Physical dissipation and the method of controlled Lagrangians

C. A. Woolsey, A. M. Bloch, N. E. Leonard, J. E. Marsden

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Scopus citations

Abstract

We describe the effect of physical dissipation on stability of equilibria which have been stabilized, in the absence of damping, using the method of controlled Lagrangians. This method applies to a class of underactuated mechanical systems including 'balance' systems such as the pendulum on a cart. Since the method involves modifying a system's kinetic energy metric through feedback, the effect of dissipation is obscured. In particular, it is not generally true that damping makes a feedback-stabilized equilibrium asymptotically stable. Damping in the unactuated directions does tend to enhance stability, however damping in the controlled directions must be 'reversed' through feedback. In this paper, we suggest a choice of feedback dissipation to locally exponentially stabilize a class of controlled Lagrangian systems.

Original languageEnglish (US)
Title of host publication2001 European Control Conference, ECC 2001
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2570-2575
Number of pages6
ISBN (Electronic)9783952417362
DOIs
StatePublished - 2001
Event6th European Control Conference, ECC 2001 - Porto, Portugal
Duration: Sep 4 2001Sep 7 2001

Publication series

Name2001 European Control Conference, ECC 2001

Other

Other6th European Control Conference, ECC 2001
CountryPortugal
CityPorto
Period9/4/019/7/01

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Keywords

  • Dissipative and Energy-based Design
  • Stabilization of Non-linear Systems

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    Woolsey, C. A., Bloch, A. M., Leonard, N. E., & Marsden, J. E. (2001). Physical dissipation and the method of controlled Lagrangians. In 2001 European Control Conference, ECC 2001 (pp. 2570-2575). [7076315] (2001 European Control Conference, ECC 2001). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ecc.2001.7076315