Abstract
This paper deals with the design of an ultra-local model control. The proposed approach is based on the estimation of the ultra-local model parameters using least squares resolution technique instead of numerical derivation technique. The closed-loop control is implemented through an adaptive PI in order to reject the influences of the disturbance and noise output signals. Its main advantages are: its simplicity and its robustness with respect to the parameter uncertainties of system. In this paper, it is processed to test the efficiency of the parameter estimation method compared with the performance of numerical derivation technique. The method is applied to the water level control of a two-tank-system. Numerical simulations show that the generated desired trajectory is followed in an efficient way even with severe operating conditions.
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References
Fliess M, Join C (2008) Commande sans modèle et commande à modèle restreint. e-STA 5:1–23
Fliess M, Join C (2013) Model-free control. Int J Control 810345. doi:10.1080/00207179
Fliess M, Join C, Riachy S (2011) Rien de plus utile qu’une bonne théorie : la commande sans modèle, 4èmes Journées Doctorales /Journées Nationales MACS, JDJN-MACS’2011, Marseille
Fliess M, Join C (2008) Non-linear estimation is easy. Int J Model Identif Control 4:12–27
Abouaïssa H, Fliess M, Iordanova V, Join C (2011) Prolégomènes à une régulation sans modèle du trafic autoroutier. Conférence Méditerranéenne sur l’Ingénierie sûre des Systèmes Complexes, Agadir
Fliess M, Join C, Mboup M (2010) Algebraic change-point detection, applicable algebra in engineering. Commun Comput 21:131–143
Fliess M, Join C, Perruquetti W (2008) Real-time estimation for switched linear systems. In: 47th IEEE conference on decision and control, Cancun, pp 409–414
Fliess M, Join C, Riachy S (2011) Revisiting some practical issues in the implementation of model-free control. In: 18th IFAC world congress, Milan
Join C, Masse J, Fliess M (2008) Etude préliminaire d’une commande sans modèle pour papillon de moteur, a model-free control for an engine throttle: a preliminary study. Journal européen des systèmes automatisés 42:337–354
Join C, Robert G, Fliess M (2010) Model-free based water level control for hydroelectric power plants. In: IFAC conference on control methodologies and tecnologies for energy efficiency, CMTEE’2010, Vilamoura
Mboup M, Join C, Fliess M (2007) A revised look at numerical differentiation with an application to nonlinear feedback control. In: Proceedings of the 15th mediterranean conference on control and automation, MED’2007, Athnes
Mboup M, Join C, Fliess M (2009) Numerical differentiation with annihilators in noisy environment. Numer Algorithm 50:439–467
Michel L, Join C, Fliess M, Sicard P, Chériti A (2010) Model-free control of DC/DC converters. In: 12th IEEE workshop on control and modeling for power electronics, COMPEL’2010, Boulder
Rezk S, Join C, El Asmi S (2012) Inter-beat (R–R) intervals analysis using a new time delay estimation technique. In: 20th European signal processing conference, EUSIPCO’2012, Bucarest
Litrico X, Fromion V (2009) Modeling and control of hydrosystems. Springer, London
Zhuan X, Xia X (2007) Models and control methodologies in open water flow dynamics: a survey. IEEE Africon, Windhoek
Join C, Robert G, Fliess M (2010) Vers une commande sans modèle pour aménagements hydroélectriques en cascade, 6ème Conférence Internationale Francophone d’Automatique, CIFA’2010, Nancy
Ayadi M, Haggège J, Bouallègue S, Benrejeb M (2008) A digital flatness-based control system of a DC motor. Stud Inform Control SIC 17:201–214
Fliess M, Lévine J, Martin P, Rouchon P (1995) Flatness and defect of non-linear systems: introductory theory and examples. Int J Control 61:1327–1361
Rotella F, Zambettakis I (2007) Commande des systèmes par platitude, Éditions Techniques de l’ingénieur, S7450
Aström KJ, Hägglund T (2006) Advanced PID controllers, 2nd edn. Instrument Society of America, Research Triangle Park
García Collado FA, d’AndrÌa-Novel B, Fliess M, Mounier H (2009) Analyse fréquentielle des dérivateurs algébriques. XXIIe Coll, GRETSI, Dijon
Rotella F, Borne P (1995) Théorie et pratique du calcul matriciel. Éditions Technip, Paris
Ben-Israel A, Greville TNE (1974) Generalized inverses: theory and applications. Wiley, New York
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Thabet, H., Ayadi, M. & Rotella, F. Towards an ultra-local model control of two-tank-system. Int. J. Dynam. Control 4, 59–66 (2016). https://doi.org/10.1007/s40435-014-0105-6
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DOI: https://doi.org/10.1007/s40435-014-0105-6