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                    四旋翼吊掛運輸系統動態反饋線性化軌跡控制

                    梁曉 胡欲立

                    梁曉, 胡欲立. 四旋翼吊掛運輸系統動態反饋線性化軌跡控制. 自動化學報, 2020, 46(9): 1993?2002 doi: 10.16383/j.aas.c180857
                    引用本文: 梁曉, 胡欲立. 四旋翼吊掛運輸系統動態反饋線性化軌跡控制. 自動化學報, 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

                    四旋翼吊掛運輸系統動態反饋線性化軌跡控制

                    doi: 10.16383/j.aas.c180857
                    詳細信息
                      作者簡介:

                      梁曉:西北工業大學航海學院兵器科學與技術專業博士研究生.主要研究方向為無人機運輸系統控制.本文通信作者. E-mail: lzy20131110@sina.com

                      胡欲立:西北工業大學航海學院水下航行器研究所教授. 主要研究方向為水下航行器設計與制造. E-mail: zx670821@nwpu.edu.cn

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

                    • 摘要: 三維空間下的四旋翼吊掛運輸系統是一種欠驅動、強耦合、多變量的非線性系統. 根據系統的動力學特點, 將系統分解為雙質點系繩連接子系統和四旋翼姿態控制子系統. 選擇與系統自由度維數相同的廣義坐標并基于虛位移原理計算對應的廣義力, 從而建立系統的拉格朗日動力學方程. 利用微分平滑特性證明了運輸系統存在平凡零動態, 因此可通過動態反饋轉化為線性和能控系統. 經過2次動態擴展和變量代換, 原系統擴展為總相對階等于系統狀態維度的線性能控系統. 基于赫爾維茨穩定性判據, 設計了跟蹤誤差指數收斂的動態反饋控制律. 該方法可作為一類非線性系統控制器設計的標準方法. 最后以三維空間的螺旋曲線及水平面內頻率變化的圓周曲線為參考軌跡進行仿真, 仿真結果驗證了控制系統的有效性.
                    • 圖  1  四旋翼吊掛運輸系統

                      Fig.  1  A quadrotor with cable-suspended load

                      圖  2  跟蹤控制系統結構圖

                      Fig.  2  Tracking controller block diagram

                      圖  3  兩種控制方法下螺旋曲線跟蹤軌跡對比((a)動態反饋控制方法; (b)幾何控制方法)

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

                      圖  4  兩種控制方法下跟蹤螺旋曲線誤差收斂情況對比((a)動態反饋控制方法; (b)幾何控制方法)

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

                      圖  5  xoy平面螺旋曲線跟蹤軌跡

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

                      圖  6  xoz平面螺旋曲線跟蹤軌跡

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

                      圖  7  螺旋曲線跟蹤過程中控制力曲線

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

                      圖  8  螺旋曲線跟蹤過程中系繩振蕩角曲線

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

                      圖  9  兩種控制方法跟蹤圓周曲線軌跡對比(a)動態反饋控制方法; (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

                      圖  10  兩種控制方法跟蹤圓周曲線誤差收斂情況對比((a)動態反饋方法; (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)

                      圖  11  跟蹤過程中四旋翼位置變化曲線

                      Fig.  11  Position curve of quadrotor when tracking

                      圖  12  跟蹤過程中 $ \beta $ 角變化曲線

                      Fig.  12  Curve of $ \beta $ when tracking

                      表  1  仿真中使用的模型參數

                      Table  1  Model parameters in the simulations

                      變量 參數 單位
                      mq 0.4 kg
                      ml 0.1 kg
                      l1 0.8 m
                      l2 0.2 m
                      g ?9.8 m·s?2
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                    • 收稿日期:  2018-12-27
                    • 錄用日期:  2019-06-02
                    • 網絡出版日期:  2020-09-28
                    • 刊出日期:  2020-09-28

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