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Keywords:
adaptive observers; nonlinear systems; bioprocess
adaptive observers; nonlinear systems; bioprocess
Summary:
The adaptive version of the high gain observer for the strictly triangular systems subjected to constant unknown disturbances is proposed here. The adaptive feature is necessary due to the fact that the unknown disturbance enters in a way that cannot be suppressed by the high gain technique. The developed observers are then applied to a culture of microorganism in a bioreactor, namely, to the model of the continuous culture of Spirulina maxima. It is a common practice that just the biomass (or substrate) concentration is directly measured as the output of the process for monitoring and control purposes. This paper thereby shows both by theoretical analysis and numerical simulation that the adaptive high-gain observers offer a realistic option of online software sensors for substrate estimation.
References:
[1] Abbaszadeh, M., Marquez, H. J.: A generalized framework for robust nonlinear Hinfty filtering of Lipschitz descriptor systems with parametric and nonlinear uncertainties. Automatica 48 (2012), 5, 894-900. DOI 10.1016/j.automatica.2012.02.033
[2] Agrawal, P., Lim, H.: Analyses of various control schemes for continuous bioreactors. Advances in Biochemical Engineering/ Biotechnology 30 (1984), 61-90. DOI 10.1007/bfb0006380
[3] Bastin, G., Gevers, M.: Stable adaptive observers for nonlinear time-varying systems. IEEE Trans. Automat. Control 33 (1988), 7, 650-658. DOI 10.1109/9.1273
[4] Bejarano, F., Fridman, L.: High order sliding mode observer for linear systems with unbounded unknown inputs. Int. J. Control 83 (2010), 1920-1929. DOI 10.1080/00207179.2010.501386 | MR 2724205
[5] Besancon, G., Leon-Morales, J. de, Huerta-Guevara, O.: On adaptive observers for state affine systems. Int. J. Control 79 (2006), 6, 581-591. DOI 10.1080/00207170600552766 | MR 2216743
[6] al., A. R. Bocanegra-Domínguez et: Estudio teórico práctico de la remoción de contaminantes presentes en el río de Los Remedios, Estado de México. Tecnología y Ciencias del Agua 24.2 (2009), 81-91. (In Spanish)
[7] Bornard, G., Celle-Couenne, F., Gilles, G.: Observability and Observers. In: Nonlinear Systems - T.1, ‘Modeling and Estimation’. Chapman and Hall, London 1995, pp. 173-216. DOI 10.1007/978-1-4615-2047-4_6 | MR 1359309
[8] Canizares, R. O., Domínguez, A. R.: Growth of Spirulina maxima on swine waste. Bioresource Technol. 45 (1993), 1, 73-75. DOI 10.1016/0960-8524(93)90148-5
[9] Diop, S., Fliess, M.: Nonlinear observability, identifiability, and persistent trajectories. In: Proc. 30th IEEE Conference on Decision and Control 1 (1991), pp. 714-719. DOI 10.1109/cdc.1991.261405
[10] Efimov, D., Fridman, L.: Global sliding-mode observer with adjusted gains for locally Lipschitz systems. Automatica 47 (2011), 3, 565-570. DOI 10.1016/j.automatica.2010.12.003
[11] Farza, M., Bouraou, I., Menard, T., Abdennou, R., M'Saad, M.: Adaptive observers for a class of uniformly observable systems with nonlinear parametrization and sampled outputs. Automatica 50 (2014), 2951-2960. DOI 10.1016/j.automatica.2014.10.032 | MR 3276636
[12] Farza, M., M'saad, M., Maatou, T., Kamoun, M.: Adaptive observers for nonlinearly parameterized class of nonlinear systems. Automatica 45 (2009), 2292-2299. DOI 10.1016/j.automatica.2009.06.008 | MR 2890790
[13] Fridman, L., Shtessel, Y., Edwards, C., Yan, X.: Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems. Int. J. Robust Nonlinear Control 18 (2008), 399-412. DOI 10.1002/rnc.1198 | MR 2392130
[14] Gauthier, J. P., Hammouri, H., Othman, S.: A simple observer for nonlinear systems applications to bioreactors. IEEE Trans. Automat. Control 37 (1991), 875-880. DOI 10.1109/9.256352 | Zbl 0775.93020
[15] Gerd, L., Narendra, K.: An adaptive observer and identifier for a linear system. IEEE Trans. Automat. Control 18 (1973), 5, 496-499. DOI 10.1109/tac.1973.1100369
[16] Guoping, L., Ho, D: Full-order and reduced-order observers for Lipschitz descriptor systems: the unified LMI approach. IEEE Trans. Circuits Systems II: Express Briefs 53 (2006), 7, 563-567. DOI 10.1109/tcsii.2006.875332
[17] Hammouri, H., Nadri, M.: An observer design for a class of implicit systems. Systems Control Lett. 62 (2013), 3, 256-261. DOI 10.1016/j.sysconle.2012.11.001 | MR 3015290
[18] Hermann, R., Krener, A.: Nonlinear controllability and observability. IEEE Trans. Automat. Control 22 (1977), 5, 728-740. DOI 10.1109/tac.1977.1101601
[19] Hamid-Reza, K., Zapateiro, M., Luo, N.: A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations. J. Franklin Inst. 347 (2010), 6, 957-973. DOI 10.1016/j.jfranklin.2010.03.004
[20] Karimi, H. R., Zapateiro, M., N., Luo: A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations. J. Franklin Inst. 347 (2010), 6, 957-973. DOI 10.1016/j.jfranklin.2010.03.004 | MR 2653874
[21] Khalil, H.: Nonlinear Systems. Third edition. Prentice Hall, Englewood Cliffs, NJ 2002.
[22] Khosrowjerdi, M. J.: Mixed H2/Hinfty approach to fault-tolerant controller design for Lipschitz non-linear systems. IET Control Theory A. 5 (2011), 2, 299-307. DOI 10.1049/iet-cta.2009.0556
[23] Kreisselmeier, G.: Adaptive observers with exponential rate of convergence. IEEE Trans. Automat. Control 22 (1977), 1, 2-8. DOI 10.1109/tac.1977.1101401 | MR 0444142
[24] Lafon, F., Busvelle, E., Gauthier, J. P.: An adaptive high-gain observer for wastewater treatment systems. Journal Process Control 21 (2011), 893-900. DOI 10.1016/j.jprocont.2011.03.006
[25] Liang, X., Jiangfeng, Z., Xiaohua, X.: Adaptive synchronization for generalized Lorenz systems. IEEE Trans. Automat. Control 53 (2008), 7, 1740-1746. DOI 10.1109/tac.2008.928318 | MR 2446392
[26] al., F. Mairet et: Modelling neutral lipid production by the microalga Isochrysis aff. galbana under nitrogen limitation. Bioresource Technol. 102.1 (2011), 142-149. DOI 10.1016/j.biortech.2010.06.138
[27] Marino, R., Tomei, P.: Nonlinear Control Design. Geometric, Adaptive and Robust Approach. Prentice Hall, Englewood Cliffs, NJ 1995.
[28] Marino, R., Tomei, P.: Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems. IEEE Trans. Automat. Control 40 (1995), 7, 1300-1304. DOI 10.1109/9.400471 | MR 1344052
[29] Raghavan, S., Hedrick, J.: Observer design for a class of nonlinear systems. Int. J. Control 59 (1994), 2, 515-528. DOI 10.1080/00207179408923090 | MR 1261285 | Zbl 0802.93007
[30] Rajamani, R.: Observers for Lipschitz nonlinear systems. IEEE Trans. Automat. Control 43 (1998), 3, 397-401. DOI 10.1109/9.661604 | Zbl 0905.93009
[31] Rodríguez-Mata, A., Torres-Muñoz, J., Domínguez, A. R., Hernandez-Villagran, D., Čelikovský, S.: Nonlinear high-gain observers with integral action: Application to bioreactors. In: Proc. 8th International Conference on Electrical Engineering, Computing Science and Automatic Control, Cancun 2011, pp. 444-449. DOI 10.1109/iceee.2011.6106611
[32] Sanchez-Torres, J., Loukianov, G., Moreno, J., Drakunov, S. V.: An equivalent control based sliding mode observer using high order uniform robust sliding operators. In: Proc. American Control Conference, Montreal 2012, pp. 6160-6165.
[33] Travieso, L., Sánchez, E., Bora, R.: Evaluation of laboratory and full-scale microalgae pond for tertiary treament of piggery wastes. Enviromental Technol. 25 (2004), 565-576. DOI 10.1080/09593330.2004.9619347
[34] Wu, H.: A class of adaptive robust state observers with simpler structure for uncertain non linear systems with time varying delays. IET Control Theory Appl. 7 (2013), 218-222. DOI 10.1049/iet-cta.2012.0318
[35] Yong-Hong, L., Zhou, Y.: Non-fragile observer-based robust control for a class of fractional-order nonlinear systems. Systems Control Lett. 62 (2013), 12, 1143-1150. DOI 10.1016/j.sysconle.2013.09.007
[36] Zhang, Q.: Adaptive observer for multiple-input-multiple-output (mimo) linear time-varying systems. IEEE Trans. Automat. Control 47 (2002), 3, 525-529. DOI 10.1109/9.989154
[37] Zemouche, A., Boutayeb, M., Maatoug, T., Kamoun, M.: On LMI conditions to design observers for Lipschitz nonlinear systems. Automatica 49 (2013), 585-591. DOI 10.1016/j.automatica.2012.11.029 | MR 3004728
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