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A limit set stabilization by means of the Port Hamiltonian system approach
Author(s) -
AguilarIbañez Carlos,
MendozaMendoza Julio A.,
Martinez Juan C.,
Jesus Rubio Jose,
SuarezCasta Miguel S.
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3160
Subject(s) - control theory (sociology) , hamiltonian system , hamiltonian (control theory) , interconnection , nonlinear system , limit (mathematics) , mathematics , dc motor , limit set , partial differential equation , affine transformation , mathematical analysis , computer science , mathematical optimization , control (management) , physics , pure mathematics , computer network , quantum mechanics , artificial intelligence
Summary A solution to the stabilization problem of a compact set by means of the Interconnection and Damping Assignment Passivity‐Based Control methodology, for an affine nonlinear system, was introduced. To this end, we expressed the closed‐loop system as a Port Hamiltonian system, having the property of almost all their trajectories asymptotically converge to a convenient limit set, except for a set of measure zero. It was carried out by solving a partial differential equation (PDE) or single matching condition, which allows the desired energy level or limit set E to be shaped explicitly. The control strategy was tested using the magnetic beam balance system and the pendulum actuated by a direct current motor (DC‐motor), having obtained satisfactory results. Copyright © 2014 John Wiley & Sons, Ltd.