Multi-Input Multi-Output Mechanical Systems

  • Bongsob Song
  • J. Karl Hedrick
Part of the Communications and Control Engineering book series (CCE)


This chapter presents the Open image in new window -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 Open image in new window -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 Open image in new window gain via simulations.


Positive Definite Matrix Error Dynamic Controller Gain Biped Robot Biped Walking 
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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringAjou UniversitySuwonKorea, Republic of (South Korea)
  2. 2.Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyUSA

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