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Standard trajectory guidance for CAV reentry based on fuzzy sliding mode control
HUANG Kangqiang, ZHAO Hui , REN Yang, CAI Yawei
School of Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi'an 710038, China
Abstract: For the question that the standard trajectory guidance was too sensitive to initial value of state and robustness was worse, a new standard trajectory guidance method based on the fuzzy sliding mode control was proposed. The robustness of sliding mode control was used to improve the adaptive capacity of guidance method, in order to definitely estimate the uncertain factors, the universal approximation property of fuzzy system was used to approach uncertain factors. Through analyzing the determinate principle of membership function combined with the characteristics of reentry process, the longitudinal guidance law was established, the simulation results validate that the master control law combined fuzzy approximation with state feedback is effective. And the lateral guidance law was designed based on the scheme mentioned before. Numerical simulation results show that this method can not only ensure a high precision but also improve the robustness of standard trajectory guidance law, and simplify the calculation process greatly.
Key words: hypersonic velocity     membership function     standard trajectory guidance     fuzzy sliding mode     trajectory tracking

1 基于模糊滑模的纵向制导律设计

1.1 纵向状态方程

CAV纵向状态方程[9]可表示为

σ=σrσ,σr为观测值，Δσ为偏差，假设Δσ在较小的范围内取值,则

1.2 模糊系统设计

1.3 隶属度函数设计

 图 1 三角隶属度函数示意图 Fig. 1 Triangular membership function schematic diagram

1.4 控制器设计

1.5 稳定性证明及自适应律设计

ρ取值较大时,会弱化模糊系统对理想输出的逼近效果,由于CAV再入过程目前没有经验数据可寻,其值难以确定,目前往往采用估计的办法.

 图 2 模糊滑模制导逻辑 Fig. 2 Guidance logic of fuzzy sliding mode
1.6 控制量边界设定

2 侧向制导律设计 2.1 侧向状态方程

CAV侧向状态方程[9]可表示为

2.2 倾侧角反转逻辑

 图 3 横程参数ΔZ的定义 Fig. 3 Definition of transverse process parameter ΔZ

2.3 侧向参数反馈调节

e4e5引入滑模面,则有

2.4 攻角调整

3 仿真验证 3.1 纵向状态跟踪仿真分析

 变量 V0/(m·s-1) γ0/(°) ψ0/(°) h0/km θ0/(°) φ0/(°) 数值 7 100 0 65 81 0 0 注：下标0代表初始条件.

 变量 Vf/(m·s-1) hf/km θf/(°) φf/(°) Δs/km 数值 1 800 20 75 20 ≤50 注：下标f代表末端条件；Δs为s的变化量.

 图 4 纵向跟踪仿真结果 Fig. 4 Simulation results for longitudinal tracking

 末端误差 Δhf/m ΔVf/(m·s-1) Δγf/(°) 数值 -39.27 -7.61 0.25 注：Δhf，ΔVf，Δγf—h、V和γ的末端误差.

 气动偏差(CL/CD)/% Δhf/m ΔVf/(m·s-1) Δγf/(°) +2 -27.63 -6.67 -0.041 +5 -79.85 -7.84 -0.075 +10 -76.57 -10.68 -0.095 -2 38.74 1.06 0.005 -5 57.74 -6.37 0.080 -10 98.50 -7.64 0.136

3.2 对初始误差鲁棒性仿真

 初始参数变化 Δhf/km ΔVf/(m·s-1) Δθf/(°) Δφf/(°) V0+100 m/s 0.042 -16.69 -0.045 4 -0.066 1 V0－100 m/s 0.101 -4.68 -0.093 1 0.081 4 h0+1 km 0.082 -2.94 0.096 1 0.060 3 h0－1 km 0.086 -2.77 0.099 6 0.049 5 ψ0+2° 0.061 -5.28 0.041 0 0.160 7 ψ0－2° 0.079 -4.84 0.068 5 0.120 9 γ0+0.5° 0.005 -12.46 -0.075 9 0.098 9 γ0－0.5° 0.099 -3.41 0.108 1 0.080 7 θ0+1° 0.062 8.46 0.141 4 0.076 1 θ0－1° 0.040 -9.06 -0.128 5 0.022 6 φ0+1° 0.046 -3.96 0.041 3 0.191 1 φ0－1° 0.096 -3.61 0.069 4 0.137 9 注：Δθf—θ的末端误差.

 图 5 不同初始偏差所得仿真结果 Fig. 5 Simulation results for different initial deviation
3.3 对气动误差鲁棒性仿真

 图 6 不同气动误差条件下的三维再入轨迹 Fig. 6 Three dimensions reentry trajectory in different pneumatic error

 图 7 16次仿真结果的终端误差 Fig. 7 Terminal errors of 16 times of simulation

4 结 论

1) 针对CAV纵向再入模型,设计了模糊滑模系统,并对控制律进行稳定性分析,通过仿真发现在利用模糊滑模系统对标准轨迹进行跟踪时,利用模糊逼近与误差反馈相结合的方式能够使实际轨迹更快地实现对标准轨迹的跟踪,且对气动误差的鲁棒性很强.

2) 在纵向制导律的基础上进行了侧向制导律设计,利用倾侧角反转逻辑与侧向参数反馈调节相结合的方式,设计了三维标准轨迹制导方案,同时,针对倾侧角反转过程中产生的微小误差,采用攻角调整的方式进行补偿.

3) 对本文所设计的模糊滑模制导律进行了仿真验证,仿真结果证实了本文所设计的基于模糊滑模的标准轨迹制导方案能够满足末端精度要求,且对各种误差的鲁棒性较强,具有实际应用价值.

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#### 文章信息

HUANG Kangqiang, ZHAO Hui, REN Yang, CAI Yawei

Standard trajectory guidance for CAV reentry based on fuzzy sliding mode control

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(9): 1749-1757.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0742