Controlled Lagrangian approach to the stabilization of the inverted pendulum system

A controlled Lagrangian approach is presented for the stabilization of an inverted pendulum mounted on a cart. The stabilization strategy consists in forcing the closed-loop system to behave as an Euler-Lagrange system, with a fixed inertia matrix. For carrying it out, it is necessary to adequately...

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Detalles Bibliográficos
Autores: C. Aguilar-Ibañez, O. Octavio Gutierrez F., H. Sossa A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:México
Institución:Instituto Politécnico Nacional
Repositorio:Redalyc-IPN
OAI Identifier:oai:redalyc.org:57016047011
Acceso en línea:https://www.redalyc.org/articulo.oa?id=57016047011
Access Level:acceso abierto
Palabra clave:Física, Astronomía y Matemáticas
Euler
energy balance
Lagrange system
Lyapunov method
Descripción
Sumario:A controlled Lagrangian approach is presented for the stabilization of an inverted pendulum mounted on a cart. The stabilization strategy consists in forcing the closed-loop system to behave as an Euler-Lagrange system, with a fixed inertia matrix. For carrying it out, it is necessary to adequately shape the potential and kinetic energies of the closed-loop system. The idea behind this procedure is to make an energy-balance between the overall energy of the pendulum system and the dissipation energy produced by the action of the control force. The resulting closed-loop system is locally asymptotically stable about its unstable equilibrium point with a very large attraction domain.