Design of guidance law with multiple constraints considering maneuvering efficiency
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摘要:
针对考虑交会角约束的导引律在可用过载不足时将导致大的交会角误差问题，推导一种考虑时变过载约束的制导形式，而该导引律在实现较大机动的同时会带来较大能量损失，进而提出一种考虑导弹机动效率的多约束导引律。首先，应用最优二次型原理推导出一种时变控制项权系数的闭环制导形式；其次，将导弹机动时刻阻力系数引入时变权系数，并通过迭代分别确定可用过载与机动效率约束边界；最后，将时变过载约束表示成剩余时间的函数，代入制导指令，并进行弹道仿真。结果表明：推导的2种导引律均能较好地实现末端弹道成型要求，考虑机动效率的制导指令分配更为合理，并有效降低了拦截末端速度损耗，提高了制导精度与毁伤效果；且考虑机动效率的导引律中时变权系数无须配平求解，在保证精度的同时极大提高了迭代速度。
Abstract:Due to the guidance law with terminal intercept angle which will cause big angle error when available payload is insufficient, a guidance law considering time-varying overload constraint has been elicited, which would bring on more energy loss when much maneuver is achieved at the same time. Given this, this paper elicits a guidance law with multiple constraints considering maneuvering efficiency. First, a closed-loop guidance law with time-varying control weight coefficient is elicited according to optimal quadratic theory. Second, drag coefficient when maneuvering is introduced into time-varying control weight coefficient, and the constraint boundaries of available payload and maneuvering efficiency are obtained through iterations. Finally, the time-varying weight coefficient is changed into function of time-to-go, and the trajectories are simulated with guidance law considering available payload and maneuvering efficiency. The simulation results indicate that both the two guidance laws can meet the requirement of trajectory shaping, and the acceleration command of guidance law with constraint considering maneuvering efficiency is more reasonable, which reduces the velocity loss effectively and enhances the guidance accuracy and damage effect. Moreover, balance solution of time-varying weight coefficient is not necessary with this method, so iteration speed will be highly improved when accuracy is guaranteed.
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图 2 可用过载拟合曲线与实际可用过载曲线对比
Figure 2. Contrast between available overload fitted curve and practical available overload curve
图 4 常规防空导弹Cy/Cx(max)随Ma变化
Figure 4. Variation of common air-defense missile Cy/Cx(max) with Ma
图 5 导弹机动效率随迭代次数变化
Figure 5. Variation of missile maneuvering efficiency with iteration times
图 6 性能约束边界与剩余时间关系
Figure 6. Relationship between performance constrained boundary and time-to-go
图 7 3种导引律末制导弹道对比(匀速目标)
Figure 7. Three guidance laws' terminal trajectory contrast(constant target)
图 8 3种导引律弹目交会角对比(匀速目标)
Figure 8. Three guidance laws' missile-target intercept angle contrast(constant target)
图 9 3种导引律指令加速度对比(匀速目标)
Figure 9. Three guidance laws' command acceleration contrast (constant target)
图 10 3种导引律末制导弹道对比(机动目标)
Figure 10. Three guidance laws' terminal trajectory contrast (manevering target)
图 11 3种导引律指令加速度对比(机动目标)
Figure 11. Three guidance laws' command acceleration contrast (manevering target)
表 1 不同导引律仿真结果对比(匀速目标)
Table 1. Different guidance laws' simulation results contrast (constant target)
导引律 脱靶量/m 末端速度/(m·s-1) 末端交会角/(°) 拦截时间/s 交会角误差/(°) 交会角约束 5.75 455.2 84.29 13.63 3.29 交会角/可用过载约束 0.43 514.5 80.31 13.38 -0.69 交会角/机动效率约束 0.51 519.4 81.05 13.29 0.05 
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表 2 不同导引律仿真结果对比(机动目标)
Table 2. Different guidance laws' simulation results contrast (manevering target)
导引律 脱靶量/m 末端速度/(m·s-1) 末端交会角/(°) 拦截时间/s 交会角误差/(°) 交会角约束 1.58 570.2 -1.00 12.30 -1.00 交会角/可用过载约束 0.14 569.5 -0.66 12.29 -0.66 交会角/机动效率约束 0.22 571.1 -0.60 12.29 -0.60
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[1] 斯维特洛夫Β Γ, 戈卢别夫И C. 防空导弹设计[M]. 《防空导弹设计》编译委员会, 译. 北京: 中国宇航出版社, 2004: 111-116.SVATROV Β Γ, GRUBIEF И C.Air-defense missile design[M].Air-defense Missile Design Compliation Committee, translated.Beijing:Chinese Space Press, 2004:111-116(in Chinese). [2] RYOO C K, CHO H, TAHK M J.Time-to-go weighted optimal guidance with impact angle constraints[J].IEEE Transactions on Control System Technology, 2006, 14(3):483-492. doi: 10.1109/TCST.2006.872525 [3] SHAFERMAN V, SHIMA T.Linear quadratic guidance laws for imposing a terminal intercept angle[J].Journal of Guidance, Control, and Dynamics, 2008, 31(5):39-48. http://adsabs.harvard.edu/abs/2008JGCD...31.1400S [4] 张友安, 马培蓓.带有攻击角度和攻击时间控制的三维制导[J].航空学报, 2008, 29(4):1020-1026. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB200804042.htmZHANG Y A, MA P B.Three-dimensional guidance law with impact angle and impact time constraints[J].Acta Aeronautica et Astronautica Sinica, 2008, 29(4):1020-1026(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB200804042.htm [5] CLOUTIER J R.All-aspect acceleration limited homing guidance[C]//AIAA Guidance, Navigation, and Control Conference and Exhibit.Reston:AIAA, 2005, 8:9-11. [6] HEXNER G, SHIMA T.Stochastic optimal control guidancelaw with bounded acceleration[J].IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(1):71-78. doi: 10.1109/TAES.2007.357155 [7] 董晨, 晁涛, 王松艳, 等.带落角约束与控制约束的纵向制导律[J].固体火箭技术, 2014, 37(3):285-290. http://www.cnki.com.cn/Article/CJFDTOTAL-GTHJ201403002.htmDONG C, CHAO T, WANG S Y, et al.Longitudinal guidance law with constraints on impact angle and control[J].Journal of Solid Rocket Technology, 2014, 37(3):285-290(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-GTHJ201403002.htm [8] SONG T L, SHIN S J, CHO H.Impact angle control for planer engagements[J].IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(4):1439-1444. doi: 10.1109/7.805460 [9] RYOO C K, CHO H, TAHK M J.Closed-form solutions of optimal guidance with terminal impact angle constraint[C]//Proceedings of 2003 IEEE Conference on Control Application.Piscataway, NJ:IEEE Press, 2003:504-509. [10] 王辉, 林德福, 崔晓曦.一类扩展的弹道成型制导律[J].北京理工大学学报, 2014, 34(6):597-603. http://www.cnki.com.cn/Article/CJFDTOTAL-BJLG201406010.htmWANG H, LIN D F, CUI X X.Extended trajectory shaping guidance laws[J].Transactions of Beijing Institute of Technology, 2014, 34(6):597-603(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-BJLG201406010.htm [11] 王丽英, 张友安, 黄诘.带约束的末制导率与伪谱法轨迹优化[M].北京:国防工业出版社, 2015:92-96.WANG L Y, ZHANG Y A, HUANG J.Guidance law under multiple constrained and GPOPS trajectory optimization[M].Beijing:Nationnal Defense Industry Press, 2015:92-96(in Chinese). [12] 王青, 陈宇, 张颖昕, 等.最优控制——理论、方法与应用[M].北京:高等教育出版社, 2010:65-71.WANG Q, CHEN Y, ZHANG Y X, et al.Optimal control theory, mehod and application[M].Beijing:Higher Education Press, 2010:65-71(in Chinese). [13] ZARCHAN P.Tactical and strategic missile guidance, progress in astronautics and aeronautics[M].Reston:AIAA, 2003. [14] 钱杏芳, 林瑞雄.导弹飞行力学[M].3版.北京:北京理工大学出版社, 2008:62-63.QIAN X F, LIN R X.Missile flight dynamics[M].3rd ed.Beijing:Beijing Institute of Technology Press, 2008:62-63(in Chinese). [15] 孙未蒙. 空地制导武器多约束条件下的制导率设计[D]. 长沙: 国防科学技术大学, 2008: 8-13. http://cdmd.cnki.com.cn/Article/CDMD-90002-2010164860.htmSUN W M.Research on guidance law design with terminal impact angle constraints in air-to-surface guided weapon[D].Changsha:National University of Defense Technology, 2008:8-13(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-90002-2010164860.htm -
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