An impact angle constraint integral sliding mode guidance law for maneuvering targets interception

An integral sliding mode guidance law(ISMGL)combined with the advantages of the integral sliding mode control(SMC)method is designed to address maneuvering target interception problems with impact angle constraints.The relative motion equation of the missile and the target considering the impact angle constraint is established in the longitudinal plane,and an integral sliding mode surface is constructed.The proposed guidance law resolves the existence of a steady-state error problem in the traditional SMC.Such a guidance law ensures that the missile hits the target with an ideal impact angle in finite time and the missile is kept highly robust throughout the interception process.By adopting the dynamic surface control method,the ISMGL is designed considering the impact angle constraints and the autopilot dynamic characteristics.According to the Lyapunov stability theorem,all states of the closed-loop system are finally proven to be uniformly bounded.Simulation results are compared with the general sliding mode guidance law and the trajectory shaping guidance law,and the findings verify the effectiveness and superiority of the ISMGL.

Adaptive weighting impact angle optimal guidance law considering seeker's FOV angle constraints

In this paper, a new adaptive optimal guidance law with impact angle and seeker’s field-of-view(FOV) angle constraints is proposed. To this end, the generalized optimal guidance law is derived first. A changeable impact angle weighting(IAW) coefficient is introduced and used to modify the guidance law to make it adaptive for all guidance constraints. After integrating the closed-form solution of the guidance command with linearized engagement kinematics, the analytic predictive models of impact angle and FOV angle are built, and the available range of IAW corresponding to constraints is certain. Next, a calculation scheme is presented to acquire the real-time value of IAW during the entire guidance process. When applying the proposed guidance law, the IAW will keep small to avoid a trajectory climbing up to limit FOV angle at an initial time but will increase with the closing target to improve impact position and angle accuracy, thereby ensuring that the guidance law can juggle orders of guidance accuracy and constraints control.

Three-dimensional cooperative guidance law for multiple missiles with impact angle constraint

This paper proposes a cooperative guidance law for attacking a ground target with the impact angle constraint based on the motion camouflage strategy in the line-of-sight(LOS)frame.A dynamic model with the impact angle constraint is established according to the relative motion between multiple missiles and the target.The process of cooperative guidance law design is divided into two stages.Firstly,based on the undirected graph theory,a new finite-time consensus protocol on the LOS direction is derived to guarantee relative distances reach consensus.And the value of acceleration command is positive,which is beneficial for engineering realization.Secondly,the acceleration command on the normal direction of the LOS is designed based on motion camouflage and finite-time convergence,which can ensure the missiles reach the target with the desired angle and satisfy the motion camouflage state.The finitetime stability analysis is proved by the Lyapunov theory.Numerical simulations for stationary and maneuver targets have demonstrated the effectiveness of the cooperative guidance law proposed.

Optimal Guidance Law to Maximize Terminal Velocity for Missiles with Impact Angle Constraint

In this paper,an optimal guidance law for missiles with impact angle and miss distance constraints is proposed to achieve the maximal terminal velocity. The normal acceleration command that includes the timevarying coefficients is introduced to satisfy the desired impact angle as well as zero miss distance according to the geometric relation and relative motion parameters between missile and target. The problem is formulated as an optimal control problem by defining the angle of velocity error and flight-path angle as state variables and maximizing a performance index of the terminal velocity. The analytical form of the proposed guidance law is obtained as the solution of the optimal control problem combining optimal control theory and numerical value computation method. Nonlinear simulations of various situations demonstrate the performance and feasibility of the proposed optimal guidance law.

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

有限视场下的攻击时间和角度多约束制导律

针对精确打击任务存在导引头视场受限这一过程约束的制导问题,提出了一种考虑视场限制以及攻击角度和时间多种约束的制导律.首先,在以比例导引项实现精确命中的基础上,利用最优控制理论,采用弹目距离加权控制能耗形式的指标函数,设计了攻击角度控制项,并推导了相应的剩余飞行时间解析预测表达式.其次,基于最优误差动力学方法,设计了攻击时间相关的控制项,保证了攻击时间误差的有限时间收敛.同时,针对导引头视场有限的问题,分析了各控制项对前置角收敛性的影响,利用特定的限制函数确保前置角在整个制导过程中始终处于有效视场内,并给出了前置角的有界性及收敛性证明.数学仿真结果验证了所提出制导律对多约束制导问题的有效性.

基于落角和时间约束的巡飞弹末端协同打击策略

为解决集群巡飞弹末制导阶段协同定向打击问题,提出了一种具有落角约束的巡飞弹末端协同打击策略。基于小偏差方法,推导了一种具有落角约束的偏置比例制导律,以解决纵向平面定向打击问题。结合所提制导方案,推导了综合考虑比例控制项和角度控制项剩余时间估计方法。在侧向平面内,设计了一种具有时变系数且不存在除零奇异问题的时间控制偏置项,以解决时间控制问题。此外,以剩余时间为协调变量,利用双层协同架构来解决多枚巡飞弹协同定向打击问题。仿真结果验证了该协同制导策略良好的落角控制和协同打击性能。

入水速度对冰孔约束下圆柱体倾斜入水过程的影响分析

针对极地环境下超空泡圆柱体入水问题,基于雷诺平均方程引入流体体积模型,结合重叠网格技术建立了冰孔约束下圆柱体入水数值仿真方法。在此基础上,开展不同入水速度下圆柱体穿越冰孔入水过程仿真,分析了圆柱体入水过程中的空泡演化与载荷特性。研究结果表明:冰孔约束限制了孔内水域的流动,进而改变了表面喷溅的状态及空泡壁的形态,以至延迟了空泡表面闭合时间。随着入水速度的增大,冰孔约束对空泡形态的限制作用基本一致,圆柱体头部出现了更大范围的高压区域,且呈现出非对称分布;冰孔约束增大了圆柱体入水冲击载荷,使得圆柱体水下速度加快衰减,并促使圆柱体偏转角度大于无冰工况。研究结果可为极地超空泡武器入水稳定性提供参考。

系统收敛时间和攻击角度控制的滑模导引律

针对打击机动目标带攻击角度约束的导引律设计问题,采用滑模控制理论、任意收敛时间控制方法和干扰观测器,设计了一种攻击角度和收敛时间控制的导引律。根据弹目相对运动关系,将目标机动和建模误差等视为干扰,构建了考虑攻击角度约束的制导系统状态方程。分析了任意收敛时间控制方法在干扰情况下的性能,采用滑模控制和干扰观测器对任意收敛时间控制方法进行改进,提升鲁棒性。将该方法用于滑模面和趋近律设计中,采用干扰观测器对系统扰动进行估计,基于滑模控制理论,结合制导控制系统状态方程,推导出了收敛时间和攻击角度可控的滑模导引律。相比有限时间收敛导引律,该导引律的收敛时间和攻击角度可直接设定,无需根据制导参数计算。设置不同的目标机动方式以及不同的攻击角度和收敛时间,进行了多场景的数值仿真。结果表明,所提导引律能够有效实现攻击角度和收敛时间控制,并精确命中目标,同时相比现有导引律其制导性能更佳。

一种基于轨迹预测的滑翔制导炮弹时间约束末制导律扩展方法

针对滑翔制导炮弹末制导过程中的攻击角度与攻击时间控制问题,为简化制导律设计、方便工程应用,提出了一种将现有高性能非时间约束制导律扩展为可处理时间约束形式的方案。该方案以非线性导引模型为基础、现有制导律作用下的弹丸飞行轨迹为参考轨迹,通过为弹丸预设合理的飞行时间并结合轨迹预测的方法,将滑翔制导炮弹的末制导过程分为2个阶段。第一阶段制导炮弹在扩展后的制导律作用下飞行,通过增加参考轨迹曲率、延长弹丸飞行时间的方式使攻击时间误差在有限时间内收敛至零;第二阶段制导炮弹在原始制导律作用下飞行,直至命中目标以满足脱靶量与攻击角约束。同时,通过不同工况下的大量仿真,研究了设计参数的取值范围对第一阶段中弹丸攻击时间误差收敛性能的影响。该扩展方案的推导过程无需现有制导律的显式表达,具有一定的通用性。研究结果表明:通过合理的参数设置,扩展方案可以在现有制导律的基础上实现攻击时间控制,且制导指令光滑,需用过载较小,符合作战任务要求。

带落角与舵面饱和约束的三维制导控制一体化设计

为使制导控制系统在实际应用过程中适用所面对的多种约束条件,同时避免制导与控制系统设计过程中反复迭代带来的巨大工作量,提出了一种带有落角与舵面饱和约束的三维制导控制系统一体化设计方法。根据导弹六自由度非线性模型以及三维弹目相对运动模型建立全状态耦合的制导控制一体化模型,基于动态面控制器原理,采用4级滑模面设计,构建了能够满足落角与舵面饱和约束的控制器,并给出了控制系统闭环稳定性证明。通过仿真实验有效验证了所提方法的正确性、有效性及鲁棒性。

攻击角约束的任意时间三维制导律设计

针对攻击角约束的机动目标拦截问题,提出了一种任意时间制导律。该制导律的设计采用了任意时间稳定性理论和分段滑模方法,解决了有限时间和固定时间制导律收敛时间难求的问题,实现了视线角误差收敛时间的任意设定。此外,还利用相关稳定性理论,对所设计的制导律进行分析与证明。通过数值仿真验证了任意时间制导律的有效性,并与有限时间和固定时间制导律的仿真结果进行了比较。

考虑终端多约束条件的多项式最优制导律

针对考虑终端脱靶量、碰撞角和加速度多约束的精确制导问题,提出了一种可解析求解的多项式最优制导律。将视场角正切值设定为弹目距离的多项式函数形式,将终端多约束条件转化为多项式系数的代数关系式,并引入优化思想,得到弹目距离加权的能量最优指标下的多项式系数最优解,依据弹目运动关系将视场角正切值变化改写为相应满足终端碰撞角约束与加速度约束的制导指令解析式。针对不同加权系数、不同终端打击角度等条件对制导律制导效果进行了仿真验证,并与弹道成型制导律进行了对比。仿真结果表明,所提出的制导律可以使导弹以任意期望碰撞角准确命中目标,终端过载指令平稳收敛至0,避免了末端指令饱和现象。相较此前多项式制导相关研究,文中制导方法避免了在制导模型中引入小角度线性近似条件,提高了对轨迹与制导指令的设计精度,并能约束视场角大小从而规避系统可能出现的奇异性问题和自变量单调性问题,在终端可实现全向攻击。

过载和攻击时间约束下的非线性最优制导方法

考虑导弹过载受限条件下,对以期望时间为攻击目标的非线性最优制导问题进行了研究。首先,建立了非线性最优制导问题的理论模型,基于庞特里亚金极大值原理和饱和函数方法建立了最优轨迹的最优性条件。其次,根据最优性条件和哈密尔顿轨迹参数化方法,建立了最优轨迹的参数化微分方程组,使得通过数值积分即可生成从飞行状态到最优制导指令映射关系的数据集。然后,通过前馈神经网络对上述映射关系进行近似,实现了非线性最优制导指令的毫秒量级实时生成。最后,通过数值仿真验证了所提非线性最优制导指令生成方法的有效性。

Design of integral sliding mode guidance law based on disturbance observer

With the increasing precision of guidance,the impact of autopilot dynamic characteristics and target maneuvering abilities on precision guidance is becoming more and more significant.In order to reduce or even eliminate the autopilot dynamic operation and the target maneuvering influence,this paper suggests a guidance system model involving a novel integral sliding mode guidance law(ISMGL).The method utilizes the dynamic characteristics and the impact angle,combined with a sliding mode surface scheme that includes the desired line-ofsight angle,line-of-sight angular rate,and second-order differential of the angular line-of-sight.At the same time,the evaluation scenario considere the target maneuvering in the system as the external disturbance,and the non-homogeneous disturbance observer estimate the target maneuvering as a compensation of the guidance command.The proposed system’s stability is proven based on the Lyapunov stability criterion.The simulations reveale that ISMGL effectively intercepted large maneuvering targets and present a smaller miss-distance compared with traditional linear sliding mode guidance laws and trajectory shaping guidance laws.Furthermore,ISMGL has a more accurate impact angle and fast convergence speed.

带角度约束的三维积分二阶滑模拦截制导律

针对导弹在三维场景中以期望角度拦截加速度未知的机动目标问题,提出了一种考虑角度约束的三维拦截制导律。首先,建立了三维弹目非线性拦截制导模型;其次,设计了一种全滑动模态的积分滑模面,省去了传统滑模制导律中的滑模趋近阶段,有效地降低了拦截制导过程中的能量消耗;而后,基于设计的积分滑模面和二阶滑模控制理论,在弹目视线法向和侧向上分别设计了一种带角度约束的三维积分二阶滑模拦截制导律,有效地抑制了抖振现象,同时对目标机动造成的未知干扰进行了在线补偿;此外,对所设计算法进行了严格的Lyapunov稳定性数学证明;最后,数值仿真结果验证了本文所提三维拦截制导律的有效性、优越性以及抗干扰的鲁棒性。

含干摩擦-刚性间隙约束振动系统的动力学特性研究

建立了含干摩擦-刚性约束的单自由度振动系统动力学模型,给出在考虑干摩擦和碰撞耦合条件下分段光滑振动系统动力学约束条件,同时引入非线性刚度因素,通过协同仿真的方法得出系统响应周期运动类型和分布区域,重点讨论了质量块发生速度黏滞和位移黏滞的动力学特征,并对低频小间隙参数域内的基本周期转迁规律进行了量化表征。研究表明,质量块与皮带之间发生的速度黏滞响应主要受激励频率影响;由于干摩擦的存在,质量块与约束面首次发生碰撞的速度更为复杂;质量块与刚性约束之间的碰撞振动响应与间隙δ和激励频率ω同时存在很强的关联关系,在低频小间隙参数域涌现了丰富的动力学响应特征。

Extended optimal guidance law with impact angle and acceleration constriants

The extended optima straints of miss distance and Schwartz inequality. To reduce guidance law with terminal conmpact angle is derived by the terminal acceleration and eliminate gravity disturbance absolutely, the object function, which designs the weight of control command to be the power function of time-to-go＇s reciprocal, is given. And the gravity is considered when building the state equation. Based on the parsing express of the guidance command change with varying time and adjoint system analysis method, the command characteristics and the non-dimensional miss distance of the guidance law are analyzed, a design principle of guidance order coefficients is discussed. Finally, based on the requirement of engineering, the method to calculate the guidance condition and maximal required acceleration of the guidance law is given. The simulation demonstrates that not only the guidance law can satisfy the terminal position and impact angle constraints, but also the terminal acceleration can be converged toward zero, which will support a good situation for the terminal angle of attacking control.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired terminal impact angle constraint.To address this issue,the problem formulation including 3-D nonlinear mathematical model description,and communication topology are built firstly.Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight(LOS)which satisfies the impact time constraint.However,the normal accelerations are designed to guarantee the convergence of the LOS angular rate.Furthermore,consider the terminal impact angle constraints,a nonsingular terminal sliding mode(NTSM)control is introduced,and a finite time convergent control law of normal acceleration is proposed.The convergence of the proposed guidance law is proved by using the second Lyapunov stability method,and numerical simulations are also conducted to verify its effectiveness.The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

Numerical and experimental studies on impact dynamics of a planar flexible multibody system

In this paper a computational methodology on impact dynamics of the flexible multibody system is presented. First, the floating frame of reference approach and nodal coordinates on the basis of finite element formulation are used to describe the kinematics of planar deformable bodies. According to the kinematic description of contact conditions, the contact constraint equations of planar flexible bodies are derived. Based on the varying topology technique the impact dynamic equations for a planar multibody system are established. Then the initial conditions of the equations in each contact stage are determined according to the discontinuity theory in continuum mechanics. The experiments between the aluminum rods are performed to check the correctness of the proposed method. Through the comparison between the numerical and experimental results the proposed method is validated. Experimental results also show that the impulse momentum method cannot accurately predict the complex impact dynamic phenomena and the continuous model may lead to a serious error when used to simulate the impact problems with significant wave propagation effects.