Novel second-order sliding mode control based 3D guidance law with impact angle constraints
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摘要:
针对导弹在三维空间中攻击地面机动目标问题，提出了一种带落角约束的三维有限时间制导律。为提高收敛速度和抑制抖振现象，基于非齐异快速终端滑模面和二阶滑模控制理论设计了含耦合项的非奇异快速终端二阶滑模三维制导律，设计过程中无需对系统模型作线性化处理并且避免了奇异问题的出现。针对目标机动信息和视线角耦合带来的总扰动，设计了非齐次干扰观测器进行估计并补偿。并对制导律的稳定性和有限时间收敛特性进行了严格的数学证明。仿真验证了本文提出制导律的有效性和优越性。
Abstract:To deal with the problem of missile for attacking ground maneuvering target in 3D space, a 3D finite-time guidance law with impact angle constraints is proposed. In order to improve convergence speed and suppress chattering problem, the nonsingular fast terminal second-order sliding mode control based 3D guidance law with coupling terms is designed based on the nonsingular fast terminal sliding surface and the second-order sliding mode control theory. System model linearization is not needed and singular problem is avoided in the design process. A nonhomogeneous disturbance observer is designed to estimate and compensate the total disturbance, which is caused by target maneuvering information and coupling terms of line of sight. And the stability and finite-time convergent characteristics of the proposed guidance law are proved mathematically. The effectiveness and superiority of the proposed guidance law are verified by numerical simulation.
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表 1 导弹初始参数和期望落角
Table 1. Initial parameters and expected impact angles of missiles
导弹 初始坐标/km θm0/(°) φm0/(°) qεd/(°) qβd/(°) M1 (0, 10, 0) -25 -20 -30 -30 M2 (2, 12, 1) -10 -30 -60 -20 M3 (-2, 9, 3) 10 10 -70 -60 
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表 2 3枚导弹攻击目标主要仿真参数
Table 2. Main simulation parameters of 3 missiles attacking targets
导弹 脱靶量/m 视线倾角误差/(°) 视线偏角误差/(°) 飞行时间/s M1 0.206 9 0.011 6 0.025 7 29.768 0 M2 0.077 6 0.010 0 0.025 0 29.979 0 M3 0.296 2 0.029 3 0.015 9 30.362 0
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表 3 3种制导律仿真主要参数对比
Table 3. Main simulation parameters comparison of 3 guidance laws
制导律 脱靶量/m 视线倾角误差/(°) 视线偏角误差/(°) 飞行时间/s SO-NFTSMG 0.206 9 0.011 6 0.025 7 29.768 0 NTSMG1 0.268 1 0.023 6 0.026 1 29.706 0 NTSMG2 0.242 3 0.011 4 0.027 3 29.923 0
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