王中原 , 史金光 , 常思江 , 等 . 弹道修正弹技术发展综述 [J ] . 弹道学报 , 2021 , 33 ( 2 ): 1 - 12 . DOI: 10.12115/j.issn.1004-499X(2021)02-001 http://doi.org/10.12115/j.issn.1004-499X(2021)02-001 炮弹在发射和飞行的过程中,受各种随机误差的影响,造成射弹散布。设法减小或控制随机误差影响、改善炮弹地面密集度,始终是常规弹箭技术研究的方向。近年来研究者另辟蹊径,发展和研究了弹道修正理论与技术,即通过对一段实测飞行弹道参数的在线误差影响辨识,后续弹道预报,并通过弹上简易机构进行弹道修正调节,实现低成本下大幅度改善炮弹地面密集度。该文综合近年来国内外部分文献资料报道,结合多年的研究经验,对弹道修正弹技术的特点、难点及其工程应用中存在的射程扩展量等作一介绍,对未来的技术发展作一展望,以期为从事这方面研究的人员提供参考。

WANG Z Y , SHI J G , CANG S J , et al . Review on development of technology of trajectory correction projectile [J ] . Journal of Ballistics , 2021 , 33 ( 2 ): 1 - 12 . (in Chinese)

张民权 , 刘东方 , 王冬梅 , 等 . 弹道修正弹发展综述 [J ] . 兵工学报 , 2010 , 31 ( 增刊2 ): 127 - 130 .

ZHANG M Q , LIU D F , WANG D M , et al . A summary for trajcectory correction projectiles [J ] . Acta Armamentarii , 2010 , 31 ( S2 ): 127 - 130 . (in Chinese)

杨杰 , 刘丹 , 常思江 . 带微型扰流片旋转稳定弹外弹道建模与仿真 [J ] . 弹道学报 , 2020 , 32 ( 4 ): 7 - 13 . DOI: 10.12115/j.issn.1004-499X(2020)04-002 http://doi.org/10.12115/j.issn.1004-499X(2020)04-002 为发展修正能力更强的有控旋转稳定弹,研究了一类带有微型扰流片控制机构的旋转稳定弹。分析了该类有控弹的控制原理,针对其动力学建模问题,考虑气动非对称,建立了带扰流片旋转稳定弹的控制力和控制力矩数学模型。根据六自由度弹道模型,仿真分析了扰流片外露高度和弹丸射角、初速及启控时间对速度、弹丸稳定性和修正能力的影响。结果表明:扰流片外露高度越高,修正能力越强,但速度降越明显,攻角振荡幅度和稳态值越大,稳定性越差; 速度从亚音速向超音速变化时,修正能力先减小后增大。

YANG J , LIU D , CHANG S J . Modeling and simulation of external trajectory of spin-stabilized projectile with micro spoiler [J ] . Journal of Ballistics , 2020 , 32 ( 4 ): 7 - 13 . (in Chinese) DOI: 10.12115/j.issn.1004-499X(2020)04-002 http://doi.org/10.12115/j.issn.1004-499X(2020)04-002 In order to develop a kind of controllable spin-stabilized projectile with stronger correction ability,a kind of spin-stabilized projectile with micro spoiler control mechanism was studied. The control principle of this kind of controlled projectile was analyzed. Aiming at its dynamic modeling problem,the mathematical model of the control force and the control torque of the spin-stabilized projectile with spoiler was established by considering the aerodynamic asymmetry. According to the six degree of freedom trajectory model,the effects of the spoiler height,projectile angle,initial velocity and start-up and control time on the stability and correction ability of the projectile were analyzed. The results show that the higher the spoiler height is,the stronger the correction ability is,but the more obvious the speed drop. The larger the oscillation amplitude and stability value of the attack angle are,the earlier the start-up and control time is. When the velocity changes from subsonic to supersonic,the correction ability first decreases and then increases.

WERNERT P , LEOPOLD F , LEHMANN L . Wind tunnel tests and open-loop trajectory simulations for a 155mm canards guided spin stabilized projectile: AIAA-2008-6881 [R ] . Honolulu, HI, US:AIAA , 2008 .

纪秀玲 , 王海鹏 , 曾时明 , 等 . 可旋转鸭舵对旋转弹丸纵向气动特性的影响 [J ] . 北京理工大学学报 , 2011 , 31 ( 3 ): 265 - 268 .

JI X L , WANG H P , ZENG S M , et al . CFD prediction of longitudinal aerodynamics for a spinning projectile with fixed canard [J ] . Transactions of Beijing Institute of Technology , 2011 , 31 ( 3 ): 265 - 268 . (in Chinese)

郝永平 , 孟庆宇 , 张嘉易 . 固定翼二维弹道修正弹气动特性分析 [J ] . 弹箭与制导学报 , 2012 , 32 ( 3 ): 171 - 173 .

HAO Y P , MENG Q Y , ZHANG J Y . Aerodynamic characteristic analysis on two-dimensional trajectory corrector shell with fixed-wing [J ] . Journal of Projectiles, Rockets, Missiles and Guidance , 2012 , 32 ( 3 ): 171 - 173 . (in Chinese)

冯斌 , 于纪言 , 鞠潭 , 等 . 双旋弹道修正弹弹体非对称载荷的数值研究 [J ] . 兵工学报 , 2018 , 39 ( 11 ): 2118 - 2126 . DOI: 10.3969/j.issn.1000-1093.2018.11.005 http://doi.org/10.3969/j.issn.1000-1093.2018.11.005 固定鸭舵双旋弹道修正弹的弹体受到鸭舵非对称尾流的影响，其载荷具有非对称特性。为了研究该非对称特性，通过计算流体力学(CFD)仿真和风洞实验的结果对比验证CFD方法的有效性。对0°舵偏、2°舵偏、4°舵偏的双旋弹道修正弹模型在多马赫数、多攻角下进行CFD仿真，并通过绘制鸭舵尾流的流线图和弹体压力系数云图对流场进行定性分析，通过对比弹体截面压力系数和弹体法向力、侧向力系数对弹体受力的非对称性进行定量分析。结果表明： 0°舵偏模型的弹体压力系数呈面对称，2°舵偏模型、4°舵偏模型弹体压力系数呈非对称；在给定马赫数下，3种模型弹体法向力系数随攻角变化的曲线高度重合； 0°舵偏模型的弹体侧向力系数在0附近，2°舵偏模型、4°舵偏 模型的弹体侧向力随攻角近似线性变化，随马赫数先增大、后减小；给定攻角时，4°舵偏模型对应曲线峰值约为2°舵偏模型的2倍。

FENG B , YU J Y , JU T , et al . Numerical study of asymmetrical load on the body of dual-spin projectile [J ] . Acta Armamentarii , 2018 , 39 ( 11 ): 2118 - 2126 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2018.11.005 http://doi.org/10.3969/j.issn.1000-1093.2018.11.005 The load on dual-spin projectile's body has an asymmetrical characteristic because of the influence from asymmetrical wake flow of canards. The asymmetrical load on the projectile body is studied. The results form computational fluid dynamics (CFD) simulation and wind tunnel test are compared to prove the effectiveness of the CFD method. The dual-spin projectile models with control surface angles of 0°, 2°and 4° are simulated at various Mach numbers and angles of attack. The flow field is qualitatively analyzed by drawing the streamline diagrams of tail flow of canards and the pressure coefficient contour map of projectile body. The asymmetry of force of the projectile body is quantitatively analyzed by comparing the pressure coefficient of body section and the lateral force coefficient of body. The result shows that the body section pressure coefficient of the model with control surface angle of 0° is symmetrical, and the body section pressure coefficients of the model with control surface angles of 2°and 4°are asymmetrical. The projectile body's normal force coefficient curves of three models coincide with each other as the change in the angle of attack at a given Mach number; and the lateral force coefficient is near 0 for the model with control surface angle of 0°, but is approximately linear with the angle of attack for the models with control surface angles of 2° and 4°, and is first ascended and then descended with the Mach number. When the angle of attack is given, the peak value of the model with control surface angle of 4° is about 2 times that of the model with control surface angle of 2°. Key

冯斌 , 于纪言 , 王钰 , 等 . 固定鸭舵导引组件修正力模型改进及参数辨识 [J ] . 兵工学报 , 2019 , 40 ( 2 ): 257 - 264 . DOI: 10.3969/j.issn.1000-1093.2019.02.005 http://doi.org/10.3969/j.issn.1000-1093.2019.02.005 固定鸭舵双旋弹道修正弹通过调整固定鸭舵相位角控制修正力方向，从而改变弹体姿态，实现弹道修正。准确的导引组件修正力模型是提高修正弹修正精度的关键。本文在风洞试验基础上验证了数值计算的有效性。针对非零攻角下翼身干扰不对称现象，基于小扰动理论建立了基于4片舵片考虑翼身干扰的修正力模型。使用计算流体力学(CFD)所得数据，通过Levenberg-Marquardt算法对修正力模型进行参数辨识。辨识结果表明：基于4片舵片气动模型的y轴方向、z轴 方向修正力随相位角呈正弦规律变化；在给定马赫数情况下，所建立的气动模型弹头对舵片的干扰系数对攻角变化不敏感，干扰系数随攻角相对变化小于4.9%；所建立的修正力气动工程模型y轴 方向和z轴方向修正力的残差平方和比现有模型更小，头部修正组件的修正力模型与CFD计算结果吻合较好。

FENG B , YU J Y , WANG Y , et al . Improvement and parameter identification of correction force model for fixed-canard guidance kit [J ] . Acta Armamentarii , 2019 , 40 ( 2 ): 257 - 264 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.02.005 http://doi.org/10.3969/j.issn.1000-1093.2019.02.005 The attitude of fixed canard dual-spin trajectory correction projectile is changed by adjusting the phase angle of fixed canard to control the direction of correction force. An exact correction force model of precision guidance kit is the key to improve the correction accuracy of the correction projectile. The validity of the numerical calculation is verified on the basis of wind tunnel test. Based on the small disturbance theory, a modified correct force model of guidance kit is established for the correction projectile with four canards. Levenberg-Marquardt algorithm is used to identify the parameters of the modified correction force model based on the data of computational fluid dynamics（CFD）. The results show that y and z directions vary sinusoidally with phase angle in the correction force model based on four canards. The disturbance coefficient of warhead is insensitive to the angle of attack at a given Mach number. The change of disturbance coefficient with angle of attack is less than 4.9%. The residual sum of squares of correction forces in y and z directions in the proposed modified correction force model is smaller than that in the existing model. The calculated results of correction force model of guidance kit are in good agreement with CFD calculations. Key

钟阳 , 王良明 , 李岩 , 等 . 旋转稳定二维修正弹鸭舵法向力计算模型研究 [J ] . 弹道学报 , 2019 , 31 ( 2 ): 48 - 54 . DOI: 10.12115/j.issn.1004-499X(2019)02-009 http://doi.org/10.12115/j.issn.1004-499X(2019)02-009 为了研究修正组件滚转条件下二维修正弹鸭舵的法向气动力非线性规律,建立了鸭舵坐标系,考虑弹丸攻角、舵偏角、弹丸运动和迎风区与背风区等影响因素,采用多元泰勒展开理论,建立了动态鸭舵法向力计算模型; 采用数值计算分析了不同攻角、舵偏角组合的鸭舵法向力特性,得到了不同舵偏角下鸭舵法向力随攻角的变化规律,分析了滚转条件下舵偏角和攻角对4个鸭舵法向力系数的影响规律。结果表明:鸭舵法向力计算模型的计算结果与数值计算结果吻合较好,该模型为二维修正弹的气动力计算提供了参考。

ZHONG Y , WANG L M , LI Y , et al . Calculation model of normal force of canard on spin stabilized two-dimensional trajectory correction projectile [J ] . Journal of Ballistics , 2019 , 31 ( 2 ): 48 - 54 . (in Chinese) DOI: 10.12115/j.issn.1004-499X(2019)02-009 http://doi.org/10.12115/j.issn.1004-499X(2019)02-009 In order to study the rule of normal aerodynamic force of the canard on two-dimensional correction projectile with rolling course correction fuzes(CCF),the coordinate system of the canard was established. Considering the factors such as the angle of attack(AOA),the canard deflection,the motion of the projectile,and the windward and leeward regions,the normal force calculation model of dynamic canard was established by using the multi-element Taylor expansion theory. The change rule of canard normal force at different attack angles and canard deflections was analyzed by numerical calculation. The rules of influence of attack angle and canard deflection on the aerodynamic coefficients of four canards were analyzed when the CCF was rolling. The results show that the calculation model results are in good agreement with numerical calculation results of the canard normal-force. The model offers reference for the aerodynamic force calculation of two-dimensional corrected projectile.

黄智康 , 陈少松 , 魏恺 , 等 . 固定鸭舵双旋火箭弹超声速侧向气动特性 [J ] . 弹道学报 , 2021 , 33 ( 1 ): 55 - 64 . DOI: 10.12115/j.issn.1004-499X(2021)01-009 http://doi.org/10.12115/j.issn.1004-499X(2021)01-009 为研究加装了固定鸭舵修正组件的双旋火箭弹的气动特性,采用ANSYS Fluent软件计算弹体周围流场,采用滑移网格方法模拟弹箭旋转运动,在验证数值方法的基础上,对超声速下无鸭舵、鸭舵修正组件不旋和鸭舵修正组件反旋3种状态的双旋火箭弹进行数值模拟,重点分析了鸭舵修正组件对全弹和部件侧向力的影响。计算结果表明:加装鸭舵修正组件后,全弹阻力系数和法向力系数增加,侧向力系数随攻角大幅增加; 弹体侧向力受鸭舵的影响最大,也是全弹侧向力的主要组成部分,尾翼次之,修正组件产生的侧向力最小; 加装修正组件后,鸭舵尾涡与弹体体涡相互干扰是弹体和尾翼侧向力增加的主要原因。

HUANG Z K , CHEN S S , WEI K , et al . Lateral aerodynamics of a fixed-canard dual-spin rocket projectile at supersonic speed [J ] . Journal of Ballistics , 2021 , 33 ( 1 ): 55 - 64 . (in Chinese)

冯斌 , 于纪言 , 王晓鸣 , 等 . 固定鸭舵双旋火箭弹弹体绕流的数值研究 [J ] . 弹道学报 , 2021 , 33 ( 2 ): 21 - 27 . DOI: 10.12115/j.issn.1004-499X(2021)02-003 http://doi.org/10.12115/j.issn.1004-499X(2021)02-003 为了研究加装精确制导组件的旋转稳定火箭弹弹体的绕流特性,尤其是鸭舵尾涡对弹体绕流的影响,通过计算流体力学方法,进行了网格密度研究,并对多攻角多转速工况的流场状态进行了数值仿真,利用Q准则实现对涡核心区域的辨识,并定性分析了不同工况下的流场特性,定量对比分析了弹体受力。结果表明:鸭舵涡系使弹体上出现不对称的条带状低压区域,使弹体受力呈现不对称性; 受弹体滚转影响,鸭舵涡系发生扭转,其扭转方向与弹体滚转方向一致; 鸭舵涡系与弹体旋转的共同作用诱导产生次级涡; 存在攻角时弹体的侧向力仍然表现出明显的马格努斯效应; 与传统回转体弹丸不同的是弹体转动角速度为0时侧向力系数不为0,且与攻角相关。

FENG B , YU J Y , WANG X M , et al . Numerical study on the flow around dual-spin rocket projectile body [J ] . Journal of Ballistics , 2021 , 33 ( 2 ): 21 - 27 . (in Chinese) DOI: 10.12115/j.issn.1004-499X(2021)02-003 http://doi.org/10.12115/j.issn.1004-499X(2021)02-003 To study the characteristics of flow around spinning stabilized rocket projectile with precision guidance kit,especially the influence of canard wake vortex on the flow around projectile,grid density was studied by computational fluid dynamics(CFD)method. The flow field under different attack-angles and different rotation-speeds was numerically calculated. The <i>Q</i> criterion was used to identify the vortex core region. The flow field was qualitatively analyzed; the force on the projectile was analyzed quantitatively. The results show that the canard vortex system makes the strip-shaped low-pressure region appear on the projectile body,and asymmetric vortex system makes the projectile force asymmetrical; the canard vortex system twists due to the rotation of the projectile body,and its torsion direction is the same as the rotation direction of the projectile; the canard vortex system and the projectile rotation induce the secondary vortex. The lateral force of the projectile still shows obvious change when there is an angle of attack. Different from the traditional revolving projectile,the lateral force coefficient doesn’t equal 0 when the rotating velocity equals 0,and it is related to the angle of attack.

COSTELLO M , PETERSON A . Linear theory of a dual-spin projectile in atmospheric flight [J ] . Journal of Guidance, Control and Dynamic , 2000 , 23 ( 5 ): 789 - 797 . DOI: 10.2514/2.4639 http://doi.org/10.2514/2.4639 https://arc.aiaa.org/doi/10.2514/2.4639 https://arc.aiaa.org/doi/10.2514/2.4639

常思江 , 王中原 , 刘铁铮 . 鸭式布局双旋弹飞行动力学建模与仿真 [J ] . 弹道学报 , 2014 , 26 ( 3 ): 1 - 5 , 16. 为发展具有精确打击能力的有控旋转稳定弹,研究了一类采用双旋结构的鸭式布局旋转稳定弹。分析了该类有控弹的飞行原理,补充了其飞行动力学建模所需的坐标系; 根据牛顿第二定律和动量矩定理,建立了七自由度刚体质心运动方程和绕质心运动方程; 讨论了作用在弹体上的诸力和力矩。编制计算程序对鸭式布局双旋弹的弹道特性进行了仿真分析,揭示了无控条件下双旋弹前、后体的转速和全弹攻角、偏流的变化规律,得到了控制力和控制力矩作用下双旋弹体的攻角响应。仿真结果与其飞行原理吻合,符合外弹道规律,验证了所建模型的合理性,为后续研究该类有控旋转弹提供了理论基础。

CHANG S J , WANG Z Y , LIU T Z . Modeling and simulation of flight dynamic for dual-spin stabilized projectile equipped with canards [J ] . Journal of Ballistics , 2014 , 26 ( 3 ): 1 - 5 , 16. (in Chinese)

许诺 , 于剑桥 , 王亚飞 , 等 . 固定翼双旋弹动力学特性分析 [J ] . 兵工学报 , 2015 , 36 ( 4 ): 602 - 609 . DOI: 10.3969/j.issn.1000-1093.2015.04.005 http://doi.org/10.3969/j.issn.1000-1093.2015.04.005 固定翼双旋弹作为一种特殊的弹道修正弹，在飞行过程中其前体弹道修正引信（CCF）和后体以不同转速绕弹轴旋转。根据固定翼双旋弹气动不对称的特性，推导出固定翼双旋弹的动力学模型，经过模型简化，得到其非齐次角运动方程，根据这个角运动方程对角运动特性和飞行稳定性进行了分析。结果显示：当CCF转速固定时，转速的大小和滚转的方向都会影响弹体的角运动特性，由于弹体的共振，不合理的转速可能引起角运动的不稳定；当CCF转角固定时，弹体可以获得与CCF的鸭翼安装角近似呈正比的弹道修正能力。对固定翼双旋弹的飞行稳定性判据进行了研究，飞行稳定性判据为固定翼双旋弹前后体转速和初始射角的设计提供了参考。

XU N , YU J Q , WANG Y F , et al . Analysis of dynamic characteristics of fixed-wing dual-spin projectiles [J ] . Acta Armamentarii , 2015 , 36 ( 4 ): 602 - 609 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2015.04.005 http://doi.org/10.3969/j.issn.1000-1093.2015.04.005 Fixed-wing dual-spin projectile is a class of trajectory correction projectile, of which the forward course correction fuze (CCF) and aft body can rotate at different spin rates during flight. According to its aerodynamic asymmetry characteristics, the dynamic model of fixed-wing dual-spin projectiles is derived. Nonhomogeneous angular motion equations are calculated by simplifying the model. The angular motion characteristics and stability of fixed-wing dual-spin projectiles are studied based on the angular motion equations. The results show that, when the roll rate of the CCF is constant, the angular motion characteristics of projectile are greatly affected by both the roll rate and rolling direction, and an unreasonable roll rate may cause the instability of angular motion because of the resonance; when the spin angle of the CCF stays at any angular position, the projectile has the course correction ability which is proportional to the installation angle of the canard wings. Ultimately the stability criterion of fixed-wing dual-spin projectiles is studied.

许诺 , 于剑桥 , 王亚飞 . 基于周期平均的固定翼双旋弹弹道修正方法 [J ] . 航空学报 , 2016 , 36 ( 9 ): 2892 - 2899 .

XU N , YU J Q , WANG Y F . Trajectory correcting method of fixed-canard of dual-spin projectiles based on period average [J ] . Acta Aeronautica et Astronautica Sinica , 2016 , 36 ( 9 ): 2892 - 2899 . (in Chinese)

马国梁 . 基于修正质点弹道模型的双旋弹控制效果分析 [J ] . 北京理工大学学报 , 2019 , 39 ( 8 ): 777 - 783 .

MA G L . Control effect analysis of dual-spin projectile based on modified mass point trajectory model [J ] . Transactions of Beijing Institute of Technology , 2019 , 39 ( 8 ): 777 - 783 . (in Chinese)

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殷婷婷 , 贾方秀 , 于纪言 , 等 . 基于扩张状态观测器的双旋弹丸舵翼转速预测控制 [J ] . 北京理工大学学报 , 2019 , 39 ( 10 ): 1057 - 1062 , 1068.

YIN T T , JIA F X , YU J Y , et al . Direct model predictive rotating speed control for rudder in dual-spin projectile with output-feedback extended state observer [J ] . Transactions of Beijing Institute of Technology , 2019 , 39 ( 10 ): 1057 - 1062 , 1068. (in Chinese)

殷婷婷 , 贾方秀 , 于纪言 , 等 . 基于改进LuGre摩擦模型的双旋弹丸固定舵翼滚转位置鲁棒自适应控制算法 [J ] . 兵工学报 , 2019 , 40 ( 12 ): 2425 - 2432 . DOI: 10.3969/j.issn.1000-1093.2019.12.005 http://doi.org/10.3969/j.issn.1000-1093.2019.12.005 针对双旋弹丸舵翼滚转位置系统存在非线性摩擦、不确定性参数以及时变扰动等问题，提出一种基于连续可微LuGre摩擦模型的鲁棒自适应控制策略。以基于永磁同步发电机为电磁执行机构的舵翼滚转位置控制系统为研究对象，建立包含改进摩擦模型的系统非线性数学模型。通过对未建模扰动的上界进行自适应估计，在控制器中设计扰动补偿鲁棒反馈项将其补偿，降低扰动对控制性能的影响。对系统不确定性参数、摩擦状态量进行在线自适应估计，并结合摩擦补偿设计自适应控制律，降低系统对参数不确定性和非线性摩擦的敏感度。通过Lyapunov稳定性理论证明了闭环系统的全局稳定性。仿真结果表明：该方法能准确地对模型参数、非线性摩擦状态以及扰动进行估计和补偿，具有控制精度高、稳定性好和鲁棒性强等优点。

YIN T T , JIA F X , YU J Y , et al . Robust adaptive control of roll position of fixed rudder for dual-spin projectile with improved LuGre friction model [J ] . Acta Armamentarii , 2019 , 40 ( 12 ): 2425 - 2432 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.12.005 http://doi.org/10.3969/j.issn.1000-1093.2019.12.005 A robust adaptive control strategy based on a continuously differentiable LuGre friction model is proposed for the roll position control of fixed rudder canard in dual-spin trajectory correction projectile with nonlinear friction, uncertain parameters and time-varying disturbance. A nonlinear mathematical model, including the improved continuous friction model, is established for the electromagnetic actuator based on the permanent-magnet synchronous generator (PMSG). A robust feedback compensation term based on the estimated upper bound of un-modeled disturbance is designed to reduce the influence of external disturbance on control performance. An adaptive control law is proposed by compensating for friction and adaptively estimating the system parameters and friction states online, which can effectively reduce the sensitivity of system to parameter uncertainties and nonlinear frictions. The global stability of closed-loop system is proved by Lyapunov analysis. Simulated results show that the proposed strategy can be used to accurately estimate and compensate for time varying parameter, uncertainties, nonlinearities and disturbances, and has the advantages of high accuracy and strong robustness.Key

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ZHANG X , YAO X X . Roll control of course correction fuze for dual-spin projectile with fixed-canards [J ] . Transactions of Beijing Institute of Technology , 2020 , 40 ( 4 ): 386 - 395 . (in Chinese)

WERNERT P , THEODOULIS S . Modeling and stability analysis for a class of 155 mm spin-stabilized projectiles with course correction fuse (CCF) [C ] // Proceedings of AIAA Atmospheric Flight Mechanics Conference and Exhibit. Portland, OR , US : AIAA , 2011 .

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CHANG S J . Dynamic response to canard control and gravity for a dual-spin projectile [J ] . Journal of Spacecraft and Rockets , 2016 , 53 ( 3 ): 558 - 566 . DOI: 10.2514/1.A33485 http://doi.org/10.2514/1.A33485 https://arc.aiaa.org/doi/10.2514/1.A33485 https://arc.aiaa.org/doi/10.2514/1.A33485

常思江 , 王中原 , 刘铁铮 . 鸭式布局双旋稳定弹强迫运动理论研究 [J ] . 兵工学报 , 2016 , 37 ( 5 ): 829 - 839 . DOI: 10.3969/j.issn.1000-1093.2016.05.009 http://doi.org/10.3969/j.issn.1000-1093.2016.05.009 为深入理解鸭式布局双旋稳定弹的动力学特性，对前体鸭舵周期性干扰引起的强迫运动进行了理论研究。建立一个简化七自由度飞行动力学模型，利用双旋稳定弹的横向运动方程组，在小攻角条件下推导出线性攻角运动模型，得到周期性舵控作用强迫项对应特解的具体表达式。通过对攻角快、慢圆运动角频率及强迫振幅变化特性在不同条件下的仿真分析，讨论该强迫运动的共振条件，分析舵面偏转角、舵面位置和极转动惯量比对共振幅值的影响。对大攻角条件下的前体转速闭锁问题进行初步分析，导出了该弹发生转速闭锁的稳定方位角及临界攻角表达式。

CHANG S J , WANG Z Y , LIU T Z . A theoretical study of forced motion for dual-spin-stabilized projectiles with canards [J ] . Acta Armamentarii , 2016 , 37 ( 5 ): 829 - 839 . (in Chinese)

马国梁 , 蔡红明 , 常思江 . 固定鸭舵双旋弹动态稳定性分析 [J ] . 兵工学报 , 2019 , 40 ( 10 ): 1987 - 1994 . DOI: 10.3969/j.issn.1000-1093.2019.10.003 http://doi.org/10.3969/j.issn.1000-1093.2019.10.003 针对一种固定鸭舵双旋弹，研究了滚转角控制量任意时变条件下的动态稳定性问题。在弹体固定面坐标系中给出固定鸭舵双旋弹的力方程组和力矩方程组，建立了角运动状态空间模型。运用Lyapunov方法研究了固定鸭舵双旋弹的动态稳定性问题，证明可以通过求解一个Riccati形式的线性矩阵不等式来判断其动态稳定性。利用复数平方根计算方法得出稳定因子表达式，基于界实引理定义了绝对稳定H_∞范数。提出固定鸭舵双旋弹的绝对稳定性判据，包括稳定因子约束和绝对稳定H_∞范数约束,外弹道仿真结果验证了该稳定性判据的正确性。

MA G L , CAI H M , CHANG S J . Analysis of dynamic stability of fixed canard dual-spin Projectile [J ] . Acta Armamentarii , 2019 , 40 ( 10 ): 1987 - 1994 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.10.003 http://doi.org/10.3969/j.issn.1000-1093.2019.10.003 Dynamic stability of a fixed canard dual-spin projectile under the condition of arbitrary time-varying roll angle input is investigated. Force equations and moment equations are presented in body fixed plane frame for fixed canard dual-spin projectile, and a state space model for angular motion is established. Dynamic stability is addressed by using Lyapunov method. The dynamic stability of projectile can be determined by solving a Riccati-type linear matrix inequality. The stability factor equation is derived by using complex square root calculation method, and the H_∞ norm of absolute stability is defined based on the bounded real lemma. Absolute stability criteria for fixed canard dual-spin projectile is proposed，including stability factor constraint and H_∞ norm constraint of absolute stability, and the correctness of stability criteria is validated by using exterior ballistic simulation results. Key

朱煌 , 史金光 , 谢飞 , 等 . 高旋二维弹道修正弹的角运动特性 [J ] . 弹道学报 , 2020 , 32 ( 1 ): 23 - 30 . DOI: 10.12115/j.issn.1004-499X(2020)01-004 http://doi.org/10.12115/j.issn.1004-499X(2020)01-004 为研究高旋二维弹道修正弹舵控后的攻角与速度偏角的特性,通过在无控弹角运动基础上增加控制组件提供的控制力和力矩,建立了其角运动方程,对起始扰动作用、瞬时控制力作用、长时间控制力作用下的弹丸攻角、速度偏角规律进行了分析。数值计算结果表明:高旋二维弹道修正弹受瞬时控制力作用时,产生的平衡攻角、平均速度偏角的方向与瞬时控制力方向大致相反; 在固定方位舵控力长时间作用下,平衡攻角、平均速度偏角方向与控制力方向近似成180°,相差一个小的角度; 攻角运动是由舵控力产生相反方向的攻角与重力产生向右的动力平衡角合成的,该攻角运动规律将影响弹道的质心运动。研究结果为高旋二维弹道修正弹的控制策略与控制方案设计提供了理论依据与参考。

ZHU H , SHI J G , XIE F , et al . Angular motion characteristics of high-rotation two-dimension trajectory correction projectile [J ] . Journal of Ballistics , 2020 , 32 ( 1 ): 23 - 30 . (in Chinese)

赵新新 , 史金光 , 王中原 , 等 . 固定鸭舵双旋弹角运动特性与控制稳定性研究 [J ] . 哈尔滨工业大学学报 , 2022 , 54 ( 1 ): 123 - 131 .

ZHAO X X , SHI J G , WANG Z Y , et al . Study on angular motion characteristics and control stability with the fixed canard dual-spin projectile [J ] . Journal of Harbin Institute of Technology , 2022 , 54 ( 1 ): 123 - 131 . (in Chinese)

赵新新 , 史金光 , 王中原 , 等 . 固定鸭舵双旋弹全弹道动态稳定性及其影响因素 [J ] . 力学学报 , 2022 , 54 ( 5 ): 1366 - 1376 .

ZHAO X X , SHI J G , WANG Z Y , et al . Dynamic stability and influence factors of the whole trajectory of fixed canard dual-spin projectiles [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2022 , 54 ( 5 ): 1366 - 1376 . (in Chinese)

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