Empirical virtual sliding target guidance law design: an aerodynamic approach

We present a novel empirical virtual sliding target (VST) guidance law for the midcourse phase of a long range surface-to-air missile that uses the simplicity of the conventional proportional navigation (PN) guidance law while exploiting the aerodynamic characteristics of a missile's flight through the atmosphere to enable the missile to achieve superior performance than that achieved by conventional PN guidance laws. The missile trajectory emulates the trajectory of an optimal control based guidance law formulated on a realistic aerodynamic model of the missile-target engagement. The trajectory of the missile is controlled by controlling the speed of a virtual target that slides towards a predicted intercept point during the midcourse phase. Several sliding schemes, both linear and nonlinear, are proposed and the effect of the variation of the sliding parameters, which control the sliding speed of the virtual target, on the missile performance, are examined through extensive simulations that take into account the atmospheric characteristics as well as limitations on the missile in terms of the energy available and lateral acceleration limits. Launch envelopes for these sliding schemes for approaching and receding targets are also obtained. These results amply demonstrate the superiority of the proposed guidance law over the conventional PN law.     

Optimal guidance for acceleration constrained missile andmaneuvering target

Explicit formulas of optimal guidance laws for an acceleration-constrained, arbitrary-order missile and maneuvering target are derived. These formulas are given in terms of the transfer function and acceleration constraint of the missile and the transfer function/shaping filter of the target. Optimal full-state feedback guidance law is synthesized against a target performing a barrel roll maneuver, and compared with the performance of proportional navigation (PN) for minimum and nonminimum phase missile. Simulation of a third-order missile shows the relative gain from using the full-order guidance law     

基于偏置比例导引的垂直攻击滑模制导律

为了提高空地导弹毁伤效果,需要对地面固定目标采用大角度乃至垂直打击方式。针对这一需求,设计了一种基于偏置比例导引的垂直攻击滑模制导律。首先在传统的比例导引制导律的基础上增加了一个角度约束偏置项,并结合滑模变结构理论使其滑模变结构化。然后运用自适应滑模趋近律,并采用准滑动模态控制削弱了抖振的影响。仿真结果表明:此制导律控制落角能力较强,同时具有较高的命中精度。整个攻击过程中的弹目视线角速度变化较小,最后以垂直落角攻击目标。     

3D guidance law modeling

Proportional navigation (PN) guidance laws (GLs) have been widely used and studied in the guidance literature. But most of the guidance literature on PN has concentrated on the evaluation of empirical PNGLs or GLs obtained from very specific optimality considerations. The authors present a novel approach (called guidance laws modeling) to derive new GLs. They consider the basic requirements of capture and define a complete class of GLs that meet these requirements. It is shown that PN is a natural candidate in this class. The main consequence of this modeling process is the definition of two new GLs: one in 2D space and the other in 3D space. These new GLs can be interpreted as new generalizations of the true proportional navigation (TPN) GL. Moreover, it is shown that these generalizations allow the TPNGL to match the capturability performance of the pure proportional navigation (PPN) GL in terms of initial conditions which allow the guided object to reach its target     

基于H∞ 控制的非线性末制导律设计

 针对三维目标拦截问题,提出一种新的具有强鲁棒性的非线性H_∞末制导律。基于三维弹目相对运动学的非线性关系,将目标机动作为系统扰动,建立了弹目相对运动的数学模型。同时,基于零化弹目视线角速率的思想,提出一种全局非线性H_∞稳定控制策略,得到了连续的非线性末制导律。该方法利用Lyapunov稳定性理论严格证明了制导系统的全局渐近稳定性,并且无需求解哈密尔顿-雅可比-艾萨克斯（HJI）偏微分方程,同时也无需控制弹目相对运动速度。数字仿真表明,和比例导引律相比,这种制导律对高速大机动目标具有很强的鲁棒性和适应性,并能获得良好的制导精度。     

Performance analysis of PNG laws for randomly maneuvering targets

The performance of the conventional proportional navigation guidance (PNG) law for a randomly maneuvering target is considered. By means of the Lyapunov method, it is proved that an ideal missile guided by the conventional PNG law can always intercept a target which maneuvers with time-varying normal acceleration provided that the navigation constant is sufficiently large. The authors also propose a modified PNG (MPNG) law which seems to improve the performance of the conventional PNG law at the final phase of pursuit. Simulation results demonstrate that the MPNG law demands less missile acceleration at the final phase of pursuit than the conventional PNG law     

Application of sliding-mode control to air-air interception problem

A sliding-mode control (SMC) law is applied to a nonlinear system representing an air-air missile-target interception process. Promising results are obtained for a simple switching surface based on proportional navigation (PN). Partial robustness of the controller is demonstrated, i.e. the control is robust only with respect to uncertainties present in the control dynamics. This is illustrated by a breakdown in the control actuator for which SMC was found to be superior to PN     

基于微分对策的导弹攻击策略

利用建立的垂直平面内交战双方攻击模型,应用微分对策理论,得到导弹的最优攻击策略,对比微分对策导引律与比例导引律在多种仿真环境下的结果,说明在近距离交战中,基于微分对策理论的导引律设计具有更大的优越性。     

Three-dimensional cooperative guidance laws against stationary and maneuvering targets

This paper presents the cooperative strategies for salvo attack of multiple missiles based on the classical proportional navigation(PN) algorithm.The three-dimensional(3-D) guidance laws are developed in a quite simple formulation that consists of a PN component for target capture and a coordination component for simultaneous arrival.The centralized algorithms come into effect when the global information of time-to-go estimation is obtained, whereas the decentralized algorithms have better performance when each missile can only collect information from neighbors.Numerical simulations demonstrate that the proposed coordination algorithms are feasible to perform the cooperative engagement of multiple missiles against both stationary and maneuvering targets.The effectiveness of the 3-D guidance laws is also discussed.     

基于预测模型迭代优化的改进比例导引律

为了提高对加速度时变机动目标的制导精度,将预测决策理论与传统比例导引(PN)相结合,提出了一种通过泰勒级数预测模型迭代控制加速度修正项的改进比例导引律。首先,以预设的低阶泰勒级数预测模型预测特定时间的位移,并计算位移预测值与测量值的差值;然后,通过迭代方法逐阶增加泰勒级数预测模型阶数,直至满足精度要求;最后,计算泰勒级数预测模型的二阶导数,修正比例导引律的加速度指令。仿真结果表明,传统PN和APN的脱靶量分别约为195 m和95 m,提出的改进比例导引律的脱靶量约为8.3 m,极大地提高了制导精度。     

Biased PNG law for impact with angular constraint

A new homing guidance law is proposed to impact a target with a desired attitude angle. It is a variation of the conventional proportional navigation guidance (PNG) law which includes a supplementary time-varying bias. The proposed guidance law does not require a time-to-go estimation and has a simpler form. Analytic conditions for fulfilling the guidance goal are also provided. Simulation results demonstrate that the proposed guidance law has wider launch envelopes than the previous one and shows a good performance even against a maneuvering target     

A Lyapunov-like approach to performance analysis of 3-dimensionalpure PNG laws

The 3-dimensional PPNG (pure proportional navigation guidance) law was proposed about forty years ago, but its performance has been analyzed only on the basis of the linearized trajectory equations, which are valid locally around the collision course. We take into full account the nonlinear dynamic characteristics of pursuit situation in the 3-dimensional space to analyze the performance of the 3-dimensional PPNG law more rigorously. We prove that a missile guided by the 3-dimensional PPNG law can always intercept a target maneuvering randomly in the 3-dimensional space if 1) the target acceleration varies with a known bound, 2) the navigation constant is selected large, and either 3a) the initial heading error is small or 3b) the missile keeps the head toward the target during flight. We also propose a modified PNG law, which seems to exhibit better performance at the final phase of pursuit than the conventional PPNG law. We introduce a Lyapunov-like method that proves to be a very powerful tool in obtaining our results     

Impact time control guidance against maneuvering targets based on a nonlinear virtual relative model

Aiming at the problem of high-precision interception of air-maneuvering targets with impact time constraints, this paper proposes a novel guidance law based on a nonlinear virtual relative model in which the origin is attached to the target. In this way, the original maneuvering target is transformed into a stationary one. A polynomial function of the guidance command in the range domain with two unknown coefficients is introduced into the virtual model, one of the coefficients is determined to ...     

捷联惯性导航系统动静态误差特性分析研究

捷联惯性导航系统动静态误差特性是基于惯性的组合导航系统的主要误差来源。为此,根据捷联惯性导航系统的误差状态方程,本文分析了不同动静态情况下的捷联惯导系统的误差漂移特性。针对静基座和动基座的不同特点,分别采用了特征根和基于数值仿真分析的方法,并建立了相应的误差特性分析模型。重点研究了陀螺常值漂移、加速度计零位偏置和随机性误差对惯性导航系统误差漂移特性的影响;全面分析验证了惯性导航系统的动静态误差特性。本文的研究工作将为惯性组合导航系统误差分析建模提供了有益的参考。     

Analysis of generalized guidance laws for homing missiles

It is shown that the optimal guidance problem can be handled as a Bolza-type problem which can be solved by straightforward calculation. The solution proves to be different from that given by Yang, et al. (1989) and is verified to be a minimum performance index solution. Also presented is an alternate unified approach to the solution of the nonlinear system of differential equation of the generalized proportional navigation law discussed earlier by Yang, et al. This unified equation has been solved for all the different cases of proportional navigation for which closed-form solutions have been published by earlier authors     

Adaptive nonlinear guidance law considering control loop dynamics

A new adaptive nonlinear guidance law is proposed here. The fourth order state equation for integrated guidance and control loop is formulated taking into consideration the target uncertainties and control loop dynamics. The state equation is further changed into the normal form by nonlinear coordinate transformation. Using the normal form of state equation, an adaptive nonlinear guidance law is proposed to compensate for the uncertainties in both target acceleration and control loop dynamics. The proposed law adopts the sliding mode control approach with adaptation for unknown bound of uncertainties. The present approach can effectively solve the existing guidance problem against target maneuver and the limited performance of control loop. We have provided the stability analyses and performed simulations comparing favorably our approach to the state of the art.     

带有不确定因素的最优拦截制导律

本文从微分对策观点出发,利用极小极大原理讨论了带有不确定因素的最优拦截制导律。在选择特定的过渡时间时,最优拦截制导律具有综合形式。仍由二部分组成:一部分是变系数比例导航,另一部分是与导弹加速度有关的修正项。     

Launch Envelope Optimization of Virtual Sliding Target Guidance Scheme

This paper presents an optimization of the performance of a recently proposed virtual sliding target (VST) guidance scheme in terms of maximization of its launch envelope for three-dimensional (3-D) engagements. The objective is to obtain the launch envelope of the missile using the VST guidance scheme for different lateral launch angles with respect to the line of sight (LOS) and demonstrate its superiority over kinematics-based guidance laws like proportional navigation (PN). The VST scheme uses PN as its basic guidance scheme and exploits the relation between the atmospheric properties, missile aerodynamic characteristics, and the optimal trajectory of the missile. The missile trajectory is shaped by controlling the instantaneous position and the speed of a virtual target which the missile pursues during the midcourse phase. In the proposed method it is shown that an appropriate value of initial position for the virtual target in 3-D, combined with optimized virtual target parameters, can significantly improve the launch envelope performance. The paper presents the formulation of the optimization problem, obtains the approximate models used to make the optimization problem more tractable, and finally presents the optimized performance of the missile in terms of launch envelope and shows significant improvement over kinematic-based guidance laws. The paper also proposes modification to the basic VST scheme. Some simulations using the full-fledged six degrees-of-freedom (6-DOF) models are also presented to validate the models and technique used.     

The proportional navigation dilemma-pure or true?

Two generic classes of proportional navigation (PN) laws are compared in detail. One class consists of pursuer-velocity-referenced systems, which include pure proportional navigation (PPN) and its variants; the second category consists of line-of-sight- (LOS-) referenced systems such as true proportional navigation (TPN), generalized true proportional navigation (GTPN), and generalized guidance laws. The existing closed-form solutions are discussed in detail, and the classical linear and quasilinear analytical solutions are summarized. A critical comparison is then made with regard to the definition, implementation, and analytical aspects of the guidance laws, including the method, the nature of solution, and an appraisal of the behavior of the pursuer motion resulting from the laws. It is established that, in spite of some restricted advantages in the solvability of the equations of motion, the LOS-referenced PN schemes suffer from serious limitations in terms of implementation and trajectory behavior. Among the major drawbacks are forward velocity variation requirement, relatively large control effort requirement, restrictions on initial engagement conditions to ensure intercept, lack of robustness, and possibility of unbounded acceleration. It is concluded that PPN is a better guidance law in a practical sense than TPN and its generalizations     

机载跟踪雷达的次最优控制

 本文把机载跟踪雷达的目标视为匀速直线运动叠加一阶马尔柯夫过程,在视线坐标系内建立状态方程和观测方程。采用二次型性能指标,用E-coupling法求得次最优控制律。模拟计算表明,采用该控制律的系统具有很高的跟踪精度,比经典比例控制大约提高一个数量级,和最优控制相当。