Authors

Pablo Borja, Rafael Cisneros, Romeo Ortega

Abstract

Equilibrium stabilization 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, which is usually a difficult task. 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. A suitable selection of a controller gain makes this function positive definite, hence it is a suitable Lyapunov function for the closed-loop. The resulting controller may be interpreted as a classical PI—connections with other standard passivity-based controllers are also identified.

Keywords

Passivity; Nonlinear systems; Passivity-based control; Hamiltonian systems

Citation

BibTeX

@article{Borja_2016,
  title={{A constructive procedure for energy shaping of port—Hamiltonian systems}},
  volume={72},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2016.05.028},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Borja, Pablo and Cisneros, Rafael and Ortega, Romeo},
  year={2016},
  pages={230--234}
}

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References