四旋翼吊运系统滑模抗摆控制方法

doi:10.13229/j.cnki.jdxbgxb.20241340

吉林大学学报(工学版) ›› 2026, Vol. 56 ›› Issue (7): 1798-1810.doi: 10.13229/j.cnki.jdxbgxb.20241340

• 车辆工程·机械工程 • 上一篇

四旋翼吊运系统滑模抗摆控制方法

文斌^1,²(),吕文丹²,梅启程²,魏雅慧³(),吴凯²

^1.梯级水电站运行与控制湖北省重点实验室（三峡大学），湖北宜昌 443002
^2.三峡大学电气与新能源学院，湖北宜昌 443002
^3.三峡大学创新创业学院（大学生素质教育中心），湖北宜昌 443002

收稿日期:2024-12-18 出版日期:2026-07-01 发布日期:2026-08-12
通讯作者: 魏雅慧 E-mail:wenbin_08@126.com;weiyahui@ctgu.edu.cn
作者简介:文斌（1985-），男，讲师，博士.研究方向：鲁棒控制理论，非线性系统理论.E-mail：wenbin_08@126.com
基金资助:
国家自然科学基金项目(62273200);湖北省输电线路工程技术研究中心研究基金项目(2022KXL03);湖北省自然科学基金联合基金项目(2024AFD409)

Sliding mode anti-sway control methods for quadrotor transportation systems

Bin WEN^1,²(),Wen-dan LV²,Qi-cheng MEI²,Ya-hui WEI³(),Kai WU²

^1.Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower Station（China Three Gorges University），Yichang 443002，China
^2.College of Electrical Engineering & New Energy，China ThreeGorges University，Yichang 443002，China
^3.Innovation and Entrepreneurship College（Undergraduate Quality Education Center），China Three Gorges University，Yichang 443002，China

Received:2024-12-18 Online:2026-07-01 Published:2026-08-12
Contact: Ya-hui WEI E-mail:wenbin_08@126.com;weiyahui@ctgu.edu.cn

摘要/Abstract

摘要：

针对四旋翼吊运系统在运输任务中因负载摆动导致轨迹跟踪性能下降的问题，提出了一种基于非线性扩张状态观测器的非奇异快速滑模抗摆控制方案。通过Lagrange-Euler方程建立四旋翼吊运系统的动力学模型，并将系统分解为位置控制、姿态控制和摆角抑制3个子系统。针对各子系统分别设计非奇异快速滑模控制器，结合NESO对模型不确定性、外部扰动及传感器噪声进行实时估计与补偿。仿真结果表明：相较于无摆角抑制的控制方案，本文方法使负载摆角最大幅度减少约30%，摆动持续时间和负载振荡次数都大大降低，同时位置与姿态子系统的轨迹跟踪精度显著提升。该方案通过动态解耦与协同控制设计兼顾了系统鲁棒性与计算效率，为四旋翼吊运系统的工程应用提供了有效解决方案。

关键词: 导航制导与控制, 四旋翼吊运系统, 非奇异快速终端滑模, 非线性扩张状态观测器, 摆动抑制

Abstract:

A control scheme using non-singular fast sliding mode control and a Nonlinear Extended State Observer （NESO） is proposed to solve the problem of reduced trajectory tracking performance caused by load swinging during transport in quadrotor load transportation systems.First，the dynamic model of the quadrotor system is built using Lagrange-Euler equations.The system is divided into three parts： position control， attitude control， and swing angle suppression.Controllers are designed for each part.NESO is used to estimate and compensate for uncertainties，disturbances，and noise in real time.Simulations show that this method reduces the maximum load swing angle by about 30%，and significantly cuts swing duration and load oscillation times compared to methods without swing control.It also improves the trajectory tracking accuracy of position and attitude controls.This scheme balances robustness and efficiency through decoupled and coordinated control，offering a practical solution for quadrotor transportation systems.

Key words: navigation，guidance，and control, quadrotor transportation system, non-singular fast terminal sliding mode, nonlinear extended state observer, swing suppression

中图分类号:

TP273

文斌,吕文丹,梅启程,魏雅慧,吴凯. 四旋翼吊运系统滑模抗摆控制方法[J]. 吉林大学学报(工学版), 2026, 56(7): 1798-1810.

Bin WEN,Wen-dan LV,Qi-cheng MEI,Ya-hui WEI,Kai WU. Sliding mode anti-sway control methods for quadrotor transportation systems[J]. Journal of Jilin University(Engineering and Technology Edition), 2026, 56(7): 1798-1810.

图/表 15

图1

表1

建立模型所用变量解释"

符号	意义
$x, y, z$	四旋翼质心的位置在惯性坐标系的位置坐标
$M$	无人机的质量
$α$	吊挂绳在 $y o z$ 平面的投影与 $z$ 轴的夹角
$ω 1 ? 4$	4个旋翼的转速
$l$	四旋翼的轴距
$?, θ, ψ$	绕机体坐标系 $x b, y b, z b$ 三轴逆时针转动的角度
$m$	负载的质量
$β$	吊挂绳与 $y o z$ 平面的夹角
$g$	重力加速度
$L$	吊挂绳的长度

表1

图2

表2

四旋翼吊运系统模型参数"

符号	参数	符号	参数
$M$	2.00 kg	$m$	0.40 kg
$l$	0.20 m	$L$	0.30 m
$I x, I y$	1.25 Ns²/rad	$I z$	2.5 Ns²/rad

表2

表3

滑模控制器参数"

符号	参数	符号	参数
$a x, y, z$	0.8	$c x, y, z$	0.5
$k 1 (x, y, z)$	1	$k 2 (x, y, z)$	1
$a ?, θ, ψ, α, β$	5	$c ?, θ, ψ, α, β$	1
$k 1 (?, θ, ψ, α, β)$	2	$k 2 (?, θ, ψ, α, β)$	2

表3

表4

三阶扩张状态观测器参数"

符号	参数	符号	参数
$μ 1 x, y, z$	100	$μ 1 (?, θ, ψ)$	50
$μ 2 x, y, z$	50	$μ 2 (?, θ, ψ)$	10
$μ 3 x, y, z$	20	$μ 3 (?, θ, ψ)$	10

表4

图3

表5

图4

图5

图6

图7

图8

图9

表6

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负载质量/kg	最大摆动幅度/rad		摆动持续时间/s
负载质量/kg	有抑制	无抑制	有抑制	无抑制
0.2	0.456	0.742	5.006	>20
0.3	0.456	0.744	5.018	>20
0.4	0.456	0.744	5.022	>20
0.5	0.455	0.732	5.032	>20
0.6	0.454	0.707	5.040	>20

指标	本文方法	ADRC^［16］	BPNN-ADRC ^［17］
最大摆动幅度/rad	0.451	0.595	0.574
摆动持续时间/s	5.022	5.285	5.101
振荡次数/次	1	3	2

四旋翼吊运系统滑模抗摆控制方法

Sliding mode anti-sway control methods for quadrotor transportation systems

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