考虑视场角约束的碰撞角控制预设性能制导律

doi:10.7527/S1000-6893.2023.28764

Abstract

Abstract:

To address the problem of guided missiles against non-maneuvering targets， a prescribed performance guidance law with seeker Field-of-View （FOV） and impact angle constraints is proposed. Firstly， a prescribed time performance function is designed to enable direct setting of the convergence time， the upper and lower bounds of the tracking error. Through error transformation， the tracking error control problem under performance boundary constraints is transformed into an unconstrained stable control problem. Secondly， the guidance law is designed as the sum of a pure proportional guidance term and a bias term. The bias term is derived based on the optimal error dynamics method to control the transformation error within a bound， ensure that the tracking error consistently converges within the performance boundary， and ultimately achieve terminal impact angle constraint. Furthermore， based on the proposed guidance law， the in-depth analysis of the parameters in the performance function is conducted， and reasonable parameters ranges are provided. Moreover， considering seeker FOV limitation and moving target scenario， an auxiliary function and the predicted interception point concept are introduced to improve the guidance law respectively， which realize the FOV constraint and the extension of proposed law against moving target. Finally， the effectiveness of the proposed guidance law is verified through numerical simulations.

Key words: guided missiles, impact angle control, prescribed performance control, optimal error dynamics, field-of-view constraint, predicted interception point

CLC Number:

V448.2

Haojian LI, Yuanhe LIU, Yangang LIANG, Kebo LI. Prescribed performance guidance law with field-of-view and impact angle constraints[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(15): 528764-528764.

Figures/Tables 14

Fig.1

Fig.2

Fig. 3

Fig.4

Table 1

Main simulation parameters

变量名称	符号	数值	单位
导弹初始位置	（x_m0，y_m0）	（0，0）	m
目标初始位置	（x_t0，y_t0）	（5 000，0）	m
导弹速度	v_m	200	m/s
导弹初始速度前置角	φ_m0	30	（°）
比例导引系数	N	3	1
误差动力学系数	K	3	1
权重函数参数	n	5	1
上界预设性能函数参数	$χ u p$	0.4	1
下界预设性能函数参数	$χ l o w$	0.8	1
预设性能函数初值参数	λ₀	0.5	rad
预设性能函数终值参数	λ_f	0.01	rad

Table 1

Fig.5

Table 2

Fig.6

Fig.7

Table 3

Fig.8

Table 4

Realistic simulation parameters

变量名称	符号	数值	单位
导弹质量	m	25	kg
参考面积	S_ref	0.11	m²
升力气动导数	$C L α$	0.3
零升阻力系数	$C D 0$	0.04
诱导阻力系数	$C D α$	0.003
海平面大气密度	ρ₀	1.24	kg/m³
密度缩放高度	y_s	7.142 9×10⁶	m
重力加速度	g	9.8	m/s²
导弹初始速度	v_m0	400	m/s

Table 4

Fig.9

Fig.10

References 35

1	KIM M， GRIDER K. Terminal guidance for impact attitude angle constrained flight trajectories［J］. IEEE Transactions on Aerospace and Electronic Systems， 1973， AES-9（6）： 852-859.
2	RYOO C K， TAHK M J. Time-to-go weighted optimal guidance with impact angle constraints［J］. IEEE Transactions on Control Systems Technology， 2006， 14（3）： 483-492.
3	LI R， WEN Q Q， TAN W C. Adaptive weighting impact angle optimal guidance law considering seeker’s FOV angle constraints［J］. Journal of Systems Engineering and Electronics， 2018， 29（1）： 142-151.
4	KIM J， CHO S. Optimal guidance law for impact angle and acceleration constraints with time-varying gains［J］. International Journal of Aeronautical and Space Sciences， 2022， 23（3）： 609-621.
5	KUMAR S R， RAO S， GHOSE D. Sliding-mode guidance and control for all-aspect interceptors with terminal angle constraints［J］. Journal of Guidance， Control， and Dynamics， 2012， 35（4）： 1230-1246.
6	BISWAS B， KUMAR S R， MAITY A. Three-dimensional nonlinear impact angle guidance for maneuvering targets［J］. IFAC-PapersOnLine， 2018， 51（1）： 47-52.
7	KIM H G， KIM H J. All-aspect guidance with impact angle constraint against unknown target maneuver［J］. IEEE Transactions on Aerospace and Electronic Systems， 2019， 55（2）： 830-845.
8	ZHOU Z M， YAO X X. Polynomial guidance law for impact angle control with a seeker look angle limit［J］. Proceedings of the Institution of Mechanical Engineers， Part G： Journal of Aerospace Engineering， 2020， 234（3）： 857-870.
9	HU Q L， CAO R H， HAN T， et al. Field-of-view limited guidance with impact angle constraint and feasibility analysis［J］. Aerospace Science and Technology， 2021， 114： 106753.
10	FU S N， ZHOU G Q， XIA Q L. A trajectory shaping guidance law with field-of-view angle constraint and terminal limits［J］. Journal of Systems Engineering and Electronics， 2022， 33（2）： 426-437.
11	黎克波，廖选平，梁彦刚，等. 基于纯比例导引的拦截碰撞角约束制导策略［J］. 航空学报， 2020， 41（S2）： 724277.
	LI K B， LIAO X P， LIANG Y G， et al. Guidance strategy with impact angle constraint based on pure proportional navigation［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（S2）： 724277 （in Chinese）.
12	SHIN H S， Li K B. An improvement in three-dimensional pure proportional navigation guidance［J］. IEEE Transactions on Aerospace and Electronic Systems， 2021， 57（5）： 3004-3014.
13	LI K B， SHIN H S， TSOURDOS A， et al. Performance of 3-D PPN against arbitrarily maneuvering target for homing phase［J］. IEEE Transactions on Aerospace and Electronic Systems， 2020， 56（5）： 3878-3891.
14	LI K B， SHIN H S， TSOURDOS A， et al. Capturability of 3D PPN against lower-speed maneuvering target for homing phase［J］. IEEE Transactions on Aerospace and Electronic Systems， 2020， 56（1）： 711-722.
15	KIM B S， LEE J G， HAN H S. Biased PNG law for impact with angular constraint［J］. IEEE Transactions on Aerospace and Electronic Systems， 1998， 34（1）： 277-288.
16	ERER K S， MERTTOPÇUOĜLU O. Indirect impact-angle-control against stationary targets using biased pure proportional navigation［J］. Journal of Guidance， Control， and Dynamics， 2012， 35（2）： 700-704.
17	KIM T H， PARK B G， TAHK M J. Bias-shaping method for biased proportional navigation with terminal-angle constraint［J］. Journal of Guidance， Control， and Dynamics， 2013， 36（6）： 1810-1816.
18	闫梁，赵继广，沈怀荣，等. 带末端碰撞角约束的三维联合偏置比例制导律设计［J］. 航空学报， 2014， 35（7）： 1999-2010.
	YAN L， ZHAO J G， SHEN H R， et al. Three-dimensional united biased proportional navigation guidance law for interception of targets with angular constraints ［J］. Acta Aeronautica et Astronautica Sinica， 2014， 35（7）： 1999-2010 （in Chinese）.
19	XU X Y， LIANG Y. Biased optimal guidance law with specified velocity rendezvous angle constraint［J］. The Aeronautical Journal， 2015， 119（1220）： 1287-1299.
20	LEE C H， KIM T H， TAHK M J. Interception angle control guidance using proportional navigation with error feedback［J］. Journal of Guidance， Control， and Dynamics， 2013， 36（5）： 1556-1561.
21	HE S M， LEE C H. Optimality of error dynamics in missile guidance problems［J］. Journal of Guidance， Control， and Dynamics， 2018， 41（7）： 1624-1633.
22	李斌，林德福，何绍溟，等. 基于最优误差动力学的时间角度控制制导律［J］. 航空学报， 2018， 39（11）： 322215.
	LI B， LIN D F， HE S M， et al. Time and angle control guidance law based on optimal error dynamics［J］. Acta Aeronautica et Astronautica Sinica， 2018， 39（11）： 322215 （in Chinese）.
23	LI H Y， WANG J， HE S M， et al. Nonlinear optimal impact-angle-constrained guidance with large initial heading error［J］. Journal of Guidance， Control， and Dynamics， 2021， 44（9）： 1663-1676.
24	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.
25	CHENG Z T， WU H， WANG B， et al. Fixed-time convergent guidance law with impact angle control［J］. Complexity， 2020， 2020： 1-9.
26	SONG Y D， WANG Y J， HOLLOWAY J， et al. Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time［J］. Automatica， 2017， 83： 243-251.
27	PAL A K， KAMAL S， NAGAR S K， et al. Design of controllers with arbitrary convergence time［J］. Automatica， 2020， 112： 108710.
28	BECHLIOULIS C P， ROVITHAKI G A. Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems［J］. Automatica， 2009， 45（2）： 532-538.
29	LI X， YE J K， ZHOU C J， et al. Prescribed performance guidance law with multiple constraints［J］. International Journal of Aerospace Engineering， 2022， 2022： 1-17.
30	LYU S， YAN X D， TANG S. Prescribed performance interceptor guidance with terminal line of sight angle constraint accounting for missile autopilot lag［J］. Aerospace Science and Technology， 2017， 69： 171-180.
31	LYU S， ZHU Z H， TANG S， et al. Prescribed performance slide mode guidance law with terminal line-of-sight angle constraint against maneuvering targets［J］. Nonlinear Dynamics， 2017， 88（3）： 2101-2110.
32	BU X W， QI Q， JIANG B X. A Simplified finite-time fuzzy neural controller with prescribed performance applied to waverider aircraft［J］. IEEE Transactions on Fuzzy Systems， 2022， 30（7）： 2529-2537.
33	李旭，叶继坤，邵雷，等. 基于有限时间小超调预设性能控制的三维滑模末制导律设计［J］. 航空兵器，2022 （in press）.
	LI X， YE J K， SHAO L， et al. Design of three dimensional sliding mode terminal guidance law based on finite-time and small-overshoot prescribed performance control［J］. Aero Weaponry， 2022 （in press）（in Chinese）.
34	HE S M， LEE C H， SHIN H S， et al. Optimal guidance and its applications in missiles and UAVs［M］. Cham： Springer International Publishing， 2020： 54-58.
35	ZHANG W J， FU S N， LI W， et al. An impact angle constraint integral sliding mode guidance law for maneuvering targets interception［J］. Journal of Systems Engineering and Electronics， 2020，31（1）： 168-184.

导弹编号	制导律	主要参数
导弹1	所提制导律	η=2， t_p=25 s
导弹2	CPPC-IACG	M_min=-1， M_max=1， λ_c0=0.09 rad， λ_c∞=0.01 rad， l=0.1
导弹 3	CPPC-IACG	M_min=-1， M_max=3， λ_c0=0.09 rad， λ_c∞=0.01 rad， l=0.1
导弹 4	OED-IACG	K=N=3

目标编号	目标速度大小v_t/（m·s^-1）	目标速度倾角φ_t/（°）
目标 1	10	0
目标 2	30	10

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Prescribed performance guidance law with field-of-view and impact angle constraints

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