基于最优误差动力学的变速导弹飞行路程控制制导律
收稿日期: 2022-01-07
修回日期: 2022-02-21
录用日期: 2022-06-13
网络出版日期: 2022-06-24
基金资助
国家自然科学基金(12002370)
Flying range control guidance for varying⁃speed missiles based on optimal error dynamics
Received date: 2022-01-07
Revised date: 2022-02-21
Accepted date: 2022-06-13
Online published: 2022-06-24
Supported by
National Natural Science Foundation of China(12002370)
针对基于常速假设的飞行时间控制制导律在实际应用中存在性能下降的问题，将飞行时间控制问题转化为飞行路程控制问题，提出一种适用于变速导弹的飞行路程控制制导方案。首先，基于古典微分几何曲线原理构建弧长域内导弹打击固定目标的相对运动方程，消除了导弹速度大小变化的影响。其次，基于高斯超几何函数，推导了纯比例导引律制导下变速导弹对固定目标的剩余飞行路程精确解。然后，进一步基于最优误差动力学方法，在不考虑小角假设和其他近似假设的前提下，设计了变速导弹全局非线性飞行路程控制制导律。最后，通过数值仿真验证了所提方法的有效性。
关键词： 古典微分几何曲线原理; 变速导弹; 高斯超几何函数; 最优误差动力学; 飞行路程控制
刘远贺 , 黎克波 , 何绍溟 , 梁彦刚 . 基于最优误差动力学的变速导弹飞行路程控制制导律[J]. 航空学报, 2023 , 44(7) : 326909 -326909 . DOI: 10.7527/S1000-6893.2022.26909
To solve the problem of performance degradation of current impact time control guidance based on constant speed assumption in practical application， a feasible flying range control guidance scheme with time-varying speed is proposed in this paper. The relative motion equation of the missile against the stationary target in the arc-length domain is derived based on the classical differential geometric curve principle， which reduces the influence of time-varying speed on the relative motion of missile and target. Furthermore， the exact solution for the range-to-go guided by pure proportional navigation is derived using the Gaussian hypergeometric function. On this basis， a flying range control guidance law is designed with the optimal error dynamics method， and the effectiveness of the proposed guidance is verified by simulation.
| 1 | JEON I S， LEE J I， TAHK M J. Impact-time-control guidance law for anti-ship missiles ［J］. IEEE Transactions on Control Systems Technology， 2006， 14（2）： 260-266. |
| 2 | 魏明英， 崔正达， 李运迁. 多弹协同拦截综述与展望［J］. 航空学报， 2020， 41（S1）： 723804. |
| WEI M Y， CUI Z D， LI Y Q. Review and future development of multi-missile coordinated interception ［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（S1）： 723804 （in Chinese）. | |
| 3 | CHO N， KIM Y. Modified pure proportional navigation guidance law for impact time control ［J］. Journal of Guidance， Control， and Dynamics， 2016， 39（4）： 852-872. |
| 4 | TAHK M J， SHIM S W， HONG S M， et al. Impact time control on time-to-go prediction for sea skimming anti-ship missiles ［J］. IEEE Transactions on Aerospace and Electronic Systems， 2018， 54（4）： 2043-2052. |
| 5 | HE S M， LEE C H. Optimality of error dynamics in missile guidance problems ［J］. Journal of Guidance， Control， and Dynamics， 2018， 41（7）： 1620-1629. |
| 6 | HE S M， LEE C H， SHIN H S， et al. Optimal three-dimensional impact time guidance with seeker’s field-of-view constraint ［J］. Chinese Journal of Aeronautics， 2021， 34（2）： 240-251. |
| 7 | WANG C Y， DONG W， WANG J N， et al. Guidance law design with fixed-time convergent error dynamics ［J］. Journal of Guidance， Control， and Dynamics， 2021， 44（7）： 1389-1398. |
| 8 | DONG W， WANG C Y， WANG J N， et al. Fixed-time terminal angle constrained cooperative guidance law against maneuvering target ［J］. IEEE Transactions on Aerospace and Electronic Systems， 2022， 58（2）： 1352-1366. |
| 9 | KUMAR S R， GHOSE D. Impact time guidance for large heading errors using sliding mode control ［J］. IEEE Transactions on Aerospace and Electronic Systems， 2015， 51（4）： 3123-3138. |
| 10 | AI X L， WANG L L， YU J Q， et al. Field-of-view constrained two-stage guidance law design for three-dimensional salvo attack of multiple missiles via an optimal control approach ［J］. Aerospace Science and Technology， 2019， 85： 334-346. |
| 11 | KUMAR S R， MUKHERJEE D. Three-dimensional nonsingular impact time guidance with limited field-of-view ［J］. IEEE Transactions on Control Systems Technology， 2022， 30（4）： 1448-1459. |
| 12 | CHIOU Y C， KUO C Y. Geometric approach to three-dimensional missile guidance problem ［J］. Journal of Guidance， Control， and Dynamics， 1998， 21（2）： 335-341. |
| 13 | KUO C Y， SOETANTO D， CHIOU Y C. Geometric analysis of flight control command for tactical missile guidance ［J］. IEEE Transactions on Control Systems Technology， 2001， 9（2）： 234-243. |
| 14 | LI K B， CHEN L， TANG G J. Algebraic solution of differential geometric guidance command and time delay control ［J］. Science China： Technological Sciences， 2015， 58（3）： 565-573. |
| 15 | LI K B， SU W S， CHEN L. Performance analysis of differential geometric guidance law against high-speed target with arbitrarily maneuvering acceleration ［J］. Proceedings of the Institution of Mechanical Engineers， Par G： Journal of Aerospace Engineering， 2019， 233（10）： 3547-3563. |
| 16 | 黄景帅， 张洪波， 汤国建， 等. 机动目标拦截新型微分几何制导律设计［J］. 系统工程与电子技术， 2018， 40（10）： 2288-2295. |
| HUANG J S， ZHANG H B， TANG G J， et al. Design of differential geometric guidance law against maneuvering target ［J］. Systems Engineering and Electronics， 2018， 40（10）： 2288-2295 （in Chinese）. | |
| 17 | LU P. Intercept of nonmoving targets at arbitrary time-varying velocity ［J］. Journal of Guidance， Control， and Dynamics， 1998， 21（1）： 176-178. |
| 18 | LU P， DOMAN D B， SCHIERMAN J D. Adaptive terminal guidance for hypervelocity impact in specified direction ［J］. Journal of Guidance， Control， and Dynamics， 2006， 29（2）： 269-278. |
| 19 | WANG P Y， GUO Y N， MA G F. New differential geometric guidance strategies for impact-time control problem ［J］. Journal of Guidance， Control， and Dynamics， 2019， 42（9）： 1982-1992. |
| 20 | TEKIN R， ERER K S， HOLZAPFEL F. Adaptive impact time control via looking-angle shaping under varying velocity ［J］. Journal of Guidance， Control， and Dynamics， 2017， 40（12）： 3247-3245. |
| 21 | WANG J W， ZHANG R. Terminal guidance for a hypersonic vehicle with impact time control ［J］. Journal of Guidance， Control， and Dynamics， 2018， 41（8）： 1789-1797. |
| 22 | SUN G X， WEN Q Q， XU Z Q， et al. Impact time control using biased proportional navigation for missiles with varying velocity ［J］. Chinese Journal of Aeronautics， 2020， 33（3）： 956-964. |
| 23 | JEON I S， LEE J I， TAHK M J. Homing guidance law for cooperative attack of multiple missiles ［J］. Journal of Guidance， Control， and Dynamics， 2010，33（1）： 275-280. |
| 24 | LI K B， LIU Y H， LIANG Y G， et al. Performance of PPN guided missile with arbitrary time-varying speed against stationary targets： new findings ［C］∥Proceedings of the 5th International Symposium on Autonomous Systems. Hangzhou： IEEE， 2022： 1-8. |
/
| 〈 |
|
〉 |
CJA