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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/8510

Title: Total energy shaping control of mechanical systems: Simplifying the matching equations via coordinate changes
Authors: VIOLA, G
ORTEGA, R
BANAVAR, R
ACOSTA, JA
ASTOLFI, A
Keywords: passivity-based control
hamiltonian-systems
damping assignment
interconnection
stabilization
Issue Date: 2007
Publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Citation: IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 52(6), 1093-1099
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 Furma's pendulum are used to illustrate the results.
URI: http://dx.doi.org/10.1109/TAC.2007.899064
http://dspace.library.iitb.ac.in/xmlui/handle/10054/8510
http://hdl.handle.net/10054/8510
ISSN: 0018-9286
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