Swing-Up Control Design for Spring Attatched Passive Joint Acrobot
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International Journal of Precision Engineering and Manufacturing https://doi.org/10.1007/s12541-020-00374-0
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Swing‑Up Control Design for Spring Attatched Passive Joint Acrobot Inhyuk Baek1 · Hyeonguk Kim2 · Seungchan Lee1 · Soonwoong Hwang3 · Kyoosik Shin4 Received: 18 December 2019 / Revised: 7 June 2020 / Accepted: 15 June 2020 © Korean Society for Precision Engineering 2020
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. Keywords Acrobot · Lyapunov function · Swing-up control · Underactuated mechanical system
1 Introduction An underactuated mechanical system (UMS) has fewer control inputs than degrees of freedom (DOF) of the system. Because of this, UMS has directions in which the controller * Kyoosik Shin [email protected] Inhyuk Baek [email protected] Hyeonguk Kim [email protected] Seungchan Lee [email protected] Soonwoong Hwang [email protected] 1
Department of Mechatronics Engineering, Hanyang University, 55 Hanyangdeahak‑ro, Sangnok‑gu, Ansan‑si, Gyeonggi‑do 15588, Republic of Korea
2
The Future Technology Research Team, Hyundai Mobis, 37, Cheoldobangmulgwan‑ro, Uiwang‑si, Gyeonggi‑do 16082, Republic of Korea
3
The Industrialization Support Division, Korea Institute of Manufacturing Innovation, 55 Hanyangdeahak‑ro, Sangnok‑gu, Ansan‑si, Gyeonggi‑do 15588, Republic of Korea
4
Department of Robot Engineering, Hanyang University, 55 Hanyangdeahak‑ro, Sangnok‑gu, Ansan‑si, Gyeonggi‑do 15588, Republic of Korea
cannot accelerate the system immediately. Also, since it generally has nonlinearity, a nonholonomic constraint, and no full-state feedback linearization, it is hard to apply classical linear control theory to UMS directly [1]. For the above reasons, UMS is more difficult to control than fully actuated systems. So, many researchers have been interested in simple versions of UMS, such as 2-DOF. For example, some researchers presented 2-DOF UMSs to study active vibration damping [2, 3]. In some cases, the bridge and hoist motions of the overhead crane were fixed to make a 2-DOF UMS [4]. Besides these systems, the Cart-pole, inertia wheel pendulum (IWP), translational oscillator with rotational actuator (TORA), Acrobot, and Pendubot are also representative UMSs designed to study control, etc. The
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