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摘要:
针对四旋翼无人机姿态自抗扰控制（ADRC）系统应对复杂干扰时，基于传统fal函数设计的扩张状态观测器（ESO）抗扰动能力不足、易产生抖振的问题，提出一种改进型ADRC并用于四旋翼姿态控制。基于正弦函数构建一种新型光滑非线性xfal函数以改进ESO，利用Lyapunov函数对改进ESO的稳定性进行证明。通过仿真平台，与其他ADRC进行比较。实验结果表明：改进型ADRC和标准ADRC相比，当四旋翼无人机不受干扰时，在其抖振区间内，俯仰角均方误差降低了约38.7%；当四旋翼无人机分别受到连续干扰、突发干扰、复杂干扰时，在各自计算区间内，俯仰角均方误差分别降低了约78.4%、80.2%、83.3%。因此，改进型ADRC在有效减小抖振的同时，还具备优良的抗干扰能力。
Abstract:An improved active disturbance rejection control (ADRC) was proposed for quadrotor attitude control to address the extended state observer (ESO) based on the traditional fal function's problems with easy chattering and insufficient anti-interference ability when responding to complex disturbances. A new smooth nonlinear xfal function was constructed based on the sine function to improve ESO. The stability of the improved ESO was proved by Lyapunov function. Finally, the improved ADRC was compared with other ADRCs through simulation platform. The results demonstrate that when compared to the standard ADRC, the mean square error of the pitch angle is reduced by approximately 38.7% in its chattering interval, and by approximately 78.4%, 80.2%, and 83.3% in their respective calculation intervals when the quadrotor was subjected to continuous interference, sudden interference, and complex interference, respectively. This indicates that the improved ADRC has excellent anti-interfere capabilities.
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表 1 四旋翼无人机仿真参数
Table 1. Four-rotor UAV simulation parameters
参数 数值 质量m/kg 0.057 力臂d/m 0.059 转动惯量Ix/(kg·m2) 4.45×10−4 转动惯量Iy/(kg·m2) 4.29×10−4 转动惯量Iz/(kg·m2) 8.6×10−4 油门-拉力系数${C'_{{T} } }$/N 3.8×10−4 油门$\sigma $ 0~1000 
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表 2 TD和NLSEF参数
Table 2. TD and NLSEF parameters
类型 r h ${\alpha _1}$ ${\alpha _2}$ ${\beta _{01}}$ ${\beta _{02}}$ $\delta $ TD 800 0.005 NLSEF 0.75 0.75 80 4 0.005
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表 3 ESO参数
Table 3. ESO parameters
参数 fal faln galn xfal b0 40 40 40 40 ${\alpha _1}$ 0.5 0.5 0.4 ${\alpha _2}$ 0.25 0.25 0.35 ${\beta _1}$ 180 180 180 180 ${\beta _2}$ 2160 2160 2160 2160 ${\beta _3}$ 24000 24000 24000 24000 h 0.005 0.005 0.005 0.005 $\delta $ 0.025 0.025 ${K_1}$ 3 ${K_2}$ 4 R1 2 R2 2
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表 4 无人机在各个干扰下的均方误差
Table 4. Mean square error of UAV under various disturbances
控制器 无干扰 正弦波 方波 白噪声 综合干扰 fal 0.00163 2.0968 6.9385 0.2621 7.1904 faln 0.00163 2.0968 7.2880 0.2574 * galn 0.00098 0.4564 * 0.2456 * xfal 0.00100 0.4542 1.3747 0.2910 1.1975 注：“*”表示失控，无均方差。
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