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...
| Autores: | , , |
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| 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 |
| 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. |
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