﻿ 四旋翼无人机轨迹稳定跟踪控制
 控制与决策  2020, Vol. 35 Issue (2): 349-356 0

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LI Jun-fang, LI Feng, JI Yue-hui, GAO Qiang. Trajectory stable tracking control of quadrotor UAV[J]. Control and Decision, 2020, 35(2): 349-356. DOI: 10.13195/j.kzyjc.2018.0639.
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### 文章历史

Trajectory stable tracking control of quadrotor UAV
LI Jun-fang , LI Feng , JI Yue-hui , GAO Qiang
School of Electrical and Electronic Engineering, Tianjin University of Technology, Tianjin 300384, China
Abstract: Aiming at the problem of stable tracking control of quadrotor trajectory, a double-loop robust control system is designed to suppress the influence of external disturbance and parameter uncertainty. Firstly, the output regulator is designed for position control based on the dynamic surface internal model method, which can solve the problems of asymptotic tracking and disturbance rejection. Then, the higher order sliding mode is used to design the attitude controller, which can realize the global finite-time convergence, eliminate the chattering and relative order limitation of the system. In order to further improve the control precision, a robust accurate differentiator is adopted to accurately differentiate the attitude angle command signal. Finally, the strict mathematical proof for the stability of the system is given, and compared with PID control and traditional sliding mode control, the simulation results verify the superiority and robustness of the proposed control strategy.
Keywords: quadrotor    output regulation    dynamic surface    higher order sliding mode
0 引言

1 四旋翼无人机动力学模型与分析

 图 1 惯性坐标系与机体坐标系结构示意

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2 位置控制器设计 2.1 系统状态方程及外系统

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2.2 位置系统内模设计 2.2.1 计算零误差不变流形

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2.2.2 系统浸入与内模变换

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ϕ=Γ{T - 1}, η=Tτ, 利用确定性等价原则得到内模的标准参数化形式如下:

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2.3 位置增广系统镇定控制器设计

step 1:设ez1 = σz1 - σz1d, 取σz1d = 0.选取关于ez1的Lyapunov候选函数

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σz2通过一阶滤波器, 有

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step 2:定义

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3 姿态控制器设计

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β1, β2, β3均大于0, 且要保证多项式λ3 + β3λ2 + β2λ + β1满足Hurwitz稳定性判据, αi(i = 1, 2, 3)满足, i = 2, 3, α4 = 1.

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4 稳定性分析

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k1, k2, ..., kn > 0, 使得Sn + knSn - 1 +... + k2s + k1为Hurwitz多项式, 考虑如下系统[22]:

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5 仿真结果及分析

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 图 2 x, y, z, ψ跟踪仿真对比结果

 图 3 横滚角φ和俯仰角θ仿真对比结果

 图 4 控制量仿真结果

 图 5 正弦波干扰下轨迹跟踪仿真对比结果

 图 6 白噪声干扰下轨迹跟踪仿真对比结果

6 结论