Early lumping observer design and sensor placement for transport-reaction systems

Distributed parameter systems; Interpolation techniques; Linear matrix inequalities; Nonisothermal tubular reactors; State estimation; Design placement; Design problems; Linear matrix in equalities; Observer performance; Observers designs; Sensor placement; Transport reaction; Control and Systems Engineering; Modeling and Simulation; Computer Science Applications; Industrial and Manufacturing Engineering

Abstract :

[en] This paper deals with the observer design problem for a class of one-dimensional multi-species transport-reaction systems satisfying sector bounded nonlinearities and considering measurements distributed over the spatial domain. A design method is proposed based on a reduced-order model and a Lyapunov function, which provides sufficient conditions in terms of standard linear matrix inequalities (LMIs) to ensure the exponential convergence of the estimation error with a prescribed decay rate. The observer performance is further improved through an offline optimal sensor placement algorithm considering a parameterized reduced-order output matrix. A nonisothermal tubular reactor is presented to demonstrate the observer performance as well as the advantages of the proposed sensor placement optimization scheme.

Disciplines :

Chemical engineering

Author, co-author :

Tello, Ivan F.Y. ; Systems, Estimation, Control, and Optimization (SECO), University of Mons, Belgium ; Postgraduate Program in Engineering of Automation and Systems, Federal University of Santa Catarina, Brazil

Vande Wouwer, Alain ; Université de Mons - UMONS > Faculté Polytechnique > Service Systèmes, Estimation, Commande et Optimisation

Coutinho, Daniel; Postgraduate Program in Engineering of Automation and Systems, Federal University of Santa Catarina, Brazil

Language :

English

Title :

Early lumping observer design and sensor placement for transport-reaction systems

Publication date :

26 February 2022

Journal title :

Journal of Process Control

ISSN :

0959-1524

Publisher :

Elsevier Ltd

Volume :

112

Pages :

12 - 20

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0959152422000178?httpAccept=text/xml

Research institute :

R100 - Institut des Biosciences
R200 - Institut de Recherche en Energie

Funders :

CAPES - Coordenação de Aperfeicoamento de Pessoal de Nível Superior [BR]

Funding text :

I.F.Y.T. gratefully acknowledges funding from CAPES (Brazil). All authors have read and agreed to the published version of the manuscript.

Available on ORBi UMONS :

since 20 September 2022

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Bibliography

M. Achhab, M. Laabissi, J. Winkin, D. Dochain, Analysis of a Nonlinear dynamical model of an axial dispersion nonisothermal reactor, in: Proc. 14th International Symposium On The Mathematical Theory Of Networks And Systems (MTNS 2000), CD-Rom, Paper B, 82, 2000.
Laabissi, M., Achhab, M., Winkin, J., Dochain, D., Trajectory analysis of nonisothermal tubular reactor nonlinear models. Systems Control Lett. 42:3 (2001), 169–184.
Vande Wouwer, A., Zeitz, M., State estimation in distributed parameter systems. Control Systems, Robotics And Automation–Volume XIV: Nonlinear, Distributed, And Time Delay Systems-III, 2009, EOLSS Publications, 92.
Mitchell, A.R., Griffiths, D.F., The finite difference method in partial differential equations. 1980, A Wiley-Interscience Publication.
Brenner, S.C., Scott, L.R., Scott, L.R., The Mathematical Theory Of Finite Element Methods, Vol. 3. 2008, Springer.
LeVeque, R.J., et al. Finite Volume Methods For Hyperbolic Problems, Vol. 31. 2002, Cambridge University Press.
Boyd, J.P., Chebyshev And Fourier Spectral Methods. 2001, Courier Corporation.
Vande Wouwer, A., Saucez, P., Vilas, C., Simulation Of Ode/Pde Models With Matlab, Octave And Scilab. 2014, Springer.
Finlayson, B.A., The Method Of Weighted Residuals And Variational Principles, vol. 73. 2013, SIAM.
Katz, R., Fridman, E., Constructive method for finite-dimensional observer-based control of 1-D parabolic PDEs. Automatica, 122, 2020, 109285.
Marko, L., Mennemann, J.-F., Jadachowski, L., Kemmetmüller, W., Kugi, A., Early-and late-lumping observer designs for long hydraulic pipelines: Application to pumped-storage power plants. Int. J. Robust Nonlinear Control 28:7 (2018), 2759–2779.
Kharkovskaya, T., Efimov, D., Polyakov, A., Richard, J.-P., Design of interval observers and controls for PDEs using finite-element approximations. Automatica 93 (2018), 302–310.
Wu, H.-N., Wang, H.-D., Guo, L., Finite dimensional disturbance observer based control for nonlinear parabolic PDE systems via output feedback. J. Process Control 48 (2016), 25–40.
Kharkovskaia, T., Efimov, D., Polyakov, A., Richard, J.-P., Interval observers for PDEs: approximation approach. IFAC-PapersOnLine 49:18 (2016), 915–920.
Vande Wouwer, A., Point, N., Porteman, S., Remy, M., An approach to the selection of optimal sensor locations in distributed parameter systems. J. Process Control 10:4 (2000), 291–300.
Alonso, A.A., Frouzakis, C.E., Kevrekidis, I.G., Optimal sensor placement for state reconstruction of distributed process systems. AIChE J. 50:7 (2004), 1438–1452.
Demetriou, M.A., Robust sensor location optimization in distributed parameter systems using functional observers. Proceedings Of The 44th IEEE Conference On Decision And Control, 2005, IEEE, 7187–7192.
Gunder, T., Sehlinger, A., Skoda, R., Mönnigmann, M., Sensor placement for reduced-order model-based observers in hydraulic fluid machinery. IFAC-PapersOnLine 51:13 (2018), 414–419.
Lefèvre, L., Dochain, D., De Azevedo, S.F., Magnus, A., Optimal selection of orthogonal polynomials applied to the integration of chemical reactor equations by collocation methods. Comput. Chem. Eng. 24:12 (2000), 2571–2588.
Zemouche, A., Boutayeb, M., Bara, G.I., Observer design for nonlinear systems: An approach based on the differential mean value theorem. Proceedings Of The 44th IEEE Conference On Decision And Control, 2005, IEEE, 6353–6358.
Açıkmeşe, B., Corless, M., Observers for systems with nonlinearities satisfying incremental quadratic constraints. Automatica 47:7 (2011), 1339–1348.
Arcak, M., Kokotović, P., Nonlinear observers: a circle criterion design and robustness analysis. Automatica 37:12 (2001), 1923–1930.
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., Linear matrix inequalities in system and control theory. 1994, SIAM.
Khalil, H.K., Nonlinear Systems. third Ed., 2002, Prentice Hall.
Vande Wouwer, A., Zeitz, M., Point, N., Remy, M., On-line implementation of a nonlinear distributed observer for a multizone furnace—comparative study with a nonlinear filter. Control Eng. Pract. 1:6 (1993), 947–955.
Papachristodoulou, A., Anderson, J., Valmorbida, G., Prajna, S., Seiler, P., Parrilo, P.A., Sum of squares optimization toolbox for MATLAB user's guide. 2013, University of Oxford.
van Doesburg, H., De Jong, W., Transient behaviour of an adiabatic fixed-bed methanator—I: experiments with binary feeds of CO or CO2 in hydrogen. Chem. Eng. Sci. 31:1 (1976), 45–51.