Authors

Dimitri Jeltsema, Jacquelien M.A. Scherpen, Romeo Ortega

Abstract

This paper first addresses the question when a given (possibly nonlinear) RGLC circuit can be rewritten as a port-Hamiltonian (PH) system—with state variables the inductor currents and capacitor voltages instead of the fluxes and charges, respectively. The question has an affirmative answer for a class of circuits that fulfills a certain regularity condition. This class includes circuits where all dynamic elements are linear, and the associated resistors and conductors are passive—though possibly nonlinear. Interestingly, the resulting Hamiltonian function is related with the circuits instantaneous reactive power associated with the inductors and capacitors. This novel circuit representation, called a reactive port-Hamiltonian description, naturally suggests a new set of non-standard passive outputs, which are shown to be useful for the design of reactive power compensation schemes. A Van der Pol oscillator circuit is used to illustrate the developments throughout the paper.

Keywords

Passivity; Stabilization; Nonlinear Systems; RGLC circuits; Hamiltonian Systems; Brayton-Moser Circuits; Van der Pol oscillator

Citation

  • Journal: IFAC Proceedings Volumes
  • Year: 2004
  • Volume: 37
  • Issue: 13
  • Pages: 49–56
  • Publisher: Elsevier BV
  • DOI: 10.1016/s1474-6670(17)31199-0
  • Note: 6th IFAC Symposium on Nonlinear Control Systems 2004 (NOLCOS 2004), Stuttgart, Germany, 1-3 September, 2004

BibTeX

@article{Jeltsema_2004,
  title={{A reactive port-hamiltonian circuit description and its control implications}},
  volume={37},
  ISSN={1474-6670},
  DOI={10.1016/s1474-6670(17)31199-0},
  number={13},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Jeltsema, Dimitri and Scherpen, Jacquelien M.A. and Ortega, Romeo},
  year={2004},
  pages={49--56}
}

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References