| Resumen |
This study presents the design of a feedback-based smooth and continuous control action, for the movement stabilization of a mechanical system consisting of a dampen pendulum mounted on a cart. The design assumes that the pendulum is initialized in the upper-half plane. Also assumes that the involved viscous friction force is known. The control strategy is based on some nonlinear transformations that allow rewriting the system as if it were a simple chain of integrators of fourth-degree, perturbed by a nonlinear function. This nonlinear function, which models the dynamics of the original system, vanishes at the origin. Once the system has been transformed, the simple control action, consisted of two parts, one linear and other nonlinear or linear by parts (saturation function), is applied. After that, the linear part of the control action brought the pendulum near to the origin. The stability analysis, was carried out using several positive functions. Convincing numerical simulations and laboratory experiments were included.
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