考虑目标机动和落角约束的二阶滑模制导律

Second Order Sliding Mode Guidance Law Considering Target Maneuver and Impact Angle Constraint

针对末制导阶段导弹以期望的终端落角攻击高机动目标的需求,将Super-twisting算法与自适应滑模扰动观测器相结合,提出一种满足终端落角约束的二阶滑模制导律。目标机动带来的干扰导致系统扰动的上界未知,将目标加速度视为系统扰动,设计自适应滑模扰动观测器对系统扰动进行在线估计,通过对观测器增益进行自适应调整,克服传统观测器选取增益时依赖扰动上界的缺陷。设计改进的Super-twisting算法作为制导律的趋近律,在降低抖振的同时使制导律可充分利用导弹的过载能力,从而提升系统的收敛速度,解决传统Super-twisting算法中系统状态远离平衡点时收敛速度慢的问题。基于李雅普诺夫稳定性理论,证明该制导系统能在有限时间内收敛。数学仿真结果表明:自适应滑模扰动观测器和所设计制导律有效,自适应滑模扰动观测器能够准确跟踪系统扰动,所设计的制导律能够满足期望的终端落角约束,且具有较高的命中精度,脱靶量小于0.2 m。

To meet the requirement of missiles attacking high maneuvering targets with desired impact angles during terminal guidance,a second-order sliding mode guidance law satisfying impact angle constraint is proposed by combining the super-twisting algorithm with adaptive sliding mode disturbance observer.The disturbance caused by target maneuver leads to the unknown upper bound of system disturbance.Taking target acceleration as system disturbance,an adaptive sliding mode disturbance observer is designed for on-line system disturbance estimation.By adaptively adjusting the observer gain,the defect that the traditional observer depends on the upper bound of disturbance when selecting the gain can be overcome.The improved super-twisting algorithm is designed as the reaching law of the guidance law,enabling the guidance law to make full use of the overload capacity of the missile while reducing the chattering,thus improving the convergence speed of the system,and solving the problem of slow convergence speed when the system state is far from the equilibrium point in the traditional super-twisting algorithm.Based on the Lyapunov stability theory,it is proven that the guidance system can converge in finite time.Finally,the effectiveness of the adaptive sliding mode disturbance observer and the designed guidance law is verified by mathematical simulation.The adaptive sliding mode disturbance observer can accurately track system disturbance,and the designed guidance law can meet the expected terminal angle constraint and has high impact accuracy,with the miss-distance smaller than 0.2 m.