Influence of roll-pitch seeker DRR and parasitic loop on Lyapunov stability of guidance system

doi:10.23919/JSEE.2021.000127

Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (6): 1509-1526.doi: 10.23919/JSEE.2021.000127

• CONTROL THEORY AND APPLICATION • Previous Articles Next Articles

Influence of roll-pitch seeker DRR and parasitic loop on Lyapunov stability of guidance system

Yue LI¹(), Xianghua WEN^2,*(), Wei LI²(), Lan WEI²(), Qunli XIA¹()

¹ School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
² No. 5718 Factory, Chinese People’s Liberation Army, Guilin 541002, China

Received:2020-06-16 Online:2022-01-05 Published:2022-01-05
Contact: Xianghua WEN E-mail:liyue627167955@163.com;495460738@qq.com;lion_lee1994@126.com;389968247@qq.com;1010@bit.edu.cn
About author:|LI Yue was born in 1995. He received his B.E. degree from Beijing Institute of Technology in 2016. He is currently a doctoral student in School of Aerospace Engineering, Beijing Institute of Technology. His main research interests include flight vehicle design, guidance and control. E-mail: liyue627167955@163.com||WEN Xianghua was born in1982. He received his B.E. degree in ammunition control major from Changsha University of Science and Technology in 2006, and Master’s degree in control engineering from Beijing University of Aeronautics and Astronautics in 2015. He is a senior engineer working in the No. 5718 Factory of the Chinese People’s Liberation Army. His research interests include guidance and control. E-mail: 495460738@qq.com||LI Wei was born in 1994. He received his B.E. degree from Beijing Institute of Technology in 2015. He is currently a doctoral student in School of Aerospace Engineering, Beijing Institute of Technology. His main research interests include flight vehicle design, guidance and control. E-mail: lion_lee1994@126.com||WEI Lan was born in 1994. She received her B.E. degree in electronic information engineering from North University of China in 2017. She is a master in Beijing Institute of Technology. Her research interest is aircraft control. E-mail: 389968247@qq.com||XIA Qunli was born in 1971. He received his B.E. degree in launcher and design major from Beijing Institute of Technology in 1993, and Master’s degree in flight mechanics from Beijing Institute of Technology in 1996. He received his Ph.D. degree in aircraft design from Beijing Institute of Technology in 1999. He is an adjunct professor in Beijing Institute of Technology. His research interests include control and guidance technology. E-mail: 1010@bit.edu.cn
Supported by:
This work was supported by the Defense Science and Technology Key Laboratory Fund of Luoyang Electro-optical Equipment Institute, Aviation Industry Corporation of China (6142504200108).

Abstract

Abstract:

This paper focuses on the influence of the disturbance rejection rate (DRR) and parasitic loop parameters on the stability domain of the roll-pitch seeker’s guidance system. The DRR models of the roll-pitch seeker caused by different types of disturbance torques and the scale deviation of different sensors are established. The optimal DRR model of the roll-pitch seeker, which contains the scale deviation model, is proposed by formula derivation. The model of the roll-pitch seeker’s guidance system is established and equivalently simplified by the dimensionless method. The Lyapunov stability criterion for stability analysis of the guidance system is given by means of the passivity theorem and related definitions and lemmas. A simplified model of the roll-pitch seeker’s guidance system, which is suitable for the Lyapunov stability criterion, is established by formula derivation and equivalent transformation. Three conditions that satisfy the Lyapunov stability criterion are obtained. Mathematical simulation with Nyquist plots is used to analyze the influence of different DRR parameters on the stability domain of the roll-pitch seeker’s guidance system. Simulation results of this paper can provide reference for the stability analysis of systems related to the roll-pitch seeker.

Key words: roll-pitch seeker, guidance system, disturbance rejection rate (DRR), parasitic loop, Lyapunov stability, Nyquist analysis

Yue LI, Xianghua WEN, Wei LI, Lan WEI, Qunli XIA. Influence of roll-pitch seeker DRR and parasitic loop on Lyapunov stability of guidance system[J]. Journal of Systems Engineering and Electronics, 2021, 32(6): 1509-1526.

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References 35

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Disturbance torque	DRRTF	Equivalent coefficient
Spring torque	${R_n}(s) = \dfrac{ { {K_s} - {K_r} } }{ { {T_s}s + 1} }$	${K_s} = \dfrac{ { {K_n} } }{ { {K_1}{K_2} } }$
Damping torque	${R_\omega }(s) = \dfrac{ {s{K_v} - {K_r} } }{ { {T_s}s + 1} }$	${K_v} = \dfrac{ { {K_\omega } } }{ { {K_1}{K_2} } }$

Parameter	Physical meaning	Parameter type	Values range
${\bar T_s}$	Dimensionless equivalent time constant	Constant	0.01
$N$	Proportional guidance coefficient	Constant	4
${{{V_c}} / {{V_m}}}$	The ratio of relative velocity to missile velocity	Constant	1.5
${\bar T_\alpha }$	Dimensionless angle of attack time constant	Variable	1?3
${\bar t_f}/{\rm{s}}$	Dimensionless terminal guidance time	Variable	6?15
${K_s}$	Spring torque equivalent coefficient	Variable	0?0.01
${K_v}$	Damping torque equivalent coefficient	Variable	0?0.01
${K_r}$	DRR equivalent coefficient	Variable	?0.03?0.03

Figure	Torque	Parameter	Description
Fig. 24	Spring	${\bar T_\alpha } = 3$ , ${K_s} = 0.01$ , ${K_r} \in [ - 0.03, 0.03]$	Verify Conclusion 1: the influence of ${K_r}$ on the stability of the system
Fig. 24	Damping	${\bar T_\alpha } = 3$ , ${K_v} = 0.01$ , ${K_r} \in [ - 0.03, 0.03]$
Fig. 25	Spring	${\bar T_\alpha } = 3$ , ${K_r} = 0.03$ , ${K_s} \in [0, 0.01]$	Verify Conclusion 2: the influence of ${K_s}$ on the stability of the system
Fig. 25	Spring	${\bar T_\alpha } = 3$ , ${K_r} = - 0.03$ , ${K_s} \in [ 0, 0.01]$
Fig. 26	Damping	${\bar T_\alpha } = 3$ , ${K_r} = 0.03$ , ${K_v} \in [ 0, 0.01]$	Verify Conclusion 2: the influence of ${K_v}$ on the stability of the system
Fig. 26	Damping	${\bar T_\alpha } = 3$ , ${K_r} = - 0.03$ , ${K_v} \in [ 0, 0.01]$
Fig. 27	Spring	${K_r} = 0.03$ , ${K_s} = 0.01$ , ${\bar T_\alpha } \in [ 1, 6]$	Verify Conclusion 3: the influence of ${\bar T_\alpha }$ on the stability of the system
Fig. 27	Spring	${K_r} = - 0.03$ , ${K_s} = 0.01$ , ${\bar T_\alpha } \in [ 1, 3]$
Fig. 28	Damping	${K_r} = 0.03$ , ${K_v} = 0.01$ , ${\bar T_\alpha } \in [ 1, 6]$	Verify Conclusion 3: the influence of ${\bar T_\alpha }$ on the stability of the system
Fig. 28	Damping	${K_r} = - 0.03$ , ${K_v} = 0.01$ , ${\bar T_\alpha } \in [1, 3]$

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Influence of roll-pitch seeker DRR and parasitic loop on Lyapunov stability of guidance system

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