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摘要: 主要考虑了四旋翼无人机（Unmanned aerial vehicle，UAV）吊挂飞行系统的位置控制及负载摆动抑制的设计问题.在存在欠驱动特性以及未知系统参数的约束下，本文基于能量法设计了一种非线性控制策略，实现了对无人机位置的精确控制和飞行过程中负载摆动的快速抑制.基于Lyapunov方法的稳定性分析证明了闭环系统的稳定性，位置误差的收敛及摆动的抑制.实验结果表明本文提出的控制策略取得了较好的控制效果.Abstract: In this paper, position control and load swing suppression design for a quadrotor unmanned aerial vehicle (UAV) with a slung-load are investigated. Under the constraints of underactuated feature and unknown system parameters, a nonlinear control strategy is designed based on energy method, which achieves accurate position control of the UAV as well as payload swing fast suppression during the flight. The stability of the closed-loop system, convergence of position error and payload swing suppression are proved by Lyapunov-based stability analysis method. Experimental results show that the proposed control strategy has better control performance.
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图 3 无人机位置$y(t), z(t)$及负载摆角$\theta(t)$
Fig. 3 $y(t), z(t)$ of UAV and payload swing $\theta(t)$
表 1 非线性控制器和LQR控制器调节时间对比
Table 1 Comparison of the settling time between nonlinear controller and LQR controller
调节时间 非线性控制器 LQR控制器 $t_s$$_y$ 16 s 22 s $t_s$$_z$ 4 s 15 s $t_s$$_\theta$ 6 s 14 s 
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表 2 非线性控制器和LQR控制器稳态误差均值对比
Table 2 Comparison of the steady-state mean error between nonlinear controller and LQR controller
稳态误差均值 非线性控制器 LQR控制器 $\bar{y}$ 0.0116 m 0.0529 m $\bar{z}$ 0.0088 m 0.0188 m $\bar{\theta}$ 0.2013 $^{\circ}$ 0.2448 $^{\circ}$
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表 3 非线性控制器和LQR控制器稳态均方误差对比
Table 3 Comparison of the steady-state mean square error between nonlinear controller and LQR controller
稳态均方误差 非线性控制器 LQR控制器 $\sigma_y$ 3.7716$\times10^{-4}$ 4.6072$\times10^{-4}$ $\sigma_z$ 1.9433$\times10^{-4}$ 8.8264$\times10^{-5}$ $\sigma_\theta$ 0.4890 0.4570
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表 4 非线性控制器和LQR控制器稳态最大偏差对比
Table 4 Comparison of the steady-state maximum deviation between nonlinear controller and LQR controller
稳态最大偏差 非线性控制器 LQR控制器 $e_y$$\mathrm {_m}$$\mathrm {_a}$$\mathrm {_x}$ 0.0440 m 0.1038 m $e_z$$\mathrm {_m}$$\mathrm {_a}$$\mathrm {_x}$ 0.0584 m 0.0557 m $e_\theta$$\mathrm {_m}$$\mathrm {_a}$$\mathrm {_x}$ 0.1989 $^{\circ}$ 0.9888 $^{\circ}$
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