Abstract

AGUILAR-IBANEZ, C.; GUTIERREZ F., O. Octavio  and  SOSSA A., H.. Controlled Lagrangian approach to the stabilization of the inverted pendulum system. Rev. mex. fis. [online]. 2008, vol.54, n.4, pp.329-335. ISSN 0035-001X.

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.

Keywords : Euler-Lagrange system; energy balance; Lyapunov method.

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