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摘要:
针对地空导弹攻击机动目标的制导律设计问题，提出了一种有限时间稳定的新型二阶滑模制导律。在弹目相对运动模型的基础上，将制导问题转化为一阶系统的控制问题。在超螺旋（ST）算法中引入线性项和一种新的参数自适应律，提出了一种快速自适应超螺旋（FAST）算法，该算法不需要已知系统不确定性的边界且收敛速度较快。利用类二次型Lyapunov函数证明了系统有限时间稳定性，给出了收敛时间估计公式。通过与自适应滑模制导律、ST制导律和光滑二阶滑模制导律的仿真对比，验证了所设计的制导律在保证制导精度的同时，能够在有限时间内提高滑模变量的收敛速度，并且避免了参数选择困难的问题。
Abstract:A new second-order sliding-mode guidance law with finite time stability is proposed for the design of the guidance law of surface-to-air missile attacking maneuvering target. Based on the relative motion model of the missile and the target, guidance problem is transformed into control problem of first-order system. A fast adaptive super-twisting (FAST) algorithm is proposed by introducing linear terms and a new parameter adaptive law in super-twisting (ST), which improves convergence speed without the prior knowledge of upper bound parameters of uncertainties. A quadratic Lyapunov function is adopted to verify the stability of the system in finite time and compute the convergence time. A comparison with adaptive sliding mode guidance, ST guidance and smooth second-order sliding-mode guidance shows that the proposed method can improve the convergence speed of sliding variable and avoid the difficulty of choosing parameters, and can guarantee the guidance accuracy at the same time.
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图 3 滑模变量及其一阶导数变化曲线(情形1)
Figure 3. Variation curves of sliding-mode variable and its first-order derivative (Case 1)
图 6 滑模变量及其一阶导数变化曲线(情形2)
Figure 6. Variation curves of sliding-mode variable and its first-order derivative (Case 2)
表 1 仿真实验结果(情形1)
Table 1. Simulation experimental results (Case 1)
制导律 Δ/m treach/s 
tf/s ASMG 0.462 2 7.36 10.53 14.94 SSOSMG 0.518 6 12.2 21.83 14.91 STG 1.175 6 6.65 12.25 14.92 FASTG 0.616 0 5.30 14.64 14.90 
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表 2 仿真实验结果(情形2)
Table 2. Simulation experimental results (Case 2)
制导律 Δ/m treach/s 
tf/s ASMG 0.549 4 — 20.31 12.57 SSOSMG 0.566 2 10.91 21.30 11.92 STG 0.319 7 — 20.43 11.97 FASTG 0.875 3 1.79 18.98 11.74
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