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四旋翼吊挂运输系统动态反馈线性化轨迹控制

梁晓 胡欲立

梁晓, 胡欲立. 四旋翼吊挂运输系统动态反馈线性化轨迹控制. 自动化学报, 2020, 46(9): 1993−2002 doi: 10.16383/j.aas.c180857
引用本文: 梁晓, 胡欲立. 四旋翼吊挂运输系统动态反馈线性化轨迹控制. 自动化学报, 2020, 46(9): 1993−2002 doi: 10.16383/j.aas.c180857
Liang Xiao, Hu Yu-Li. Trajectory control of quadrotor with cable-suspended load via dynamic feedback linearization. Acta Automatica Sinica, 2020, 46(9): 1993−2002 doi: 10.16383/j.aas.c180857
Citation: Liang Xiao, Hu Yu-Li. Trajectory control of quadrotor with cable-suspended load via dynamic feedback linearization. Acta Automatica Sinica, 2020, 46(9): 1993−2002 doi: 10.16383/j.aas.c180857

四旋翼吊挂运输系统动态反馈线性化轨迹控制

doi: 10.16383/j.aas.c180857
详细信息
    作者简介:

    梁晓:西北工业大学航海学院兵器科学与技术专业博士研究生.主要研究方向为无人机运输系统控制.本文通信作者. E-mail: lzy20131110@sina.com

    胡欲立:西北工业大学航海学院水下航行器研究所教授. 主要研究方向为水下航行器设计与制造. E-mail: zx670821@nwpu.edu.cn

Trajectory Control of Quadrotor With Cable-Suspended Load via Dynamic Feedback Linearization

  • 摘要: 三维空间下的四旋翼吊挂运输系统是一种欠驱动、强耦合、多变量的非线性系统. 根据系统的动力学特点, 将系统分解为双质点系绳连接子系统和四旋翼姿态控制子系统. 选择与系统自由度维数相同的广义坐标并基于虚位移原理计算对应的广义力, 从而建立系统的拉格朗日动力学方程. 利用微分平滑特性证明了运输系统存在平凡零动态, 因此可通过动态反馈转化为线性和能控系统. 经过2次动态扩展和变量代换, 原系统扩展为总相对阶等于系统状态维度的线性能控系统. 基于赫尔维茨稳定性判据, 设计了跟踪误差指数收敛的动态反馈控制律. 该方法可作为一类非线性系统控制器设计的标准方法. 最后以三维空间的螺旋曲线及水平面内频率变化的圆周曲线为参考轨迹进行仿真, 仿真结果验证了控制系统的有效性.
  • 图  1  四旋翼吊挂运输系统

    Fig.  1  A quadrotor with cable-suspended load

    图  2  跟踪控制系统结构图

    Fig.  2  Tracking controller block diagram

    图  3  两种控制方法下螺旋曲线跟踪轨迹对比((a)动态反馈控制方法; (b)几何控制方法)

    Fig.  3  Track a spiral curve via two control methods. ((a) Dynamic feedback control; (b) Geometry control)

    图  4  两种控制方法下跟踪螺旋曲线误差收敛情况对比((a)动态反馈控制方法; (b)几何控制方法)

    Fig.  4  Position errors convergence when tracking a spiral curve via two control methods. ((a) Dynamic feedback control; (b) Geometry control)

    图  5  xoy平面螺旋曲线跟踪轨迹

    Fig.  5  Trajectory in xoy plane when tracking a spiral curve

    图  6  xoz平面螺旋曲线跟踪轨迹

    Fig.  6  Trajectory in xoz plane when tracking a spiral curve

    图  7  螺旋曲线跟踪过程中控制力曲线

    Fig.  7  Curve of the control force when tracking a spiral curve

    图  8  螺旋曲线跟踪过程中系绳振荡角曲线

    Fig.  8  Curve of swing angel on the cable when tracking a spiral curve

    图  9  两种控制方法跟踪圆周曲线轨迹对比(a)动态反馈控制方法; (b)分段控制方法

    Fig.  9  Track a circle via two control methods. (a) Dynamic feedback control; (b) Two-time-scale control

    图  10  两种控制方法跟踪圆周曲线误差收敛情况对比((a)动态反馈方法; (b)分段控制方法)

    Fig.  10  Position errors convergence when tracking a circle curve via two control methods. ((a) Dynamic feedback control; (b) Two-time-scale control)

    图  11  跟踪过程中四旋翼位置变化曲线

    Fig.  11  Position curve of quadrotor when tracking

    图  12  跟踪过程中 $ \beta $ 角变化曲线

    Fig.  12  Curve of $ \beta $ when tracking

    表  1  仿真中使用的模型参数

    Table  1  Model parameters in the simulations

    变量 参数 单位
    mq 0.4 kg
    ml 0.1 kg
    l1 0.8 m
    l2 0.2 m
    g −9.8 m·s−2
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-12-27
  • 录用日期:  2019-06-02
  • 网络出版日期:  2020-09-28
  • 刊出日期:  2020-09-28

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