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Bond Graph Modelling of Engineering Systems pp 179–194Cite as

Coaxially Coupled Inverted Pendula: Bond Graph-Based Modelling, Design and Control

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Abstract

A bond graph method is used to examine qualitative aspects of a class of unstable under-actuated mechanical systems. It is shown that torque actuation leads to an unstabilisable system, whereas velocity actuation gives a controllable system which has, however, a right-half plane zero. The fundamental limitations theory of feedback control when a system has a right-half plane zero and a right-half plane pole is used to evaluate the desirable physical properties of coaxially coupled inverted pendula. An experimental system which approximates such a system is used to illustrate and validate the approach.

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Notes

  1. 1.

    Octave is the open-source high-level language, primarily intended for numerical computations (similar to the commercial product Matlab), available at www.octave.org

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Acknowledgments

The experimental work was accomplished while the first author was a visiting professor at the University of New South Wales within the Systems and Control Research Group of the School of Electrical Engineering &; Telecommunications supported by the Royal Academy of Engineering International Travel Grant ITG C7-292. At this time, the second author was undertaking a Master’s research project in control engineering. Both authors would like to thank David Clements, Tim Hesketh and Chris Lu for suggesting the project.

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Authors and Affiliations

  1. School of Engineering, University of Glasgow, Scotland, UK

    P.J. Gawthrop

  2. Commonwealth Scientific and Industrial Research Organisation (CSIRO), Hobart, Tasmania, Australia

    F. Rizwi

Authors
  1. P.J. Gawthrop
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  2. F. Rizwi
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Correspondence to P.J. Gawthrop .

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Editors and Affiliations

  1. of Applied Sciences, Bonn-Rhein-Sieg University, Sankt Augustin, 53754, Germany

    Wolfgang Borutzky

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Gawthrop, P., Rizwi, F. (2011). Coaxially Coupled Inverted Pendula: Bond Graph-Based Modelling, Design and Control. In: Borutzky, W. (eds) Bond Graph Modelling of Engineering Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9368-7_5

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  • DOI: https://doi.org/10.1007/978-1-4419-9368-7_5

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-9367-0

  • Online ISBN: 978-1-4419-9368-7

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