Boundary control with integral action for hyperbolic systems of conservation laws:: Stability and experiments

被引:76
|
作者
Dos Santos, V. [1 ,2 ,3 ]
Bastin, G. [4 ]
Coron, J. -M. [5 ,6 ]
d'Andrea-Novel, B. [7 ]
机构
[1] Univ Lyon, F-69003 Lyon, France
[2] Univ Lyon 1, CNRS, UMR 5007, LAGEP, F-69622 Villeurbanne, France
[3] ESCPE, F-69622 Villeurbanne, France
[4] Univ Catholique Louvain, CESAME, B-1348 Louvain, Belgium
[5] Univ Paris 11, Inst Univ France, F-91405 Orsay, France
[6] Univ Paris 11, Dept Math, F-91405 Orsay, France
[7] Ecole Mines, Ctr Robot, F-75272 Paris 06, France
关键词
Lyapunov stability; Saint-Venant equations; systems of conservation laws; Riemann invariants;
D O I
10.1016/j.automatica.2007.09.022
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A strict Lyapunov function for boundary control with integral actions of hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants, is presented. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions and the integral control gains. Previous stability results are extended to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state measured only at the boundaries. The control design method is illustrated with a hydraulic application, namely the level and flow regulation in a reach of the Sambre river and in the micro-channel of Valence, respectively through simulations and experimentations. (c) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1310 / 1318
页数:9
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