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Dynamic Surface Control of Uncertain Nonlinear Systems pp 123–151Cite as

Multi-Input Multi-Output Mechanical Systems

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Part of the book series: Communications and Control Engineering ((CCE))

Abstract

This chapter presents the -gain analysis of Dynamic Surface Control (DSC) for a holonomic system which is a class of interconnected mechanical systems. First, the preliminary design procedure of DSC for multi-input multi-output (MIMO) interconnected mechanical systems of N particles is presented. Then, to provide a closed-loop form with provable stability properties, augmented error dynamics for a nonlinear holonomic system with DSC are derived. Second, a numerical algorithm to calculate the -gain of the augmented error dynamics is presented in the framework of convex optimization. Furthermore, the proposed analysis and design methodology of DSC is extended to a holonomic system of N interconnected rigid bodies, and is applied to biped walking of a 5-link biped robot. Finally the performance of the controller for single-leg support phase in biped walking will be shown in terms of gain via simulations.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Ajou University, San 5, Wonchon-dong, Yeongtong-gu, 443-749, Suwon, Korea, Republic of (South Korea)

    Bongsob Song

  2. Department of Mechanical Engineering, University of California at Berkeley, 5104 Etcheverry Hall, Mailstop 1740, 94720, Berkeley, USA

    J. Karl Hedrick

Authors
  1. Bongsob Song
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  2. J. Karl Hedrick
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Correspondence to Bongsob Song .

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© 2011 Springer-Verlag London Limited

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Song, B., Hedrick, J.K. (2011). Multi-Input Multi-Output Mechanical Systems. In: Dynamic Surface Control of Uncertain Nonlinear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-632-0_6

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  • DOI: https://doi.org/10.1007/978-0-85729-632-0_6

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-631-3

  • Online ISBN: 978-0-85729-632-0

  • eBook Packages: EngineeringEngineering (R0)

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