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

  • Authors:

  • V. Dos Santos;G. Bastin;J. -M. Coron;B. d'Andréa-Novel

  • Affiliations:

  • Université de Lyon, Lyon, F-69003, France and Université Lyon 1, CNRS, UMR 5007, LAGEP, Villeurbanne, F-69622, France and ESCPE, Villeurbanne, F-69622, France;Center for Systems Engineering and Applied Mechanics (CESAME), Université Catholique de Louvain, 4, Avenue G. Lemaítre, 1348 Louvain-la-Neuve, Belgium;Institut universitaire de France et Département de Mathématique, Université Paris-Sud, Bítiment 425, 91405 Orsay, France;Centre de Robotique, Ecole des Mines de Paris, 60, Boulevard Saint Michel, 75272 Paris Cedex 06, France

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

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Abstract

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.