Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems

Authors

Kameswarie Nunna, Mario Sassano, Alessandro Astolfi

Abstract

The Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) problem for port-controlled Hamiltonian systems is revisited. We propose a methodology that exploits the novel notion of algebraic solution of the so-called matching equation. This notion is instrumental for the construction of an energy function, defined on an extended state-space, which does not rely upon the solution of any partial differential equation. This yields, differently from the classical solution, a dynamic state feedback that stabilizes a desired equilibrium point. In addition, conditions that allow to preserve the port-controlled Hamiltonian structure in the extended closed-loop system are provided. The theory is validated on two physical systems: the magnetic levitated ball and a third order food-chain system. A dynamic control law is constructed for both these systems by assigning a damping factor that cannot be assigned by the classical IDA-PBC.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2015
• Volume: 60
• Issue: 9
• Pages: 2350–2361
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2015.2400663

BibTeX

@article{Nunna_2015,
  title={{Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems}},
  volume={60},
  ISSN={1558-2523},
  DOI={10.1109/tac.2015.2400663},
  number={9},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Nunna, Kameswarie and Sassano, Mario and Astolfi, Alessandro},
  year={2015},
  pages={2350--2361}
}

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