Abstracto
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A solvability of the direct Lyapunov first matching condition in terms of the generalized coordinates method is presented for the stabilization of underactuated, inverted pendulum cart. This work represents a continued development of previously published techniques for the exact controller design formulation without introducing control law terms or approximations. The use of the control law, instead of inverse dynamics to determine the coordinate histories for the unspecified axes, produced good performance results showing a faster response to stabilize both the actuated and non-actuated axes. The stability is achieved from the proper shape of the potential, the positive definiteness of the KD matrix, and the non-positive rate of change of the Lyapunov function.
Authors: Deyka García, Marcelo Coronado and Antony García