Swing-Up Control Design for Spring Attatched Passive Joint Acrobot

Abstract

This paper presents the conditions and PD controller to swing-up the Acrobot to which a spring is attached at the passive joint (first joint). Because the motion of the system is in the vertical plane, there are some system parameters associated with gravity. The range of a spring constant and controller gain that allow the PD controller to swing-up the system is defined depending on these parameter values. To prove that the PD controller makes the system approach the equilibrium points, one of which is swing-up state (upright equilibrium point, UEP), the motion of the first link is analyzed according to the motion of the second link and the torque on the active joint (second joint) with an actuator. Among these equilibrium points, the conditions that can only converge to the UEP of the system are found.