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IEEE Transactions on Automatic Control
Article . 2007 . Peer-reviewed
License: IEEE Copyright
Data sources: Crossref
https://doi.org/10.1007/978-3-...
Part of book or chapter of book . 2007 . Peer-reviewed
Data sources: Crossref
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Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Authors: Romeo Ortega; José Ángel Acosta; Ravi N. Banavar; G. Viola; Alessandro Astolfi; Alessandro Astolfi;

Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Abstract

Total energy shaping is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Lagrangian or Hamiltonian structure with a desired energy function - that qualifies as Lyapunov function for the desired equilibrium. The success of the method relies on the possibility of solving two PDEs which identify the kinetic and potential energy functions that can be assigned to the closed loop. Particularly troublesome is the partial differential equation (PDE) associated to the kinetic energy which is nonlinear and inhomogeneous and the solution, that defines the desired inertia matrix, must be positive-definite. In this note, we prove that we can eliminate or simplify the forcing term in this PDE by modifying the target dynamics and introducing a change of coordinates in the original system. Furthermore, it is shown that, in the particular case of transformation to the Lagrangian coordinates, the possibility of simplifying the PDEs is determined by the interaction between the Coriolis and centrifugal forces and the actuation structure. The examples of pendulum on a cart and Furuta's pendulum are used to illustrate the results.

Country
India
Keywords

Passivity-Based Control, Damping Assignment, Energy Shaping, Hamiltonian-Systems, Interconnection, Stabilization, 531, Mechanical Systems, Nonlinear Control

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
99
Top 10%
Top 10%
Top 10%
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