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针对空地导弹具有终端角度约束条件的制导律设计问题,提出了一种在有限时间内稳定的新型二阶滑模制导律。首先,在弹目相对运动学模型基础上,将终端弹道倾角约束转化为终端视线(LOS)角度约束,作为制导系统的终端控制目标。其次,通过选取一种新型二阶滑模面,结合螺旋控制算法的思想,设计了一种二阶滑模变结构制导律,来抑制系统中的不确定性因素,从而满足零化视线角速率和制导系统的终端角度约束条件的要求。采用一种新的Lyapunov函数,基于Lyapunov稳定性理论,严格证明了制导系统在有限时间内的稳定性。最后,对空地导弹制导系统进行数字仿真,通过和一阶传统滑模制导律以及基于超螺旋算法的二阶滑模制导律进行对比分析,验证了所设计的制导律在保证制导精度的同时,更能在有限时间内提高终端约束角度的精度,并且避免了超螺旋算法中参数选取较多的问题。
Aiming at the problem of guidance law design for air-to-ground missiles with terminal angle constraints, a new type of second-order sliding mode guidance law is proposed which is stable in finite time. Firstly, based on the relative kinematics model of the projectile, the terminal ballistic inclination constraint is transformed into the terminal line of sight (LOS) angle constraint, which is used as the terminal control target of the guidance system. Second, by choosing a new type of second-order sliding mode and combining with the idea of helix control algorithm, a second-order sliding mode variable structure guidance law is designed to suppress the uncertainties in the system so as to satisfy the zero line of sight angular rate And guidance system terminal angle constraints requirements. A new Lyapunov function is used to prove the stability of guidance system in finite time based on Lyapunov stability theory. Finally, the numerical simulation of air-to-ground missile guidance system is carried out. Compared with the first-order traditional sliding mode guidance law and the second-order sliding mode guidance law based on super-helix algorithm, it is verified that the guided guidance law, while ensuring the guidance accuracy, It can improve the accuracy of the terminal constraint angle in a limited time and avoid the problem of more parameter selection in the super-helix algorithm.