The matching equations of energy shaping controllers for mechanical systems are not simplified with generalized forces - CentraleSupélec Access content directly
Conference Papers Year : 2012

The matching equations of energy shaping controllers for mechanical systems are not simplified with generalized forces

Naveena Crasta
  • Function : Author
Roméo Ortega
  • Function : Author
  • PersonId : 848065
Harish Pillai
  • Function : Author

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. The success of the method relies on the possibility of solving two partial dierential equations (PDE) which identify the kinetic and potential energy functions that can be assigned to the closed-loop. Particularly troublesome is the PDE associated to the kinetic energy which is quasi-linear and inhomogeneous and the solution, that denes the desired inertia matrix, must be positive denite. This task is simplied by the inclusion of gyroscopic forces in the target dynamics, which translates into the presence of a free skew-symmetric matrix in the matching equations that reduces the number of PDE's to be solved. Recently, it has been claimed that considering a more general form for the target dynamic forces, that relax the skew-symmetry condition, further reduces the number of PDE's. The purpose of this paper is to prove that this claim is wrong.

Dates and versions

hal-00776843 , version 1 (16-01-2013)

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Naveena Crasta, Roméo Ortega, Harish Pillai, Jose Guadalupe Romero Velazquez. The matching equations of energy shaping controllers for mechanical systems are not simplified with generalized forces. LHMNLC 2012, Aug 2012, Bertinoro, Italy. pp.48-53, ⟨10.3182/20120829-3-IT-4022.00023⟩. ⟨hal-00776843⟩
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