Shaping the energy of port-Hamiltonian systems without solving PDE's

Authors

Pablo Borja, Rafael Cisneros, Romeo Ortega

Abstract

Equilibrium stabilisation of nonlinear systems via energy shaping is a well-established, robust, passivity-based controller design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations. In this paper a new, fully constructive, procedure to shape the energy for a class of port-Hamiltonian systems that obviates the solution of partial differential equations is proposed. Proceeding from the well-known passive, power shaping output we propose a nonlinear static state-feedback that preserves passivity of this output but with a new storage function. This function contains some tuning gains used to ensure it is positive definite, hence a suitable Lyapunov function for the closed-loop. Connections with other standard passivity-based controllers are indicated and it is shown that the new controller design is applicable to two benchmark examples.

Citation

• Journal: 2015 54th IEEE Conference on Decision and Control (CDC)
• Year: 2015
• Volume:
• Issue:
• Pages: 5713–5718
• Publisher: IEEE
• DOI: 10.1109/cdc.2015.7403116

BibTeX

@inproceedings{Borja_2015,
  title={{Shaping the energy of port-Hamiltonian systems without solving PDE’s}},
  DOI={10.1109/cdc.2015.7403116},
  booktitle={{2015 54th IEEE Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Borja, Pablo and Cisneros, Rafael and Ortega, Romeo},
  year={2015},
  pages={5713--5718}
}

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References

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