Design methodology of a mini-missile considering flight performance and guidance precision

doi:10.23919/JSEE.2024.000007

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (1): 195-210.doi: 10.23919/JSEE.2024.000007

• CONTROL THEORY AND APPLICATION • Previous Articles

Design methodology of a mini-missile considering flight performance and guidance precision

Licong ZHANG¹(), Chunlin GONG¹^,*(), Hua SU¹(), Da Ronch ANDREA²()

¹ Shaanxi Aerospace Flight Vehicle Design Key Laboratory, School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China
² Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO171BJ, United Kingdom

Received:2022-02-28 Online:2024-02-18 Published:2024-03-05
Contact: Chunlin GONG E-mail:zhanglicong@mail.nwpu.edu.cn;leonwood@nwpu.edu.cn;su@nwpu.edu.cn;A.Da-Ronch@soton.ac.uk
About author:
ZHANG Licong was born in 1995. He received his B.S. degree from the Honors College, Northwestern Polytechnical University, Xi’an, China in 2018. He is currently a doctoral candidate at the School of Astronautics, Northwestern Polytechnical University. His research interests include flight vehicle design, engineering optimization, and uncertainty analysis in nonlinear dynamics. E-mail: zhanglicong@mail.nwpu.edu.cn

GONG Chunlin was born in 1980. He received his B.S., M.S., and Ph.D. degrees from Northwestern Polytechnical University, Xi’an, China in 2001, 2004, and 2007, respectively. He is currently a professor and Ph.D. supervisor at the School of Astronautics, Northwestern Polytechnical University. His research interests include system engineering of flight vehicles, design of hypersonic flight vehicles, and multidisciplinary design optimization. E-mail: leonwood@nwpu.edu.cn

SU Hua was born in 1985. He received his B.S., M.S., and Ph.D. degrees from Northwestern Polytechnical University, Xi’an, China in 2008, 2010, and 2014, respectively. He is an assistant researcher and M.S. supervisor at the School of Astronautics, Northwestern Polytechnical University. His research interests include the design of missiles and launch vehicles, multidisciplinary design optimization, and design software for flight vehicles. E-mail: su@nwpu.edu.cn

ANDREA Da Ronch was born in 1980. He received his B.S. and M.S. degrees from Politecnico di Milano in Italy, and Ph.D. degree from University of Liverpool in the UK. He is currently an associate professor and Ph.D. supervisor at the Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, England. His research interests include aerospace engineering, fluid mechanics, structural dynamics, numerical analysis, flight control, aeroelasticity, fluid flow, and CFD simulation. E-mail: A.Da-Ronch@soton.ac.uk

Abstract

Abstract:

The design of mini-missiles (MMs) presents several novel challenges. The stringent mission requirement to reach a target with a certain precision imposes a high guidance precision. The miniaturization of the size of MMs makes the design of the guidance, navigation, and control (GNC) have a larger-than-before impact on the main-body design (shape, motor, and layout design) and its design objective, i.e., flight performance. Pursuing a trade-off between flight performance and guidance precision, all the relevant interactions have to be accounted for in the design of the main body and the GNC system. Herein, a multi-objective and multidisciplinary design optimization (MDO) is proposed. Disciplines pertinent to motor, aerodynamics, layout, trajectory, flight dynamics, control, and guidance are included in the proposed MDO framework. The optimization problem seeks to maximize the range and minimize the guidance error. The problem is solved by using the nondominated sorting genetic algorithm II. An optimum design that balances a longer range with a smaller guidance error is obtained. Finally, lessons learned about the design of the MM and insights into the trade-off between flight performance and guidance precision are given by comparing the optimum design to a design provided by the traditional approach.

Key words: mini-missiles (MMs), guidance, navigation, and control (GNC) system, multi-objective optimization, multidisciplinary design optimization (MDO), flight performance, guidance precision

Licong ZHANG, Chunlin GONG, Hua SU, Da Ronch ANDREA. Design methodology of a mini-missile considering flight performance and guidance precision[J]. Journal of Systems Engineering and Electronics, 2024, 35(1): 195-210.

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References 43

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T_a	Actuator				Battery
T_a	Rise time/s	Overshoot/%	Mass/kg	Length/mm	Mass/kg	Length/mm
0	0.0267	3.42	0.150	58.2	0.13	34
1	0.0374	3.42	0.144	57.4	0.12	32.4
2	0.0418	1.40	0.152	60.0	0.12	30.8
3	0.0481	3.42	0.138	54.5	0.11	28.7
4	0.0456	4.78	0.128	50.7	0.10	26.1
5	0.0730	1.02	0.130	52.5	0.09	24.4

T_s	LOS angle error/(º)	Mass/kg	Length/mm
0	0.05	0.134	40.0
1	0.10	0.128	38.2
2	0.20	0.122	36.3
3	0.30	0.114	33.9
4	0.40	0.104	30.9
5	0.50	0.097	29.0

Error sources	Description	Nominal value	Error range		Uncertain type
v₀/(m/s)	Launch velocity	20	∆v₀:	[−5, 5]	Uniform
θ₀/(º)	Launch longitudinal angle	15	∆θ₀:	[−2, 2]	Uniform
ψ₀/(º)	Launch lateral angle	0	∆ψ₀:	[−2, 2]	Uniform
m₀/kg	Initial mass	1.5	∆m₀:	[−0.075, 0.075]	Uniform
v_g-lon/(m/s)	Longitudinal gust velocity	0	∆v_g-lon:	[−5, 5]	Uniform
v_g-lat/(m/s)	Lateral gust velocity	0	∆v_g-lat:	[−2.5, 2.5]	Uniform

ID	Factor						ID	Factor
ID	∆v₀/ (m/s)	∆θ₀/ (º)	∆ψ₀/ (º)	∆m₀/ kg	∆v_g-lon/ (m/s)	∆v_g-lat/ (m/s)	ID	∆v₀/ (m/s)	∆θ₀/ (º)	∆ψ₀/ (º)	∆m₀/ kg	∆v_g-lon/ (m/s)	∆v_g-lat/ (m/s)
1	5	2	2	0.075	5	2.5	7	−5	2	−2	−0.075	5	2.5
2	5	2	2	0.075	5	−2.5	8	−5	2	−2	0.075	−5	−2.5
3	5	2	−2	−0.075	−5	2.5	9	−5	2	2	−0.075	−5	−2.5
4	5	−2	2	−0.075	−5	2.5	10	−5	−2	−2	0.075	5	2.5
5	5	−2	−2	0.075	−5	−2.5	11	−5	−2	2	−0.075	5	−2.5
6	5	−2	−2	−0.075	5	−2.5	12	−5	−2	2	0.075	−5	2.5

Parameter			Description	Type	Lower bound	Baseline	Upper bound
Design variable	x_P	L_c/mm	Length of the combustion chamber	Continuous	100.00	127.00	144.00
		D_t/mm	Diameter of throat	Continuous	5.00	6.00	8.00
		e	Nozzle area expansion ratio	Continuous	1.00	2.50	3.00
	x_L	x_battery/mm	Position of battery	Continuous	85.00	87.00	240.00
		x_computer/mm	Position of computer	Continuous	85.00	200.00	240.00
		x_IMU/mm	Position of IMU	Continuous	85.00	230.00	240.00
	x_A	x_rudder/mm	Position of rudder	Continuous	85.00	138.50	200.00
		c_rudder/mm	Chord of rudder	Continuous	8.00	13.00	17.00
		s_rudder/mm	Span of rudder	Continuous	10.00	27.00	35.00
		c_fin/mm	Chord of fin	Continuous	40.00	50.00	80.00
		s_fin/mm	Span of fin	Continuous	20.00	28.50	30.00
	x_C	K_r	Parameter 1 for control tuning	Continuous	0	11.37	20
		K_ω	Parameter 2 for control tuning	Continuous	−30	17.84	30
		K_n	Parameter 3 for control tuning	Continuous	−20	4.502	20
		T_a	Type of actuator	Discrete	0	0	5
	x_G	N	Proportional constant	Continuous	2.00	3.00	6.00
	x_G	T_s	Type of seeker	Discrete	0	0	5
Constraints and objective	g_L	m_tot/kg	Total mass	−	−	1.53	1.6
		S_ij-min/mm	Minimum separation	−	0	4.00	−
		S_tot/mm	Total separation	−	0	24.00	35.00
	g_P	p_c/MPa	Pressure in the combustion chamber	−	6.00	8.99	−
	f_M.B.	R/m	Range	−	−	2004.20	Maximization
	f_GNC, g_G	E/m	Guidance error	−	Minimization	3.93	5

Design methodology of a mini-missile considering flight performance and guidance precision

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		Baseline value	OPT 1						OPT 2
Parameter			Optimum A		Optimum B		Optimum C		Optimum S
			Value	∆/%	Value	∆/%	Value	∆/%	Value	∆/%
Design variables of the missile: x_P, x_L, and x_A	L_c/mm	127.00	123.38	−2.85	128.88	1.48	128.93	1.52	128.99	1.57
	D_t/mm	6.00	5.54	−7.68	5.00	−16.67	5.00	−16.64	5.00	−16.66
	e	2.50	1.93	−22.95	2.99	19.63	2.99	19.78	2.96	18.57
	x_rudder/mm	138.50	127.96	−7.61	123.02	−11.18	145.21	4.84	85.19	−38.49
	x_battery/mm	87.00	195.99	125.28	194.16	123.17	75.66	−13.03	200.19	130.10
	x_computer/mm	200.00	85.00	−57.50	85.00	−57.50	110.01	−45.00	169.19	−15.41
	x_IMU/mm	230.00	234.99	2.17	232.46	1.07	202.51	−11.95	146.19	−36.44
	c_rudder/mm	13.00	15.36	18.16	16.40	26.12	16.97	30.51	17.00	30.76
	s_rudder/mm	22.00	30.57	38.96	31.65	43.85	33.86	53.90	34.95	58.88
	c_fin/mm	50.00	65.89	31.77	53.98	7.96	45.63	−8.74	40.27	−19.47
	s_fin/mm	29.00	28.48	−1.80	29.83	2.85	29.99	3.43	29.93	3.22
	T_a	0	0	−	1	−	2	−	1	−
	T_s	0	0	−	0	−	5	−	0	−
Performances	m_tot/kg	1.53	1.56	1.87	1.54	0.53	1.46	−4.52	1.51	−1.45
	R/m	2004.20	1775.03	−11.43	2399.43	19.72	2700.21	34.73	2521.80	25.83
	CEP/m	2.33	0.08	−96.74	0.16	−92.96	0.67	−71.21	1.13	−51.81

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