IDA-PBC for Underactuated Mechanical Systems in Implicit Port-Hamiltonian Representation

Authors

Oscar B. Cieza, Johann Reger

Abstract

Partial differential equations (PDEs) persist to be a stumbling block in Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). Lately, for a class of mechanical systems an energy shaping controller has been investigated that avoids PDEs by exploiting implicit port-Hamiltonian representations. Following the same research line, in this paper we generalize the total energy shaping IDA-PBC for underactuated mechanical systems in the implicit framework and propose an algebraic solution for a class of systems. Besides, under some additional conditions we are also able to produce a respective output feedback. A reduction of the closed loop system in explicit coordinates is presented. We test our results on the inclined cart-pole system and portal crane.

Citation

• Journal: 2019 18th European Control Conference (ECC)
• Year: 2019
• Volume:
• Issue:
• Pages:
• Publisher: IEEE
• DOI: 10.23919/ecc.2019.8795994

BibTeX

@inproceedings{Cieza_2019,
  title={{IDA-PBC for Underactuated Mechanical Systems in Implicit Port-Hamiltonian Representation}},
  DOI={10.23919/ecc.2019.8795994},
  booktitle={{2019 18th European Control Conference (ECC)}},
  publisher={IEEE},
  author={Cieza, Oscar B. and Reger, Johann},
  year={2019}
}

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References

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