Nous considérons un bac de fluide soumis à un déplacement longitudinal. Nous modélisons le mouvement du fluide par les équations de Saint-Venant dont les équations linéarisées ne sont pas stabilisables. A l'aide d'une approche Lyapunov, nous déduisons des lois de contrôles qui numériquement stabilisent l'état du fluide et du bac.
We consider a tank containing a fluid. The tank is subjected to a one-dimensional horizontal move and the motion of the fluid is described by the shallow water equations. By means of a Lyapunov approach, we deduce control laws to stabilize the fluid's state and the tank's position. Although global asymptotic stability is yet to be proved, we numerically simulate the system and observe the stabilization for different control situations.
@article{JEDP_2002____A13_0,
author = {Prieur, Christophe and de Halleux, Jonathan},
title = {Stabilization of a {1-D} tank modeled by the shallow water equations},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {13},
publisher = {Universit\'e de Nantes},
year = {2002},
doi = {10.5802/jedp.611},
mrnumber = {1968209},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/jedp.611/}
}
TY - JOUR AU - Prieur, Christophe AU - de Halleux, Jonathan TI - Stabilization of a 1-D tank modeled by the shallow water equations JO - Journées équations aux dérivées partielles PY - 2002 DA - 2002/// PB - Université de Nantes UR - http://archive.numdam.org/articles/10.5802/jedp.611/ UR - https://www.ams.org/mathscinet-getitem?mr=1968209 UR - https://doi.org/10.5802/jedp.611 DO - 10.5802/jedp.611 LA - en ID - JEDP_2002____A13_0 ER -
Prieur, Christophe; de Halleux, Jonathan. Stabilization of a 1-D tank modeled by the shallow water equations. Journées équations aux dérivées partielles (2002), article no. 13, 13 p. doi : 10.5802/jedp.611. http://archive.numdam.org/articles/10.5802/jedp.611/
[1] (2001). Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations. Preprint, Université Paris-Sud, number 2001-28. | Numdam | MR 1932962
[2] , and (1999). A lyapunov approach to control irrigation canals modeled by saint-venant equations. European Control Conference. Karlsruhe, Germany.
[3] (1994). Nonlinear water waves, Academic Press, Boston. | MR 1266390 | Zbl 0793.76001
[4] et , Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation, rapport de recherche numéro RR- 4084, INRIA Rocquencourt, 2000. | MR 1821555
[5] (1998). Fluvial Hydraulics. John Wiley & Sons.
[6] , Iterative optimal control of liquid slosh in an industrial packaging machine, Conference on Decision and Control, Sydney, Australie, 2000. XIII-11
[7] , and (1999).Motion planning and nonlinear simulations for a tank containing a fluid. European Control Conference. Karlsruhe, Germany.
[8] and (1995). Boundary value problems for quasilinear hyperbolic systems. Duke University, Durham. | MR 823237 | Zbl 0627.35001
[9] (1994). Modelisation, Analysis and LQR Optimal Control of an Irrigation Canal. PhD thesis, LAAS-CNRS-ENGREF-Cemagref, France.
[10] and (1996). Adding integrations, saturated controls, and stabilization for feedforward systems. IEEE Trans. Automat. Control, 41 (11), 1559-1578. | MR 1419682 | Zbl 0865.93049
[11] (2000). Controllability and stabilization of a canal with wave generators. SIAM J. Control Optimization, 38 (3), 711-735. | MR 1741435 | Zbl 0966.76015
[12] (2000). Controllability and stabilizability of liquid vibration in a container during transportation. Conference on Decision and Control. Sydney, Australy.
[13] and (2000). Dynamics and solutions to some control problems for water-tank systems. CIT-CDC, (00-004). XIII-12
[14] , Diverses méthodes pour des problèmes de stabilisation, thèse, université Paris-Sud, 2001.
[15] (1971). Théorie du mouvement non-permanent des eaux avec applications aux crues des rivières et à l'introduction des marées dans leur lit, Comptes-rendus de l'académie des Sciences, Paris, 73, 148-154, 237-240. | JFM 03.0482.04
[16] (1996
Cité par Sources :
