Distributed PCHD-Systems, from the Lumped to the Distributed Parameter Case

  • Kurt Schlacher
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 353)


The Hamiltonian approach has turned out to be an effective tool for modeling, system analysis and controller design in the lumped parameter case. There exist also several extensions to the distributed parameter case. This contribution presents a class of extended distributed parameter Hamiltonian systems, which preserves some useful properties of the well known class of Port Controlled Hamiltonian systems with Dissipation. In addition, special ports are introduced to take the boundary conditions into account. Finally, an introductory example and the example of a piezoelectric structure, a problem with two physical domains, show, how one can use the presented approach for modeling and design.


Distributed Parameter Systems Hamiltonian Systems with Input and Dissipation 


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  1. 1.
    Choquet-Bruhat Y, Witt-Morette C (1982) Analysis, Manifolds and Physics. Elsevier, AmsterdamzbMATHGoogle Scholar
  2. 2.
    Curtain R F, Zwart H J (1995) An Introduction to Infinite-Dimensional Linear System Theory. Springer VerlagGoogle Scholar
  3. 3.
    Ennsbrunner H (2006) Infinite Dimensional Euler-Lagrange and Port Hamiltonian Systems, PhD Thesis at the Johannes Kepler University, Linz, AustriaGoogle Scholar
  4. 4.
    Ennsbrunner H, Schlacher K (2005) On the geometrical representation and interconnection of infinite dimensional port controlled hamiltonian systems, Proceedings of 44th IEEE Conference on Decision and ControlGoogle Scholar
  5. 5.
    Giachetta G, Mangiarotti L, Sardanashvily G (1997) New Lagrangian and Hamiltonian Methods in Field Theory. World Scientific, SingaporezbMATHGoogle Scholar
  6. 6.
    Hebey E (2000) Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities. Courant Institute of Mathematical Sciences, New YorkzbMATHGoogle Scholar
  7. 7.
    Isidori A (1995) Nonlinear Control Systems. Springer Verlag, LondonzbMATHGoogle Scholar
  8. 8.
    Nowacki W (2006) Static and Dynamic Coupled Fields in Bodies with Piezoeffects or Polarization Gradient. Springer VerlagGoogle Scholar
  9. 9.
    Olver P J (1986) Applications of Lie Groups to Differential Equations. Springer Verlag, New YorkzbMATHGoogle Scholar
  10. 10.
    Schlacher K (2006) Mathematical modelling for nonlinear control-a hamiltonian approach, Proceedings of 5th Vienna Symposium on Mathematical ModellingGoogle Scholar
  11. 11.
    van der Schaft A J (2000) L 2-Gain and Passivity Techniques in Nonlinear Control. Springer Verlag, New YorkzbMATHGoogle Scholar
  12. 12.
    van der Schaft A J, Maschke B M (2002) Hamiltonian formulation of distributed-parameter systems with boundary energy flow, Journal of Geometry and Physics, 42:166–194zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Zeidler E (1995) Applied Functional Analysis. Springer Verlag, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Kurt Schlacher
    • 1
  1. 1.Institute of Automatic Control and Control Systems TechnologyJohannes Kepler University LinzLinz

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