Abstract
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.
Original language | English |
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Pages (from-to) | 329-335 |
Number of pages | 7 |
Journal | Revista Mexicana de Fisica |
Volume | 54 |
Issue number | 4 |
State | Published - Aug 2008 |
Keywords
- Energy balance
- Euler-Lagrange system
- Lyapunov method