On the modeling, linearization and energy shaping control of mechanical systems

Abstract : In this work some recent results on the linearization and passivity-based control of mechanical systems are reviewed from a unified perspective. This is established by adopting a generalization of the Poisson bracket formalism to more general structures than smooth functions. In this manner, the corresponding geometric structures as well as their respective energy terms are all expressed by simple, identifiable terms. More precisely, the objective consists in illustrating that the proposed framework captures the essential terms involved in the conditions of the literature, reveals the connection between the results in linearization and stabilization, and reduces the cumbersome calculations. In this direction, the generalized Poisson bracket is shown to be an effective tool that leads to (i) the refinement of well-known results on interconnection and damping assignment passivity-based control (IDA-PBC), (ii) the derivation of a new set of simplified conditions for partial linearization via a change of coordinates, and (iii) the identification of certain relationships connecting the Hamiltonian with the Euler-Lagrange description.
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Submitted on : Wednesday, January 16, 2013 - 12:04:36 PM
Last modification on : Thursday, December 5, 2019 - 5:18:51 PM

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Ioanis Sarras, Roméo Ortega, Arjan van der Schaft. On the modeling, linearization and energy shaping control of mechanical systems. LHMNLC 2012, Aug 2012, Bertinoro, Italy. pp.161-166, ⟨10.3182/20120829-3-IT-4022.00040⟩. ⟨hal-00776826⟩

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