| 引用本文: | 张永立,程会锋,李洪兴.三级倒立摆的自动摆起与稳定控制[J].控制理论与应用,2011,28(1):37~45.[点击复制] |
| ZHANG Yong-li,CHENG Hui-feng,LI Hong-xing.The swing-up and stabilization of the triple inverted pendulum[J].Control Theory and Technology,2011,28(1):37~45.[点击复制] |
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| 三级倒立摆的自动摆起与稳定控制 |
| The swing-up and stabilization of the triple inverted pendulum |
| 摘要点击 3493 全文点击 3045 投稿时间：2009-11-23 修订日期：2010-03-17 |
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| DOI编号 10.7641/j.issn.1000-8152.2011.1.CCTA091491 |
| 2011,28(1):37-45 |
| 中文关键词 三级倒立摆 逆系统前馈控制 两点边值问题 增益调度反馈控制 变增益LQR |
| 英文关键词 triple inverted pendulum inversion-based feedforward control two-point boundary value problem feedback control based on gain-scheduled variable-gain linear quadratic regulator(VGLQR) |
| 基金项目 教育部高等学校博士学科点专项科研基金资助项目(20090041110003); 国家自然科学基金资助项目(60774049, 60834004); 国家“973”计划资助项目(2009CB320602). |
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| 中文摘要 |
| 采用非线性逆系统轨迹控制实现三级倒立摆的自动摆起, 并设计了变增益LQR控制器将其稳定在竖直倒立位置. 首先, 三级倒立摆从静止下垂状态摆起到竖直倒立位置的过程, 从数学角度看是一个两点边值问题, 通过求解该两点边值问题获得摆起的标称轨迹, 利用逆系统方法设计前馈控制, 同时结合增益调度反馈控制使摆起过程稳定; 其次, 在稳定控制阶段, 采用基于逐点线性化的变增益LQR控制器, 实现倒立摆的稳定控制. 仿真实验验证了本方案的有效性. |
| 英文摘要 |
| The swing-up of the triple inverted pendulum is achieved by inversion-based trajectory control. The variablegain linear quadratic regulator is designed to stabilize the triple inverted pendulum in the upward position. The transient process of swing-up of the triple inverted pendulum is treated as a nonlinear two-point boundary value problem. The normal trajectories of swing-up are obtained by solving a two-point boundary value problem, and a feedforward control is designed by using the inverse system method. A gain-scheduled feedback is used to stabilize the system during the swing-up. In addition, the triple inverted pendulum in the upward position is stabilized by utilizing the variable-gain linear quadratic regulator. Simulation results demonstrate the effectiveness of the proposed control scheme. |