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On the matching equations of energy shaping controllers for mechanical systems

DSpace at IIT Bombay

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Title On the matching equations of energy shaping controllers for mechanical systems
 
Creator CRASTA, N
ORTEGA, R
PILLAI, HK
 
Subject PASSIVITY-BASED CONTROL
CONTROLLED LAGRANGIANS
DAMPING ASSIGNMENT
HAMILTONIAN-SYSTEMS
STABILIZATION
INTERCONNECTION
energy shaping
mechanical systems
interconnection and damping assignment
 
Description Total energy shaping is a controller design methodology that achieves (asymptotic) stabilisation 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 differential equations (PDEs) 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 (KE) which is quasi-linear and non-homogeneous, and the solution that defines the desired inertia matrix must be positive definite. This task is simplified by the inclusion of gyroscopic forces in the target dynamics, which translates into the presence of a free skew-symmetric matrix in the KE matching equation that reduces the number of PDEs 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 KE PDEs. The purpose of this paper is to prove that this claim is wrong.
 
Publisher TAYLOR & FRANCIS LTD
 
Date 2016-01-15T07:54:28Z
2016-01-15T07:54:28Z
2015
 
Type Article
 
Identifier INTERNATIONAL JOURNAL OF CONTROL, 88(9)1757-1765
0020-7179
1366-5820
http://dx.doi.org/10.1080/00207179.2015.1016453
http://dspace.library.iitb.ac.in/jspui/handle/100/18101
 
Language en