Research on Time/Frequency-Domain Index Mapping of Air-Defense Missile Rolling Channel Control

doi:10.3969/j.issn.1009-086x.2024.04.004

Abstract

Abstract:

In the design of air-defense missile control system， how to quickly and efficiently design the control system to meet the given index has always been a hot issue. In this paper， the control structure is designed from the mathematical point of view. Taking the design of the rolling channel control system as an example， the mapping relationship between the time-domain index， the frequency-domain index and the control parameters， and the mapping relationship between the time-domain index and the frequency-domain index are established by using the analytical method， the root locus method and the amplitude-phase characteristic Bode diagram method. The mapping relationship can give consideration to both time-domain and frequency-domain indexes to design control parameters more quickly and efficiently， and can also obtain the rule of index changes when control parameters change. Finally， the correlation among system time constant， rise time， cut-off frequency and closed loop bandwidth is established analytically. Through this correlation， a clearer physical understanding of the system can be established， which is helpful to guide how to take measures when the system oscillates or diverges in engineering design.

Key words: control structure, time-domain index, frequency-domain index, control parameters, mapping relation

摘要：

在防空导弹控制系统设计时，如何快速高效设计出满足给定指标的控制系统一直是热点问题。以滚动通道控制设计为例，从数学角度出发设计控制结构，采用解析法、根轨迹法和幅相特性Bode图法建立了时/频域指标与控制参数之间的映射关系，以及时/频域指标之间的映射关系。该映射关系可兼顾时域指标和频域指标来更快速高效设计控制参数，而且还可以得到控制参数变化时指标变化的规律。这有助于根据系统需要实现的性能指标进行控制系统的设计。最后用解析法建立系统时间常数、上升时间、截止频率和闭环带宽之间的关联关系。通过该关联关系对系统可建立更加清晰的物理认识，有利于指导在工程设计中当系统出现振荡或者发散现象时如何采取解决措施。

关键词: 控制结构, 时域指标, 频域指标, 控制参数, 映射关系

CLC Number:

TJ765.2

Shuaihao YAN, Mingying WEI, Yongbin ZHENG. Research on Time/Frequency-Domain Index Mapping of Air-Defense Missile Rolling Channel Control[J]. Modern Defense Technology, 2024, 52(4): 33-44.

闫帅豪, 魏明英, 郑勇斌. 基于防空导弹滚动通道控制时/频域指标映射关系研究[J]. 现代防御技术, 2024, 52(4): 33-44.

Figures/Tables 32

Fig. 1 Exponential function curve for negative

Fig. 2 Block diagram of system control structure

Fig. 3 System σ%,γ and ξ relationship diagram

Fig. 4 Damping and frequency range

Fig. 5 Range of control parameters k2

Fig. 6 System root trajectory after parameters are determined

Fig. 7 Unit step response curve of the system

Fig. 8 System open-loop logarithmic amplitude-phase characteristic curve

Fig. 9 Poles of an underdamped second-order system

Table 1 Influence of pole position on time domain index

极点位置	闭环传函	$ξ, w n$	$t s$	超调量 $σ %$
$1 . (- 2, ± 23)$	$16 s 2 + 4 s + 16$	$ξ = 0.5 ω n = 4$	$1.75$	$16.3 %$
$2 . (- 2, ± 43)$	$52 s 2 + 4 s + 52$	$ξ = 0.28 ω n = 7.21$	$1.75$	$40.4 %$
$3 . (- 4, ± 23)$	$28 s 2 + 8 s + 28$	$ξ = 0.76 ω n = 5.29$	$0.875$	$2.7 %$
$4 . (- 4, ± 43)$	$64 s 2 + 8 s + 64$	$ξ = 0.5 ω n = 8$	$0.875$	$16.3 %$

Table 1 Influence of pole position on time domain index

极点位置	闭环传函	$ξ, w n$	$t s$	超调量 $σ %$
$1 . (- 2, ± 23)$	$16 s 2 + 4 s + 16$	$ξ = 0.5 ω n = 4$	$1.75$	$16.3 %$
$2 . (- 2, ± 43)$	$52 s 2 + 4 s + 52$	$ξ = 0.28 ω n = 7.21$	$1.75$	$40.4 %$
$3 . (- 4, ± 23)$	$28 s 2 + 8 s + 28$	$ξ = 0.76 ω n = 5.29$	$0.875$	$2.7 %$
$4 . (- 4, ± 43)$	$64 s 2 + 8 s + 64$	$ξ = 0.5 ω n = 8$	$0.875$	$16.3 %$

Fig. 10 Influence of pole position on time-domain index

Fig. 11 Root locus curve as k1 increases

Fig. 12 System response when k1 changes

Fig. 13 Adjustment time curve when k1 changes

Fig. 14 Overshoot change curve when k1 changes

Fig. 15 Curve of peak time change when k1 changes

Fig. 16 Root locus as k2 is increased

Fig. 17 System response when k2 changes

Fig. 18 Adjustment time curve when k2 changes

Fig. 19 Overshoot change curve when k2 changes

Fig. 20 Curve of peak time change when k2 changes

Fig. 21 (k1,k2,ts) 3D image

Fig. 22 (k1,k2,tr) 3D image

Fig. 23 (k1,k2,σ%) 3D image

Fig. 24 Bode diagram of k1 change

Fig. 25 Curve of phase margin change when k1 changes

Fig. 26 bode diagram of k2 change

Fig. 27 Curve of phase margin change when k2 changes

Fig. 28 (k1,k2,Pm) 3D image

Fig. 29 Relationship between rise time and time parameter T

Fig. 30 wn and wc relationship curve

Fig. 31 Relationship between wc and ws with increasing damping

References 15

1	斯维特洛夫. 防空导弹设计［M］. 张志鸿，译. 北京：中国宇航出版社， 2002.
	SVETLOV. Anti-aircraft Missile Design［M］. Translated by ZHANG Zhihong. Beijing： China Astronautic Publishing House， 2002.
2	MRACEK C P， RIDGELY D B. Missile Longitudinal Autopilots： Connections Between Optimal Control and Classical Topologies［C］∥AIAA Guidance， Navigation， and Control Conference and Exhibit. Reston： AIAA， 2005： AIAA 2005-6381.
3	SAFONOV M G， ATHANS M. Gain and Phase Margin for Multiloop LQG Regulators［J］. IEEE Transactions on Automatic Control， 1977， 22（2）： 173-179.
4	DE GASTON R R E， SAFONOV M G. Exact Calculation of the Multiloop Stability Margin［J］. IEEE Transactions on Automatic Control， 1988， 33（2）： 156-171.
5	SON J E， MANI A S， LATCHMAN H A. Robustness Analysis for MIMO Systems with Unstructured Uncertainties［C］∥IEEE ICCA 2010. Piscataway： IEEE， 2010： 1333-1337.
6	吴建武，吴浩，张惠平. 主动段姿态控制参数与稳定裕度映射关系研究［J］. 航天控制， 2020， 38（4）： 22-27.
	WU Jianwu， WU Hao， ZHANG Huiping. Research on Boost-Phase Mapping Relationship of Attitude Control Parameters and Stability［J］. Aerospace Control， 2020， 38（4）： 22-27.
7	赵秀伟，任建岳. 确保稳定裕度的PID稳定域计算［J］. 光学精密工程， 2013， 21（12）： 3214-3222.
	ZHAO Xiuwei， REN Jianyue. Computation of PID Stabilizing Region with Stabilized Margins［J］. Optics and Precision Engineering， 2013， 21（12）： 3214-3222.
8	MAO Qi， XU Yong， CHEN Jianqi， et al. Maximal Gain and Phase Margins Attainable by PID Control［C］∥2021 60th IEEE Conference on Decision and Control （CDC）. Piscataway： IEEE， 2021： 1820-1825.
9	李友年，郑鹍鹏，陈星阳. 三回路过载驾驶仪的快速性极限分析［J］. 弹箭与制导学报， 2013， 33（3）： 17-20， 24.
	LI Younian， ZHENG Kunpeng， CHEN Xingyang. Rapidity Limitation Analysis of Three-loop Acceleration Autopilot［J］. Journal of Projectiles， Rockets， Missiles and Guidance， 2013， 33（3）： 17-20， 24.
10	李奔. 线性系统PID参数稳定域研究［D］. 南京：南京理工大学， 2009.
	LI Ben. Research on PID Parameter Stability Region of Linear Systems［D］. Nanjing： Nanjing University of Science and Technology， 2009.
11	YANG Kunlin. A Novel Pid Tuning Method for the Missile Overload Control［C］∥2022 2nd International Conference on Computer， Control and Robotics （ICCCR）. Piscataway： IEEE， 2022： 86-89.
12	SIVADAS M. Launch Vehicle Autopilot Design Using Automated QFT-PID Controller［C］∥2020 International Conference on Futuristic Technologies in Control Systems & Renewable Energy （ICFCR）. Piscataway： IEEE， 2020： 1-6.
13	SÖNMEZ Ş， AYASUN S. Gain and Phase Margins Based Delay-Dependent Stability Analysis of Two-Area LFC System with Communication Delays［C］∥2017 10th International Conference on Electrical and Electronics Engineering （ELECO）. Piscataway： IEEE， 2017： 1409-1413.
14	胡寿松. 自动控制原理［M］. 北京：科学出版社， 2001.
	HU Shousong. Principle of Automatic Control［M］. Beijing： Science Press， 2001.
15	朱敬举，祁载康，夏群力. 三回路驾驶仪的极点配置方法设计［J］. 弹箭与制导学报， 2007， 27（4）： 8-12.
	ZHU Jingju， QI Zaikang， XIA Qunli. Pole Assignment Method for Three-Loop Autopilot Design［J］. Journal of Projectiles， Rockets， Missiles and Guidance， 2007， 27（4）： 8-12.

[1]	Rixin SU, Ou ZHANG. Research on Method of Missile Stability Control Based on Improved PID-LQR Algorithm [J]. Modern Defense Technology, 2024, 52(3): 73-79.
[2]	Rixin SU, Ou ZHANG. Research on the Discretization of Notch Filter in Missile Stability Control [J]. Modern Defense Technology, 2024, 52(2): 72-78.
[3]	XU Fei, YUAN Jie-bo, TIAN Ruo-si, DING Xiao-qin RONG Wan-ting. Design of Desktop Test System for Flight Control Dynamically Pedestal Alignment [J]. Modern Defense Technology, 2020, 48(2): 74-80.
[4]	WEI Ya-li, WANG Fei, XU Xin-peng. ADRC Controller Based on PWPF for Impulse Lateral Thrust [J]. Modern Defense Technology, 2018, 46(4): 40-44.
[5]	YANG Hua-dong, TUO Hong-ping. Simplified Calculation Method of the Voyage for the Aircraft with Track Programmable Capability [J]. Modern Defense Technology, 2018, 46(3): 35-40.
[6]	HAN Chun-yao, XIONG Jia-jun, ZHANG Kai. Method of Trajectory Prediction for Unpowered Gliding Hypersonic Vehicle [J]. Modern Defense Technology, 2018, 46(3): 146-151.