Observers design for uncertain Takagi-Sugeno systems with unmeasurable premise variables and unknown inputs. Application to a wastewater treatment plant

Journal of Process Control

Volumn 21, Issue 7, 2011, Pages 1105-1114

  Nagy Kiss, A M ^a   Marx, B ^a   Mourot, G ^a   Schutz, G ^b   Ragot, J ^a  

^a CENTRE DE RECHERCHE EN AUTOMATIQUE DE NANCY   (France)

^b LTI Unit Business and Systems Analytics   (France)

Author keywords

Linear matrix inequality; Model uncertainties; Nonlinear systems; State estimation; Unknown input estimation; Unmeasurable premise variables; Wastewater treatment plant

Indexed keywords

LINEAR MATRIX INEQUALITY FORMULATIONS; MODEL UNCERTAINTIES; MULTIPLE MODELS; NUMERICAL RESULTS; OBSERVER SYNTHESIS; PROPORTIONAL-INTEGRAL OBSERVERS; STABILITY ANALYSIS; TAKAGI-SUGENO SYSTEMS; UNCERTAIN NONLINEAR SYSTEMS; UNKNOWN INPUT ESTIMATION; UNKNOWN INPUTS; UNMEASURABLE PREMISE VARIABLES; WASTEWATER TREATMENT PLANT; WASTEWATER TREATMENT PLANTS;

FEEDBACK CONTROL; LINEAR MATRIX INEQUALITIES; LYAPUNOV METHODS; NONLINEAR ANALYSIS; NONLINEAR SYSTEMS; OBSERVABILITY; RECLAMATION; SEWAGE PUMPING PLANTS; UNCERTAINTY ANALYSIS; WASTEWATER; WATER TREATMENT PLANTS;

WASTEWATER TREATMENT;

EID: 80053617171     PISSN: 09591524     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jprocont.2011.05.001     Document Type: Article

References (38)

1. A.H. Jazwinski Stochastic Processes and Filtering Theory, Vol. 64, Mathematics in Science and Engineering 1970
2. B.F. La Scala, and R.R. Bitmead Design of an extended Kalman filter frequency tracker IEEE Transactions on Signal Processing 44 3 1996 739 742 (Pubitemid 126777465)
3. F.E. Thau Observing the state of nonlinear systems International Journal of Control 17 1973 471 479
4. R. Rajamani Observers for Lipschitz nonlinear systems IEEE Transactions on Automatic Control 43 3 1998 397 401 (Pubitemid 128737358)
5. C.W. Li, and L.W. Tao Observing nonlinear systems time-variable systems through a canonical observer International Journal of Control 44 1986 1703 1713 (Pubitemid 17481979)
6. C. Califano, S. Monaco, and D. Normand-Cyrot Canonical observer forms for multi-output systems up to coordinate and output transformations in discrete time Automatica 45 11 2009 2483 2490
7. F. Deza, E. Busvelle, J.P. Gauthier, and D. Rakotopara High gain estimation for nonlinear systems Systems & Control Letters 18 1992 295 299
8. H.K. Khalil High-gain observers in nonlinear feedback control New Directions in Nonlinear Observer Design 1999 Springer Berlin/Heidelberg
9. V.I. Utkin Variable structure systems with sliding mode, a survey IEEE Transactions on Automatic Control 22 1977 212 222
10. C. Edwards, S.K. Spurgeon, and R.J. Patton Sliding mode observers for fault detection and isolation Automatica 36 4 2000 54 553
11. R. Murray-Smith, and T.A. Johansen Multiple Model Approaches to Modeling and Control 1997 Taylor & Francis London
12. T. Takagi, and M. Sugeno Fuzzy identification of systems and its application to modelling and control IEEE Transactions on Systems, Man and Cybernetics 15 1985 166 172
13. K. Tanaka, and H.O. Wang Fuzzy Control System Design and analysis. A Linear Matrix Inequality Approach 2001 John Wiley & Sons Inc.
14. T. Johansen, R. Shorten, and R. Murray-Smith On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models IEEE Transactions on Fuzzy Systems 8 3 2000 297 313
15. J. Abonyi, R. Babuska, and F. Szeifert Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models IEEE Transactions on Systems, Man and Cybernetics Part B: Cybernetics 32 5 2002 612 621
16. G. Mourot, K. Gasso, and J. Ragot Modelling of ozone concentrations using a Takagi-Sugeno model Control Engineering Practice 7 6 1999 707 715 (Pubitemid 29471872)
17. P. Bergsten, R. Palm, and D. Driankov Observers for Takagi-Sugeno fuzzy systems IEEE Transactions on Systems, Man and Cybernetics 32 2002 114 121 (Pubitemid 34228678)
18. M. Chadli, A. Akhenak, J. Ragot, and D. Maquin On the design of observer for unknown inputs fuzzy models International Journal of Automation and Control 2 1 2008 113 125
19. W. Chen, and M. Saif Design of a TS based fuzzy nonlinear unknown input observer with fault diagnosis applications American Control Conference New York, USA 2007
20. E.J. Herrera-Lopez, B. Castillo-Toledo, and J. Ramirez-Cordova Takagi-Sugeno Fuzzy Observer for a Switching Bioprocess: Sector Nonlinearity Approach, New Developments in Robotics Automation and Control 2008 InTech Austria
21. D. Ichalal, B. Marx, J. Ragot, and D. Maquin Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi-Sugeno model with unmeasurable premise variables Mediterranean Conference on Control and Automation Thessalonique, Grece 2009
22. B. Marx, D. Koenig, and J. Ragot Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis IET Control Theory and Applications 1 5 2007 1487 1495 (Pubitemid 47283341)
23. A.M. Nagy, G. Mourot, B. Marx, G. Schutz, and J. Ragot Systematic multi-modeling methodology applied to an activated sludge reactor model Industrial & Engineering Chemistry Research 49 6 2010 2790 2799
24. A. Khedher, K. Benothman, D. Maquin, and M. Benrejeb State and sensor faults estimation via a proportional integral observer 6th International Multi-Conference on Systems, Signals and Devices 2009 1 6
25. J. Yoneyama H filtering for fuzzy systems with immeasurable premise variables: an uncertain system approach Fuzzy Sets and Systems 160 12 2009 1738 1748
26. M. Henze, C.P. Leslie Grady Jr, W. Gujer, G.v.R. Marais, T. Matsuo, Activated Sludge Model no.1. I.A.W.Q. Scientific and Technical Report No.1, Tech. rep., I.A.W.Q., London, UK, 1987.
27. I. Smets, L. Verdickt, and J. Van Impe A linear ASM1 based multi-model for activated sludge systems Mathematical and Computer Modeling of Dynamical Systems 12 5 2006 489 503 (Pubitemid 44181276)
28. W. Gujer, M. Henze, T. Mino, T. Matsuo, M.C. Wentzel, and G.v.R. Marais Basic concepts of the Activated Sludge Model no 2: biological phosphorus removal process IAWQ Specialized Seminar, Modelling and Control of Activated Sludge Processes 1994
29. W. Gujer, M. Henze, M.V. Loosdrecht, and T. Mino Activated Sludge Model no.3 Water Science and Technology 39 1 1999 183 193
30. M.A. Steffens, P.A. Lant, and R.B. Newell A systematic approach for reducing complex biological wastewater treatement models Water Research 31 3 1997 590 606
31. G. Olsson, and B. Newell Wastewater Treatment Systems. Modelling Diagnosis and Control 1999 IWA Publishing
32. B. Chachuat, Mthodologie d'optimisation dynamique et de commande optimale des petites stations d'puration boues actives, Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France, 2001 (in French).
33. B. Chachuat, N. Roche, and R. Latifi Reduction of the ASM1 model for optimal control of small-size activated sludge treatment plants Revue des Sciences de l'Eau 16 1 2003 5 26 (in French) (Pubitemid 36536822)
34. S.R. Weijers, Modelling, identification and control of activated sludge plants for nitrogen removal, Ph.D. thesis, Technische Universiteit Eindhoven, Eindhoven, 2000.
35. B. Boulkroune A nonlinear observer design for an activated sludge wastewater treatment process Journal of Process Control 19 2009 1558 1565
36. J. Alex, J.F. Beteau, J.B. Copp, C. Hellinga, U. Jeppsson, S. Marsili-Libelli, M.N. Pons, H. Spanjers, and H. Vanhooren Benchmark for evaluating control strategies in wastewater treatment plants European Control Conference Karlsruhe, Germany 1999
37. D. Koenig, and S. Mammar Design of proportional-integral observer for unknown input descriptor systems IEEE Transactions on Automatic Control 47 12 2002 2057 2062
38. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequalities in system and control theory, Studies in Applied and Numerical Mathematics, Philadelphia (1994).