谢浩怡 , 杨国伟 , 王全伟 , 等 . 2维弹道修正技术研究综述 [J ] . 兵工自动化 , 2018 , 37 ( 9 ): 66 - 69 .

XIE H Y , YANG G W , WANG Q W , et al. Summarize of two-dimensional trajectory correction technology [J ] . Ordnance Automation , 2018 , 37 ( 9 ): 66 - 69 . (in Chinese)

邢炳楠 , 杜忠华 , 杜成鑫 . 二维弹道修正弹及其制导控制技术综述 [J ] . 国防科技大学学报 , 2021 , 43 ( 4 ): 53 - 68 .

XING B N , DU Z H , DU C X . Review on two-dimensional trajectory correction projectile and its guidance and control technology [J ] . Journal of National University of Defense Technology , 2021 , 43 ( 4 ): 53 - 68 . (in Chinese)

李红云 , 申强 , 邓子龙 . 鸭式布局二维修正双旋弹角运动及转向响应特性分析 [J ] . 兵工学报 , 2024 , 45 ( 6 ): 1866 - 1876 . DOI: 10.12382/bgxb.2023.0057 http://doi.org/10.12382/bgxb.2023.0057 为研究鸭式布局双旋弹受控状态下的动态响应规律,对弹丸角运动特性及转向响应特性进行理论分析。基于7自由度刚体弹道模型,求解弹丸受控状态下的攻角瞬态及稳态解析解,并推导弹丸瞬态及稳态转向响应解析表达式。研究控制指令更新周期、射角、转速及初速对转向响应特性的影响。研究结果表明:输入控制力方向对转向响应相移角影响较小;控制指令更新周期较短时,在弹道顶点相移角瞬态解与稳态解相差较大,采用瞬态解修正后弹丸横纵向耦合程度较低,随着指令更新周期的增大,转向响应相移角瞬态解逐渐趋于稳态解;相移角稳态解随转速增加而减小,随初速增加而增加。通过实验数据验证了理论的正确性。研究结果可为鸭式布局双旋弹二维修正控制系统分析设计提供理论依据。

LI H Y , SHEN Q , DENG Z L . Analysis of angular motion and swerving response characteristics of dual-spinning two-dimensional correction projectile with canard layout [J ] . Acta Armamentarii , 2024 , 45 ( 6 ): 1866 - 1876 . (in Chinese) DOI: 10.12382/bgxb.2023.0057 http://doi.org/10.12382/bgxb.2023.0057 In order to study the dynamic response law of dual-spinning projectile with canard layout in the state of control, the angular motion and swerving response characteristics of it are analyzed theoretically. Based on the seven degrees of freedom rigid body ballistic model, the transient-state and steady-state analytical solutions of the angle of attack of projectile are solved, and the analytical expressions of projectile’s transient-state and steady-state swerving responses are derived. The effects of control command update period, elevation angle, spin rate and initial velocity on swerving response characteristics are explored. The results show that the direction of control force has little influence on the phase shift angle of swerving response. When the update period of control command is short, the transient-state and steady-state solutions of phase shift angle differ greatly at the ballistic apex, and the transverse-longitudinal coupling of projectile is low after using the transient solution correction. With the increase in update period, the transient-state solution of phase shift angle of swerving response gradually approaches to the steady-state solution. In addition, the steady-state solution of phase shift angle decreases with the increase in rotational speed and increases with the increase in projectile velocity. The correctness of the theory is verified by experimental data. This research provides some theoretical basis for the design and analysis of two-dimensional correction control system of dual-spinning projectile with canard layout.

申强 , 仇李良 , 蒲文洋 , 等 . 高旋弹二维修正引信双旋结构气动特性及气动力表征 [J ] . 北京理工大学学报 , 2024 , 44 ( 4 ): 359 - 368 .

SHEN Q , QIU L L , PU W Y , et al. Aerodynamic characteristics and characterization of the double spin structure of two-dimensional correction high-spin projectile [J ] . Transactions of Beijing Institute of Technology , 2024 , 44 ( 4 ): 359 - 368 . (in Chinese)

WANG C , DING L B , FENG Y , et al. Research on angular motion characteristics and stability of trajectory-corrected rocket projectile with Isolated rotating tail rudder [J ] . Mathematical Problems in Engineering , 2023 ,2023:5880706.

WANG C , DING L B , ZHANG H , et al. Research on control force aerodynamic model of a guided rocket with an isolated-rotating tail rudder [J ] . International Journal of Aeronautical and Space Sciences , 2022 , 23 ( 1 ): 1 - 18 .

郭首邑 , 王良明 , 傅健 , 等 . 一种新型后舵尾控修正弹的弹道控制仿真 [J ] . 兵工学报 , 2024 , 45 ( 7 ): 2209 - 2217 . DOI: 10.12382/bgxb.2023.0178 http://doi.org/10.12382/bgxb.2023.0178 为增强修正弹控制舵的快速响应能力和弹道修正效果,且理论上减弱舵片在高旋状态下对弹体的气动扰流影响,设计一种控制舵置于质心后部、与弹尾部高度配合的新型二维修正弹。建立弹体模型,设计以优化后的新式制导方案和比例微积分控制法为主体的组合控制策略,分析无控和有控状态下关键变量参数的变化规律,对基于参数最优值下的弹道修正过程进行仿真计算;采用蒙特卡洛打靶法分析扰动状态下的落点散布情况。仿真结果表明:此控制策略下后舵尾控弹的实际滚转角吻合于输入指令,整个过程速度高低角和方向角的变化范围仅为2°和7°,基于最优值的控制修正过程和扰动状态下的最终落点情况也保证了弹体进行平稳运动的同时具备更优的偏差修正能力,进一步证实了设计的新型弹体模型具有较高的可行性和参考价值。

GUO S Y , WANG L M , FU J , et al. Simulation research on ballistic control of a new tail rudder controlled correction projectile [J ] . Acta Armamentarii , 2024 , 45 ( 7 ): 2209 - 2217 . (in Chinese)

LEI X , FU J , WANG L M , et al. Research on fractional order unidirectional sliding mode control for fixed-rudder two-dimensional correction projectile [C ] //Proceedings of 2023 Chinese Intelligent Systems Conference.Belin , Germany:Springer ,2023: 747 - 759 .

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

HAO Y P , CHEN C . Research on aerodynamic characteristics and correction ability of two-dimension trajectory correction projectile of different canard rudder profile shape [C ] //Proceedings of 2017 Chinese Automation Congress.Jinan , China:IEEE ,2017: 750 - 763 .

宋谢恩 , 王伟鹏 , 丁锋 , 等 . 某型弹道修正弹落点散布规律研究 [J ] . 弹道学报 , 2021 , 33 ( 2 ): 40 - 46 . DOI: 10.12115/j.issn.1004-499X(2021)02-006 http://doi.org/10.12115/j.issn.1004-499X(2021)02-006 为了得到某型弹道修正弹的落点散布规律和射击精度评定方法,以蒙特卡洛打靶获取的落点数据为基础,通过基本的数值统计分析、直方图法、概率纸法、偏度峰度法以及SPSS软件分析等方法,对修正弹落点散布情况进行统计分析,确定了其散布服从二维正态分布,得到了相应的概率密度函数,对比了修正弹与无控弹的射击精度。结果表明,弹道修正弹射击精度的评定可以采用与无控弹同样的指标和计算方法,为修正弹项目验收的射击精度评定部分以及后续的作战使用提供了理论和技术支撑。

SONG X E , WANG W P , DING F , et al. Dispersion law of impact points of a certain type of trajectory correction projectile [J ] . Journal of Ballistics , 2021 , 33 ( 2 ): 40 - 46 . (in Chinese)

柯知非 , 高敏 , 王毅 , 等 . 旋转弹二维弹道修正组件修正能力影响因素仿真分析 [J ] . 弹箭与制导学报 , 2019 , 39 ( 3 ): 21 - 26 . DOI: 10.15892/j.cnki.djzdxb.2019.03.006 http://doi.org/10.15892/j.cnki.djzdxb.2019.03.006 为研究旋转稳定弹道修正弹修正能力,在理论上对舵进行了受力分析,并深入研究了舵结构参数、初速、海拔、射角对修正弹修正能力的影响。研究结果表明:弹丸纵向远修修正能力小于纵向近修的修正能力,横向左修修正能力小于横向右修修正能力;弹丸的绝对修正能力随着初速的增大而增大;海拔越高弹丸在射程与偏航上的修正能力越小;修正弹在纵向射程上的绝对修正能力随射角的改变不大,而偏航方向上变化较为明显。

KE Z F , GAO M , WANG Y , et al. Simulation analysis of influence factors on correction ability of 2-D trajectory correction fuze of spin stabilized projectile [J ] . Journal of Projectiles,Rockets,Missiles and Guidance , 2019 , 39 ( 3 ): 21 - 26 . (in Chinese)

王磊 , 马景权 , 张嘉易 , 等 . 二维修正弹修正能力建模与仿真分析 [J ] . 弹箭与制导学报 , 2021 , 41 ( 6 ): 127 - 131 . DOI: 10.15892/j.cnki.djzdxb.2021.06.026 http://doi.org/10.15892/j.cnki.djzdxb.2021.06.026 针对固定翼鸭舵二维修正弹外弹道运动受力及修正特点,提出了“即修即停”的修正策略与摄动落点推测算法,可对修正过程进行有效复现。推导了弹体升力、导转力矩等气动力与马赫数、攻角的映射关系,建立了外弹道飞行环境下修正弹动力学模型,实现了有控修正弹舵片的修正过程模拟。构建了由弹道模拟、气动仿真、动力学仿真、舵片测姿与控制模拟等二维弹道联合仿真系统,得到了修正时间、修正角度、修正次数等过程参数对最终落点的评测,给出了在横风等不同外界干扰环境下的修正结果。仿真与实验结果验证了所提方法的有效性。

WANG L , MA J Q , ZHANG J Y , et al. Modeling and simulation analysis of correction capability of two-dimensional correction projectile [J ] . Journal of Projectiles,Rockets,Missiles and Guidance , 2021 , 41 ( 6 ): 127 - 131 . (in Chinese)

CUI S L , LIU X , JIANG S S , et al. Design and parameter optimization of trajectory correction control strategy for air duct structure projectile [J ] . International Journal of Aerospace Engineering , 2023 ,2023:4448592.

刘颖 , 杨鹏飞 , 张立军 , 等 . 前馈神经网络和循环神经网络的鲁棒性验证综述 [J ] . 软件学报 , 2023 , 34 ( 7 ): 3134 - 3166 .

LIU Y , YANG P F , ZHANG L J , et al. Survey on robustness verification of feedforward neural networks and recurrent neural networks [J ] . Journal of Software , 2023 , 34 ( 7 ): 3134 - 3166 . (in Chinese)

YONG X , LE L R , YA J X , et al. Impact point prediction guidance of ballistic missile in high maneuver penetration condition [J ] . Defence Technology , 2023 ,26: 213 - 230 .

任济寰 , 吴祥 , 薄煜明 , 等 . 基于增强上下文信息长短期记忆网络的弹道轨迹预测 [J ] . 兵工学报 , 2023 , 44 ( 2 ): 462 - 471 . DOI: 10.12382/bgxb.2021.0489 http://doi.org/10.12382/bgxb.2021.0489 根据己方观测数据进行弹道轨迹预测是现代陆军实施精准打击的重要一环。针对现有弹道轨迹预测方法存在精度不足且实时性不强的问题,提出一种新的增强上下文信息长短期记忆(CE-LSTM)网络轨迹预测模型,进行弹道轨迹的长期精准预测。在LSTM网络可逼近任意非线性函数且具备长期记忆能力的基础上,构建隐藏层输出混合单元提取短时上下文信息,进一步逼近弹体运动状态;通过建立不同条件下的弹道轨迹的数据集,训练得到具备最优超参数的CE-LSTM网络。实验结果表明,与弹道微分方程组的数值积分解法以及高斯混合模型相比,CE-LSTM网络在预测的精度上优于其他2种方法,预测速度提高了3~10倍,且具备较强的泛化能力。

REN J H , WU X , BO Y M , et al. Ballistic trajectory prediction based on context-enhanced long short-term memory network [J ] . Acta Armamentarii , 2023 , 44 ( 2 ): 462 - 471 . (in Chinese) DOI: 10.12382/bgxb.2021.0489 http://doi.org/10.12382/bgxb.2021.0489 Trajectory prediction based on observed data is critical to the modern army's precision strike capability. Yet, the existing trajectory prediction methods have suffer from low accuracy and poor real-time performance. Thus, this study proposes a new model called Context-enhanced Long Short-Term Memory(CE-LSTM) Network to make an accurate long-term prediction of the exterior trajectory of incoming projectiles. The proposed method inherits the LSTM network's advantage in that it can approximate any nonlinear function and it has a long-term memory. Furthermore, we create a mixture output unit of the hidden layer to extract short-term context information and approximate the motion states of the incoming projectiles more accurately. The CE-LSTM network is trained with a large-scale dataset consisting of exterior trajectories under different initial conditions to obtain the optimal hyper-parameters. The experimental results show that compared with the methods like external ballistic differential equations and the Gaussian mixture model, the CE-LSTM network performs significantly better in prediction accuracy, and its prediction speed increases by three to ten times. Moreover, the proposed method is highly generalizable.

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杨泗智 , 龚春林 , 郝波 , 等 . 基于落点预测的高旋火箭弹弹道修正算法 [J ] . 航空学报 , 2020 , 41 ( 2 ): 323421 . DOI: 10.7527/S1000-6893.2019.23421 http://doi.org/10.7527/S1000-6893.2019.23421 高旋火箭弹的修正控制是基于等效力实现的二维弹道修正控制，由于弹体存在陀螺进动和马格努斯效应，在控制力作用下产生的附加攻角引起的升力与控制力的矢量合为等效力，其大小与方向在控制过程中不断变化，不能简单根据偏差量（修正量）的比例关系来确定控制力的方向。基于此，分析了控制力与等效力的关系，提出了一种基于弹道落点预测的控制算法。首先利用弹道落点预测模型实时预测落点与目标的偏差量，然后利用小扰动法构造偏差量对控制量的敏感系数矩阵，通过偏差量与敏感系数矩阵解算出纵、横两个方向的需用控制量。采用修正前后速度矢量的位置关系得到控制量的合矢量及其方位角，并利用控制量的合矢量与等效力计算出控制周期，在控制周期内按照等效力方位角调整控制力的方向实现对高旋火箭弹的精确控制，解决了非线性耦合问题。仿真结果表明该算法具有较高的控制精度，为工程应用提供理论依据。

YANG S Z , GONG C L , HAO B , et al. Trajectory correction algorithm for high-spin rockets based on impact point prediction [J ] . Acta Aeronautica et Astronautica Sinica , 2020 , 41 ( 2 ): 332421 . (in Chinese)