A hybrid proportional navigation based two-stage impact time control guidance law

doi:10.23919/JSEE.2022.000046

Abstract

Abstract:

To improve applicability and adaptability of the impact time control guidance (ITCG) in practical engineering, a two-stage ITCG law with simple but effective structure is proposed based on the hybrid proportional navigation, namely, the pure-proportional-navigation and the retro-proportional-navigation. For the case with the impact time error less than zero, the first stage of the guided trajectory is driven by the retro-proportional-navigation and the second one is driven by the pure-proportional-navigation. When the impact time error is greater than zero, both of the stages are generated by the pure-proportional-navigation but using different navigation gains. It is demonstrated by two- and three-dimensional numerical simulations that the proposed guidance law at least has comparable results to existing proportional-navigation-based ITCG laws and is shown to be advantageous in certain circumstances in that the proposed guidance law alleviates its dependence on the time-to-go estimation, consumes less control energy, and adapts itself to more boundary conditions and constraints. The results of this research are expected to be supplementary to the current research literature.

Key words: missile guidance law, impact time control, pure-proportional-navigation, retro-proportional-navigation, time-to-go estimation

Jia HUANG, Sijiang CHANG, Shengfu CHEN. A hybrid proportional navigation based two-stage impact time control guidance law[J]. Journal of Systems Engineering and Electronics, 2022, 33(2): 461-473.

Figures/Tables 13

Fig 1

Fig 2

Fig 3

Fig 4

Fig 5

Fig 6

Fig 7

Fig 8

Table 1

Fig 9

Fig 10

References 37

1	JEON I S, LEE J I, TAHK M J Impact-time-control guidance law for anti-ship missiles. IEEE Trans. on Control Systems Technology, 2006, 14 (2): 260- 266. doi: 10.1109/TCST.2005.863655
2	JEON I S, LEE J I, TAHK M J Impact-time-control guidance with generalized proportional navigation based on nonlinear formulation. Journal of Guidance, Control, and Dynamics, 2016, 39 (8): 1887- 1892.
3	ZHANG Y A, WANG X L, WU H L Impact time control guidance law with field of view constraint. Aerospace Science and Technology, 2014, 39, 361- 369. doi: 10.1016/j.ast.2014.10.002
4	ZHANG Y A, WANG X L, WU H L Impact time control guidance with field-of-view constraint accounting for uncertain system lag. Proceedings of the Institution of Mechanical Engineer, Part G: Journal of Aerospace Engineering, 2016, 230 (3): 515- 529. doi: 10.1177/0954410015594401
5	ZHANG Y A, MA G X, LIU A L Guidance law with impact time and impact angle constraints. Chinese Journal of Aeronautics, 2013, 26 (4): 960- 966. doi: 10.1016/j.cja.2013.04.037
6	ZHANG Y A, WANG X L, MA G X Impact time control guidance law with large impact angle constraint. Proceedings of the Institution of Mechanical Engineer, Part G: Journal of Aerospace Engineering, 2015, 229 (11): 2119- 2131. doi: 10.1177/0954410014568466
7	CHO N, KIM Y Modified pure proportional navigation guidance law for impact time control. Journal of Guidance, Control, and Dynamics, 2016, 39 (4): 852- 872. doi: 10.2514/1.G001618
8	TAHK M J, SANG D K Guidance law switching logic considering the seeker’s field-of-view limits. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2009, 223 (8): 1049- 1058. doi: 10.1243/09544100JAERO614
9	GHOSH S, GHOSE D, RAHA S. Three dimensional retro-PN based impact time control for higher speed nonmaneuvering targets. Proc. of the 52nd IEEE Conference on Decision and Control, 2013: 4865−4870.
10	JEON I S, LEE J I Impact-time-control guidance law with constraints on seeker look angle. IEEE Trans. on Aerospace and Electronic Systems, 2017, 53 (5): 2621- 2627. doi: 10.1109/TAES.2017.2698837
11	JEON I S, LEE J I Homing guidance law for cooperative impact of multiple missiles. Journal of Guidance, Control, and Dynamics, 2010, 33 (1): 275- 280. doi: 10.2514/1.40136
12	WANG J W, ZHANG R Terminal guidance for a hypersonic vehicle with impact time control. Journal of Guidance, Control, and Dynamics, 2018, 41 (8): 1789- 1797.
13	NARL N, BALAKRISHNAN S N Impact time and angle guidance with sliding mode control. IEEE Trans. on Control Systems Technology, 2012, 20 (6): 1436- 1449. doi: 10.1109/TCST.2011.2169795
14	KUMAR S R, GHOSE D Impact time guidance for large heading errors using sliding-mode control. IEEE Trans. on Aerospace and Electronic Systems, 2015, 51 (4): 3123- 3138. doi: 10.1109/TAES.2015.140137
15	CHO D, KIM H J, TAHK M J Nonsingular sliding mode guidance for impact time control. Journal of Guidance, Control, and Dynamics, 2016, 39 (1): 61- 68. doi: 10.2514/1.G001167
16	ZHANG X J, LIU M Y, LI Y Sliding mode control and Lyapunov based guidance law with impact time constraints. Journal of Systems Engineering and Electronics, 2017, 28 (6): 1186- 1192. doi: 10.21629/JSEE.2017.06.16
17	CHEN X T, WANG J Z Nonsingular sliding-mode control for field-of-view constrained impact time guidance. Journal of Guidance, Control, and Dynamics, 2018, 41 (5): 1214- 1222. doi: 10.2514/1.G003146
18	KUMAR S R, GHOSE D. Impact time and angle control guidance. Proc. of the AIAA Guidance, Navigation, and Control Conference, 2015: 2015-0616.
19	ZHOU J, WANG Y, ZHAO B Impact-time-control guidance law for missile with time-varying velocity. Mathematical Problems in Engineering, 2016, 2016 (1): 1- 14.
20	CHEN X T, WANG J Z Sliding-mode guidance for simultaneous control of impact time and angle. Journal of Guidance, Control, and Dynamics, 2019, 42 (2): 394- 401. doi: 10.2514/1.G003893
21	HU Q L, HAN T, XIN M Sliding-mode impact time guidance law design for various target motions. Journal of Guidance, Control, and Dynamics, 2019, 42 (1): 136- 148. doi: 10.2514/1.G003620
22	KIM M, JUNG B, HAN B, et al Lyapunov-based impact time control guidance laws against stationary targets. IEEE Trans. on Aerospace and Electronic Systems, 2015, 51 (2): 1111- 1122. doi: 10.1109/TAES.2014.130717
23	SALEEM A, RATNOO A Lyapunov-based guidance law for impact time control and simultaneous arrival. Journal of Guidance, Control, and Dynamics, 2016, 39 (1): 164- 173. doi: 10.2514/1.G001349
24	LEE J I, JEON I S, TAHK M J Guidance law to control impact time and angle. IEEE Trans. on Aerospace and Electronic Systems, 2007, 43 (1): 301- 310. doi: 10.1109/TAES.2007.357135
25	ERER K S, TEKIN R Impact time and angle control based on constrained optimal solutions. Journal of Guidance, Control, and Dynamics, 2016, 39 (10): 2448- 2454. doi: 10.2514/1.G000414
26	ARITA S, UENO S. Optimal feedback guidance for nonlinear missile model with impact time and angle constraints. Proc. of the AIAA Guidance, Navigation, and Control Conference, 2013: 2013-4785.
27	TEKIN R, ERER K S, HOLZAPFEL F Polynomial shaping of the look angle for impact-time control. Journal of Guidance, Control, and Dynamics, 2017, 40 (10): 2666- 2671.
28	TEKIN R, ERER K S, HOLZAPFEL F Adaptive impact time control via look-angle shaping under varying velocity. Journal of Guidance, Control, and Dynamics, 2017, 40 (12): 3247- 3255. doi: 10.2514/1.G002981
29	TEKIN R, ERER K S, HOLZAPFEL F Control of impact time with increased robustness via feedback linearization. Journal of Guidance, Control, and Dynamics, 2016, 39 (7): 1682- 1689. doi: 10.2514/1.G001719
30	TEKIN R, ERER K S, HOLZAPFEL F Impact time control with generalized-polynomial range formulation. Journal of Guidance, Control, and Dynamics, 2018, 41 (5): 1190- 1195. doi: 10.2514/1.G003279
31	KANG S, TEKIN R, HOLZAPFEL F Generalized impact time and angle control via look-angle shaping. Journal of Guidance, Control, and Dynamics, 2019, 42 (3): 695- 702. doi: 10.2514/1.G003765
32	ZHAO Y, SHENG Y Z, LIU X D Trajectory reshaping based guidance with impact time and angle constraints. Chinese Journal of Aeronautics, 2016, 29 (4): 984- 994. doi: 10.1016/j.cja.2016.06.012
33	SNYDER M, QU Z, HULL R, et al Quad-segment polynomial trajectory guidance for impact-time control of precision-munition strike. IEEE Trans. on Aerospace and Electronic Systems, 2016, 52 (6): 3008- 3023. doi: 10.1109/TAES.2016.140420
34	KIM T H, LEE C H, JEON I S, et al Augmented polynomial guidance with impact time and angle constraints. IEEE Trans. on Aerospace and Electronic Systems, 2013, 49 (4): 2806- 2817. doi: 10.1109/TAES.2013.6621856
35	PRASANNA H M, GHOSE D Retro-proportional-navigation: a new guidance law for interception of high-speed targets. Journal of Guidance, Control, and Dynamics, 2012, 35 (2): 377- 386. doi: 10.2514/1.54892
36	ABRAMOWITZ M, STEGUN I A. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover Publications, 1965.
37	SONE S, HA I A Lyapunov-like approach to performance analysis of 3-dimensional pure PNG laws. IEEE Trans. on Aerospace and Electronic Systems, 1994, 30 (1): 238- 248. doi: 10.1109/7.250424

ITCG law	Time-to-go estimation formula	Desired impact time $ {t_d} $ /s	Extreme acceleration $ {a_M} $ /(m $ \cdot $ s^?2)	Extreme heading error $ \phi $ /(°)	Total control energy consumption $\int_0^{{t_f}} {\left( {{{a_M^2} \mathord{\left/ {\vphantom {{a_M^2} 2}} \right. } 2}} \right){\text{d}}t} $ /(m² $ \cdot $ s^?3)	Final impact time error $ \xi $ /s
[7]	(8)	50	39.7	69.6	5.5 $ \times $ 10³	?2.0 $ \times $ 10^?4
[7]	(49)	50	40.3	72.5	6.0 $ \times $ 10³	3.1 $ \times $ 10^?3
Proposed	(8)	50	?22.0	69.8	4.1 $ \times $ 10³	?2.0 $ \times $ 10^?4
Proposed	(49)	50	?27.7	72.7	4.6 $ \times $ 10³	6.1 $ \times $ 10^?4
[2]	(8)	50	22.8	51.9	3.3 $ \times $ 10³	?2.0 $ \times $ 10^?4
[2]	(49)	50	?16.5	52.3	3.3 $ \times $ 10³	?8.5 $ \times $ 10^?4
[7]	(8)	70	98.1	112.9	1.9 $ \times $ 10⁴	?2.0 $ \times $ 10^?4
[7]	(49)	70	98.1	127.7	2.4 $ \times $ 10⁴	6.7 $ \times $ 10^?1
Proposed	(8)	70	?23.0	109.6	7.7 $ \times $ 10³	?2.0 $ \times $ 10^?4
Proposed	(49)	70	?37.9	118.6	9.3 $ \times $ 10³	5.5 $ \times $ 10^?4
[2]	(8)	70	27.3	93.8	6.7 $ \times $ 10³	?2.0 $ \times $ 10^?4
[2]	(49)	70	N/A^a	N/A	N/A	N/A