Xin Xin, Liu Yannian, Izumi Shinsaku, Yamasaki Taiga, She Jinhua
Faculty of Computer Science and Systems Engineering, Okayama Prefectural University, 111 Kuboki, Soja, Okayama 719-1197, Japan.
School of Automation, Southeast University, and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Nanjing 210018, China.
ISA Trans. 2023 Sep;140:109-120. doi: 10.1016/j.isatra.2023.06.011. Epub 2023 Jun 22.
In this paper, we address the swing-down control of the Acrobot, a two-link planar robot operating in a vertical plane with only the second joint being actuated. The control objective is to rapidly stabilize the Acrobot around the downward equilibrium point, with both links in the downward position, from almost all initial states. Under the conditions of no friction and measurability of only the angle and angular velocity of the actuated joint, we present a sinusoidal-derivative (SD) controller. This controller consists of a linear feedback of the sinusoidal function of the angle of the actuated joint and a linear feedback of its angular velocity. We prove that the control objective is achieved if the sinusoidal gain is greater than a negative constant and the derivative gain is positive. We establish crucial relationships between the relative stability of the Acrobot under the SD controller and its physical parameters, presenting analytically all optimal control gains. These gains minimize the real parts of the dominant poles of the linearized model of the resulting closed-loop system around the downward equilibrium point. We demonstrate that the resulting dominant closed-loop poles can be double complex conjugate poles, or a quadruple real pole, or a triple real pole, depending on the Acrobot's physical parameters. Simulation studies indicate that the proposed SD controller outperforms the derivative (D) controller in rapidly stabilizing the Acrobot at the downward equilibrium point.
在本文中，我们研究了杂技机器人的下摆控制问题。该机器人是一个双连杆平面机器人，在垂直平面内运行，仅第二个关节有驱动。控制目标是从几乎所有初始状态出发，使杂技机器人在两连杆均处于向下位置的向下平衡点附近快速稳定下来。在无摩擦且仅可测量驱动关节的角度和角速度的条件下，我们提出了一种正弦 - 导数（SD）控制器。该控制器由驱动关节角度的正弦函数的线性反馈及其角速度的线性反馈组成。我们证明，如果正弦增益大于一个负常数且导数增益为正，则可实现控制目标。我们建立了SD控制器作用下杂技机器人的相对稳定性与其物理参数之间的关键关系，解析地给出了所有最优控制增益。这些增益使所得闭环系统围绕向下平衡点的线性化模型的主导极点的实部最小化。我们证明，根据杂技机器人的物理参数，所得的主导闭环极点可以是一对复共轭极点、一个四重实极点或一个三重实极点。仿真研究表明，所提出的SD控制器在使杂技机器人快速稳定在向下平衡点方面优于导数（D）控制器。
