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The complexity problem of nonlinear dynamic systems appears in a great number of scientific and engineering fields. The multi-model, also known as polytopic approach, constitutes an interesting tool for modeling dynamic nonlinear systems, in the framework of stability analysis and controller/observer design. A systematic procedure to transform a nonlinear system into a polytopic one will be briefly presented and illustrated by an academical example. This procedure gives the possibility of choosing between different polytopic structures, which is a degree of freedom used to ease the controllability, observability, stability analysis studies. In addition to that, the system transformation into polytopic form does not cause any information loss, contrarily to most existing studies in the field. In the second part of this chapter, a discussion about multiple time scale nonlinear systems, also known as singularly perturbed systems is proposed, by eliminating some structural constraints and by performing the identification and the separation of the time-scales. Robust observer synthesis with respect to internal/external perturbations, modeling parametrization errors and unknown inputs are presented for the estimation of different variables of interest, the state variables. The above-mentioned points will be applied to an activated sludge wastewater treatment plant (WWTP), which is a complex chemical and biological process. The variations in wastewater flow rate/composition and the time-varying bio-chemical reactions make this process nonlinear. Despite the process nonlinearity and complexity, there is a need to control the quality of the water rejected in the nature by the WWTPs in order to achieve the requirements of the European Union in terms of environmental protection. To this end, a Benchmark, proposed by the European program COST 624 to asses the control strategies of WWTPs, is used as an example in the present chapter.
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Angelis, G. Z. (2001). System Analysis, Modeling and Control with Polytopic Linear Models. Ph.D. thesis, Technische Universiteit Eindhoven.
Bergsten, P., Palm, R., & Driankov, D. (2002). Observers for Takagi-Sugeno fuzzy systems. IEEE Transactions on Systems, Man and Cybernetics, 32(1), 114–121. CrossRef
Bezzaoucha, S., Marx, B., Maquin, D., & Ragot, J. (2013). Nonlinear joint state and parameter estimation: Application to a wastewater treatment plant. Control Engineering Practice, 21(10), 1377–1385. CrossRef
Copp, J. B. (2002). The cost simulation benchmark-description and simulator manual. Technical report, Office for Official Publications of the European Communities, Luxembourg.
Dong, G. Q., Jakobowski, L., Iafolla, M. A. J., & McMillen, D. R. (2007). Simplification of stochastic chemical reaction models with fast and slow dynamics. Journal of Biological Physics, 33(1), 67–95. CrossRef
Ichalal, D., Marx, B., Ragot, J., & Maquin, D. (2009). Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi-Sugeno model with unmeasurable premise variables. In Mediterranean Conference on Control and Automation, Thessaloniki, Greece. MATH
Ichalal, D., Marx, B., Ragot, J., & Maquin, D. (2010). State estimation of Takagi-Sugeno systems with unmeasurable premise variables. IET Control Theory and Applications, 4(5), 897–908. CrossRef
Johansen, T., Shorten, R., & Murray-Smith, R. (2000). On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models. IEEE Transactions on Fuzzy Systems, 8(3), 297–313. CrossRef
Kiss, A. N., Marx, B., Mourot, G., Schutz, G., & Ragot, J. (2011). State estimation of two-time scale multiple models. Application to wastewater treatment plant. Control Engineering Practice, 19(11), 1354–1362. CrossRef
Kumar, A., Christofides, P. D., & Daoutidis, P. (1998). Singular perturbation modeling of nonlinear processes with nonexplicit time-scale multiplicity. Chemical Engineering Science, 53(8), 1491–1504. CrossRef
Löfberg, J. (2004). YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference. Taipei, Taiwan.
Mourot, G., Gasso, K., & Ragot, J. (1999). Modelling of ozone concentrations using a Takagi-Sugeno model. Control Engineering Practice, 7, 707–715. CrossRef
Nagy, A., Mourot, G., Marx, B., Schutz, G., & Ragot, J. (2010). Systematic multi-modeling methodology applied to an activated sludge reactor model. Industrial and Engineering Chemistry Research, 49(6), 2790–2799. CrossRef
Nagy, A. M. (2010). Analyse et synthèse de multimodèles pour le diagnostic. Application à une station d’épuration. Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France.
Nagy-Kiss, A., Marx, B., Mourot, G., Schutz, G., & Ragot, J. (2011). Observers design for uncertain Takagi-Sugeno systems with unmeasurable premise variables and unknown inputs. Application to a wastewater treatment plant. Journal of Process Control, 21(7), 1105–1114. CrossRef
Nagy-Kiss, A., Schutz, G., & Ragot, J. (2015). Parameter estimation for uncertain systems based on fault diagnosis using Takagi-Sugeno model. ISA Transactions, 56, 65–74. CrossRef
Nagy-Kiss, A. M., Marx, B., Mourot, G., Schutz, G., & Ragot, J. (2012). Observer synthesis for uncertain nonlinear systems. Application to waste-water treatment plants. In 7th IFAC Symposium on Robust Control Design, Aalborg, Denmark (pp. 485–490).
Olsson, G., & Newell, B. (1999). Wastewater treatment systems: Modelling, diagnosis and control. London: IWA Publishing.
Robertson, G. A. (1992). Mathematical Modelling of Startup and Shutdown Operation of Process Plants. Ph.D. thesis, The University of Queensland, Brisbane, QLD, Australia.
Smets, I. Y., Haegebaert, J. V., Carrette, R., & Van Impe, J. F. (2003). Linearization of the activated sludge model ASM1 for fast and reliable predictions. Water Research, 37, 1831–1851. CrossRef
Steffens, M. A., Lant, P. A., & Newell, R. B. (1997). A systematic approach for reducing complex biological wastewater treatment models. Water Research, 31(3), 590–606. CrossRef
Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its application to modelling and control. IEEE Transactions on Systems, Man and Cybernetics, 15, 166–172. MATH
Tanaka, K., & Wang, H. O. (2001). Fuzzy control system design and analysis: A linear matrix inequality approach. New York: Wiley. CrossRef
Wang, H. O., Tanaka, K., & Griffin, M. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Transactions on Fuzzy Systems, 4(1), 14–23. CrossRef
Xu, S., & Lam, J. (2006). Robust control and filtering of singular systems. New York: Springer. MATH
Zamani, I., & Zarif, M. H. (2011). On the continuous-time Takagi-Sugeno fuzzy systems stability analysis. Applied Soft Computing, 11(2), 2102–2116. CrossRef
- Reducing Complexity of Nonlinear Dynamic Systems
Anca Maria Nagy-Kiss
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