Multi-Input Multi-Output Mechanical Systems

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.

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