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Hybrid iteration sliding mode control for ultra-low altitude airdrop level off
LIU Ri, SUN Xiuxia , DONG Wenhan
Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi'an 710038, China
Abstract:For the ultra-low altitude airdrop level off stage, many uncertain factors such as ground effect, sensor measurement errors and low altitude airflow interfere the precision of trajectory tracking, which exert serious threats on the aircraft safety and mission performance, a hybrid iteration sliding mode flight controller was designed. In the first order sliding mode, a global dynamic switching function was adopted, which eliminated the reaching stage of sliding mode and ensured the whole response robustness. In the second order sliding mode, a nonlinear integral switching function was adopted and the overshoot caused by the integral term was brought to the first order sliding mode, so not only the tracking accuracy was guaranteed but also the dynamic performance was improved. Lyapunov stability theory and Barbalat lemma analysis show that the flight control law can completely reject constant model perturbation and disturbances, and can control the upper bounds of the steady errors with dynamic model perturbation and disturbances. Simulation results confirm the robustness and ascendant tracking performance of the proposed approach.
Key words: ultra-low altitude airdrop     flight control     hybrid iteration sliding mode     level off control     ground effect     robustness

2 混合迭代滑模飞行控制律设计

 图 1 空投拉平纵向飞行控制系统结构图 Fig. 1 Structure diagram of the airdrop level off longitudinal flight control system

k>0，g(s1)是具有“小变量大增益,大变量小增益”特性的函数,且满足

3 鲁棒稳定性证明及跟踪性能分析

s2(0)=0<μ,因此s2可以始终收于边界层内.证毕

Is>μ/k,由sgn(g(s1))=sgn(s1),有
Is(0)=0,则

s1进行Laplace变换：

ζ=(D+ζ)/μ,对式(32)取Laplace变换有

,由式(7)、式(8)推出 证毕 4 超低空空投拉平参考轨迹设计

 图 2 本文拉平指令与传统指数拉平指令[16]对比 Fig. 2 Contrast of the level off command signal in this paper and the traditional exponential one in reference[16]

 图 3 气动参数摄动和飞行状态测量误差为常值时的空投拉平仿真 Fig. 3 Airdrop level off simulation with constant aerodynamic coefficients perturbation and flight states measurement errors

 图 4 气动参数摄动和飞行状态测量误差时变时的空投拉平仿真 Fig. 4 Airdrop level off simulation with time-varying aerodynamic coefficients perturbation and flight states measurement errors

1) 本文设计的二级混合迭代滑模变结构空投拉平控制律融合了全局滑模和积分滑模的优点,可保证控制系统在响应全程的鲁棒性,能够完全抑制常值(或最终为常值)的模型不确定性和外界扰动,可以控制动态模型不确定性和外界扰动下稳态跟踪误差的上界.通过常值气动参数摄动、常值飞行状态测量误差和动态气动参数摄动、动态飞行状态测量误差下的仿真实验,验证了控制律的强鲁棒性和良好跟踪性能.

2) 基于余弦信号的空投拉平参考轨迹大大放宽了对运输机拉平能力的要求,并可根据任务性能约束灵活设计拉平时间.此外,余弦的收敛方式在拉平初期是平滑的,从而避免了舵面偏转速率过高的问题.

3) 本文提出的控制方法和空投拉平参考轨迹可提高运输机在大风、降雨等恶劣气象条件下遂行超低空空投任务的安全性和任务完成性.

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#### 文章信息

LIU Ri, SUN Xiuxia, DONG Wenhan

Hybrid iteration sliding mode control for ultra-low altitude airdrop level off

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(1): 83-89.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0020