Design and Analysis of Terminal Guidance Law for Kinetic Interceptors based on Pulse Engine

A new terminal guidance law is proposed based on a solid propellant pulse engine and an improved proportional navigation method to address the terminal guidance issue for kinetic interceptors.On this basis,the start-stop curve of the pulse motor during the terminal guidance process is designed,along with its start-up logic.The effectiveness of the proposed guidance strategy is verified through simulation.

Integrated guidance and control design for missile with terminal impact angle constraint based on sliding mode control

Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point,a new integrated guidance and control design scheme based on variable structure control approach for missile with terminal impact angle constraint is proposed.First,a mathematical model of an integrated guidance and control model in pitch plane is established,and then nonlinear transformation is employed to transform the mathematical model into a standard form suitable for sliding mode control method design.A sufficient condition for the existence of linear sliding surface is given in terms of linear matrix inequalities（LMIs）,based on which the corresponding reaching motion controller is also developed.To verify the effectiveness of the proposed integrated design scheme,the numerical simulation of missile is made.The simulation results demonstrate that the proposed guidance and control law can guide missile to hit the target with desired impact angle and desired flight attitude angle simultaneously.

Parameters Design of Pull-off Deceptive Jamming to Terminal Guidance Radar

A deceptive pull-off jamming method to terminal guidance radar is put forward in this paper.The design rules about the important jamming parameters are discussed in detail,including the number of the decoy targets in range dimension,the velocity of the range gate pull-off,and the number of the decoy targets in velocity dimension and the velocity of the Doppler frequency pull-off.Also,the steps to design these parameters are brought out.The rules and design procedure discussed in this paper have important meaning for the choice of the reasonable jamming parameters in the practical applications,which can help to obtain good jamming effect.

Integrated guidance and control design of the suicide UCAV for terminal attack

A novel integrated guidance and control (IGC) design method is proposed to solve problems of low control accuracy for a suicide unmanned combat aerial vehicle (UCAV) in the terminal attack stage. First of all, the IGC system model of the UCAV is built based on the three-channel independent design idea, which reduces the difficulties of designing the controller. Then, IGC control laws are designed using the trajectory linearization control (TLC). A nonlinear disturbance observer (NDO) is introduced to the IGC controller to reject various uncertainties, such as the aerodynamic parameter perturbation and the measurement error interference. The stability of the closed-loop system is proven by using the Lyapunov theorem. The performance of the proposed IGC design method is verified in a terminal attack mission of the suicide UCAV. Finally, simulation results demonstrate the superiority and effectiveness in the aspects of guidance accuracy and system robustness.

Trajectory shaping guidance law based on virtual angle with terminal constraints

A trajectory shaping guidance law based on virtua angle （TSGLBVA） is proposed for a re-entry vehicle with the constraints of terminal impact angles and their time derivatives. In the view of differential properties of the maneuvering trajectory, a virtual angle and a virtual radius are defined. Also, the shaping trajectory of the vehicle is established by the polynomials of the virtual angle. Then, four optimized parameters are selected according to the theorem of parameters transformation presented in this paper. Finally, a convergent variant of the Nelder-Mead algorithm is adopted to obtain the reference trajectory, and a trajectory feedback tracking guidance law is designed. The simulation results demonstrate that the TSGLBVA ensures the re-entry vehicle to impact a target precisely from a specified direction with smal terminal load factor command, as well as to obtain a maximum or constrained terminal velocity according to various requirements.

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.

A trajectory shaping guidance law with field-of-view angle constraint and terminal limits

In this paper, a trajectory shaping guidance law,which considers constraints of field-of-view(FOV) angle, impact angle, and terminal lateral acceleration, is proposed for a constant speed missile against a stationary target. First, to decouple constraints of the FOV angle and the terminal lateral acceleration, the third-order polynomial with respect to the line-ofsight(LOS) angle is introduced. Based on an analysis of the relationship between the looking angle and the guidance coefficient,the boundary of the coefficient that satisfies the FOV constraint is obtained. The terminal guidance law coefficient is used to guarantee the convergence of the terminal conditions. Furthermore, the proposed law can be implemented under bearingsonly information, as the guidance command does not involve the relative range and the LOS angle rate. Finally, numerical simulations are performed based on a kinematic vehicle model to verify the effectiveness of the guidance law. Overall, the work offers an easily implementable guidance law with closed-form guidance gains, which is suitable for engineering applications.

Observability analysis of feature aided terminal guidance systems

Feature aided design of estimators and guidance laws can significantly improve the interception performance of the terminal guidance system. The achieved enhancement can be effectively assessed by observability analysis methods. This paper first analyzes and discusses the existing assessment methods in a typical endgame scenario with target orientation observations. To get over their deficiencies, a novel singular value decomposition（SVD） method is proposed. Employing both theoretical analysis and numerical simulation, the proposed method can represent the degree of state observability which is enhanced by integrating target features more completely and quantitatively.

Terminal Angular Constraint Integrated Guidance and Control for Flexible Hypersonic Vehicle with Dead-Zone Input Nonlinearity

This paper presents an integrated guidance and control model for a flexible hypersonic vehicle with terminal angular constraints.The integrated guidance and control model is bounded and the dead-zone input nonlinearity is considered in the system dynamics.The line of sight angle,line of sight angle rate,attack angle and pitch rate are involved in the integrated guidance and control system.The controller is designed with a backstepping method,in which a first order filter is employed to avoid the differential explosion.The full tuned radial basis function(RBF)neural network(NN)is used to approximate the system dynamics with robust item coping with the reconstruction errors,the exactitude model requirement is reduced in the controller design.In the last step of backstepping method design,the adaptive control with Nussbaum function is used for the unknown dynamics with a time-varying control gain function.The uniform ultimate boundedness stability of the control system is proved.The simulation results validate the effectiveness of the controller design.

Fast fixed-time three-dimensional terminal guidance with non-concave trajectory constraint

Focusing on the non-concave trajectory constraint,a sliding-mode-based nonsingular feedback fast fixed-time three-dimensional terminal guidance of rotor unmanned aerial vehicle landing,planetary landing and spacecraft rendezvous and docking terminal phase with external disturbance is investigated in this paper.Firstly,a fixed-time observer based on real-time differentiator is developed to compensate for the external disturbance,whose estimation error can converge to zero after a time independent of the initial state.Then,a sliding surface ensuring fixed-time convergence is presented.This sliding surface can guarantee that the vehicle achieves a non-concave trajectory,which is better for avoiding collision and maintaining the visibility of the landing site or docking port.Next,the nonsingular guidance ensuring the fixed-time convergence of the sliding surface is proposed,which is continuous and chatter free.At last,three numerical simulations of Mars landing are performed to validate the effectiveness and correctness of the designed scheme.

基于Terminal滑模的动能拦截器末制导律研究

针对大气层外动能拦截器的精确拦截问题,给出了一种基于Terminal滑模的鲁棒末制导律设计方法。在不考虑动能拦截器姿态运动的情况下,建立了动能拦截器纵向平面和侧向平面内的相对运动方程,并通过在末制导滑模中引入非线性项,去除了传统变结构制导律中的切换项,保证制导系统具有全局快速性。仿真结果表明Terminal滑模应用于动能拦截器精确末制导律设计中的有效性,较之传统的比例导引和变结构制导方法,能有效抑制视线的发散,对目标机动具有更强的鲁棒性,并具有更高的拦截精度。

基于非奇异Terminal滑模的导弹末制导律研究

结合导弹拦截的精确末制导问题,提出了一种基于非奇异Terminal滑模的鲁棒末制导设计方法。基于Terminal滑模控制中滑模面上的跟踪误差能够在有限时间内收敛到零的思想,在末制导滑模中引入非线性项,代替传统线性变结构滑动模态的设计,同时将目标的机动加速度视为已知的有界扰动,并实时对极值进行自适应估计,推导出一种非奇异Terminal滑模制导律(TSMG)。导弹在TSMG制导律的导引下,弹目视线角速度可以快速收敛,从而保证导弹有很高的命中精度。仿真结果表明非奇异Terminal滑模制导律设计的有效性。

基于非线性Terminal滑模的动能拦截器末制导律设计

滑模制导律由于具有优越的性能而得到广泛关注,其设计的关键是滑模面的选取。传统的滑模变结构制导律通常都选择线性滑动平面,并保证系统到达该平面后跟踪误差渐近地收敛到零,在此过程中对收敛时间没有约束,因此不能满足快速性要求。针对这一问题,可以采用Terminal滑模控制策略,即在滑模面设计中引入非线性函数,使跟踪误差在有限时间内收敛到零。分析了一类非线性Terminal滑模面在应用中存在的问题,针对该问题设计了一种改进形式的非线性Terminal滑模面,并推导了系统从任意初始状态到达平衡状态所需时间的表达式。之后,针对动能拦截器末制导,基于改进方法设计了一种非线性Terminal滑模制导律,仿真结果表明,相对于传统的滑模制导律,所设计的制导律可以满足动能拦截的要求,不仅能够使系统状态在有限时间内收敛,而且脱靶量更小。

带落角约束的末端机动Terminal滑模导引律设计

为了提高反舰导弹的突防概率，有效规避敌方舰空导弹的拦截，并且实现反舰导弹按预定方向精确打击目标的战术要求，首先，基于弹目之间的三维相对运动模型，应用Terminal滑模控制理论，设计了一种带有落角约束的变结构导引律；然后，通过叠加虚拟干扰的方法，在原来导引律基础上叠加了一虚拟干扰，此虚拟干扰不影响导引律的渐进稳定性，不影响反舰导弹的打击精度，并且使得反舰导弹能够产生足够大的过载，但是又不超过其可用过载，使反舰导弹产生一定的机动变轨来实现规避舰空导弹。仿真结果表明了文章设计方法的有效性。

鲁棒全局快速Terminal滑模末制导律研究

针对未来导弹拦截高速大机动目标高精度制导的需要,为使导弹制导系统具有良好的鲁棒性能和精确性;提出了一种全局快速Terminal滑模的鲁棒末制导律设计方法;全局快速Terminal滑模鲁棒末制导律通过引入非线性项,代替传统线性变结构滑动模态的设计,可使目标视线角速度在有限时间内收敛到零,可以满足导弹对目标零脱靶量的要求;通过对不同的机动目标进行仿真,结果表明该方法具有较强的鲁棒性和抗干扰能力,对各类机动目标均有较高的制导精度。

INS/GPS制导炸弹非奇异Terminal滑模制导律设计与仿真

针对INS/GPS制导炸弹的特点,提出了有落角约束的非奇异terminal滑模鲁棒制导律。该制导律能够保证在末制导阶段获得一个陡峭的飞行弹道,以减小高度测量误差的影响;同时具有强鲁棒性,能抑制视线角速度测量噪声,确保炸弹在大空域工作环境下有高的制导精度。以某型INS/GPS制导炸弹为例进行了仿真计算,仿真结果表明该制导律的有效性与可行性,为INS/GPS制导炸弹制导和控制系统设计提供了一种适用的方法。

基于非线性收敛因子的Terminal滑模制导律设计

水下动能武器在末端时刻攻击目标具有作战范围小,时间短的特性。传统滑模变结构制导律通常选取线性滑动平面,收敛速度慢,对收敛时间没有约束,不能满足系统快速收敛到平衡状态。针对这一问题,提出一种改进的Terminal滑模变结构控制方法,通过引入非线性因子,使系统跟踪误差快速收敛到零,保证系统以期望的有限时间收敛到平衡状态。采用Terminal滑模面结合指数趋近律设计有限时间快速收敛制导律,该制导律即能满足系统快速性收敛要求,又能离线计算收敛时间。理论分析表明:所设计的制导律满足系统稳定性要求,并仿真验证了其快速收敛的有效性,较传统变结构制导方法收敛速度更快,具有更强的鲁棒性。

Iterative Learning Control for homing guidance design of missiles

This paper presents an Iterative Learning Control design applied to homing guidance of missiles against maneuvering targets. According to numerical experiments, although an increase of the control energies is appreciated with respect to a previous published base controller for comparison, this strategy, which is simple to realize, is able to reduce the time to reach the head-on condition to target destruction. This fact is important to minimize the missile lateral force-level to fulfill engaging in hyper-sonic target persecutions.

Ground target localization algorithm for semi-active laser terminalcorrection projectile

A target localization algorithm,which uses the measurement information from onboard GPS and onboard laser detector to acquire the target position,is proposed to obtain the accurate position of ground target in real time in the trajectory correction process of semi-active laser terminal correction projectile.A target localization model is established according to projectile position,attitude and line-of-sight angle.The effects of measurement errors of projectile position,attitude and line-of-sight angle on localization accuracy at different quadrant elevation angles are analyzed through Monte-Carlo simulation.The simulation results show that the measurement error of line-of-sight angle has the largest influence on the localization accuracy.The localization accuracy decreases with the increase in quadrant elevation angle.However,the maximum localization accuracy is less than 7 m.The proposed algorithm meets the accuracy and real-time requirements of target localization.

Integrated guidance and control of guided projectile with multiple constraints based on fuzzy adaptive and dynamic surface

Based on fuzzy adaptive and dynamic surface(FADS),an integrated guidance and control(IGC)approach was proposed for large caliber naval gun guided projectile,which was robust to target maneuver,canard dynamic characteristics,and multiple constraints,such as impact angle,limited measurement of line of sight(LOS)angle rate and nonlinear saturation of canard deflection.Initially,a strict feedback cascade model of IGC in longitudinal plane was established,and extended state observer(ESO)was designed to estimate LOS angle rate and uncertain disturbances with unknown boundary inside and outside of system,including aerodynamic parameters perturbation,target maneuver and model errors.Secondly,aiming at zeroing LOS angle tracking error and LOS angle rate in finite time,a nonsingular terminal sliding mode(NTSM)was designed with adaptive exponential reaching law.Furthermore,combining with dynamic surface,which prevented the complex differential of virtual control laws,the fuzzy adaptive systems were designed to approximate observation errors of uncertain disturbances and to reduce chatter of control law.Finally,the adaptive Nussbaum gain function was introduced to compensate nonlinear saturation of canard deflection.The LOS angle tracking error and LOS angle rate were convergent in finite time and whole system states were uniform ultimately bounded,rigorously proven by Lyapunov stability theory.Hardware-in-the-loop simulation(HILS)and digital simulation experiments both showed FADS provided guided projectile with good guidance performance while striking targets with different maneuvering forms.