estimation strategies with application to a bioreactor , 1995 .