Article
A family of smooth controllers for swinging up a pendulum
Author/s | Aström, K. J.
Aracil Santonja, Javier Gordillo Álvarez, Francisco |
Department | Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática |
Publication Date | 2008 |
Deposit Date | 2015-03-06 |
Published in |
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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 ... 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. |
Funding agencies | Ministerio de Ciencia y Tecnología (MCYT). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
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