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A family of smooth controllers for swinging up a pendulum


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Author: Aström, K. J.
Aracil, J.
Gordillo, F.
Department: Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática
Date: 2008
Published in: Automatica, 44(7), 1841-1848.
Document type: Article
Abstract: The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law. The properties of the solution can be modified by the parameters in the control law. Control signal saturation can also be taken into account using the Hamiltonian approach.
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DOI: 10.1016/j.automatica.2007.10.040

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