高計(jì)委 張金鵬 高剛 何金剛 徐興元
摘 要:????? 針對(duì)空空導(dǎo)彈協(xié)同攻擊高速機(jī)動(dòng)目標(biāo)問題,提出一種帶有攻擊時(shí)間一致的多彈協(xié)同制導(dǎo)律。首先,在縱向平面內(nèi)建立各導(dǎo)彈與目標(biāo)交戰(zhàn)幾何模型,分析視線徑向、法向制導(dǎo)律和速度法向加速度之間關(guān)系。然后,設(shè)計(jì)固定時(shí)間協(xié)同控制律,并利用自適應(yīng)律和積分滑模算法在視線方向動(dòng)力學(xué)方程基礎(chǔ)上建立攻擊時(shí)間約束的魯棒協(xié)同制導(dǎo)律,保證多枚導(dǎo)彈同時(shí)擊中機(jī)動(dòng)目標(biāo)。通過數(shù)值仿真可得,協(xié)同時(shí)間與脫靶量差異分別為0.001 s和0.01 m,最終結(jié)果驗(yàn)證了固定時(shí)間協(xié)同制導(dǎo)律的有效性與合理性。
關(guān)鍵詞:???? 協(xié)同制導(dǎo); 協(xié)同控制;? 自適應(yīng); 攻擊時(shí)間一致性; 積分滑模; 通信拓?fù)? 導(dǎo)彈
中圖分類號(hào):???? TJ765; V249.1
文獻(xiàn)標(biāo)識(shí)碼:??? A
文章編號(hào):???? 1673-5048(2022)02-0066-06
DOI: 10.12132/ISSN.1673-5048.2021.0106
0 引? 言
導(dǎo)彈作為一種進(jìn)攻性武器,在現(xiàn)代戰(zhàn)爭(zhēng)中具有舉足輕重的作用,得到世界各國的重視與研究。隨著制空型無人作戰(zhàn)飛機(jī)和新型干擾的形成與發(fā)展,單枚導(dǎo)彈摧毀目標(biāo)的能力受到挑戰(zhàn)。在此背景下多導(dǎo)彈協(xié)同攻擊具有重要的現(xiàn)實(shí)意義,不僅增強(qiáng)了導(dǎo)彈的打擊能力,還能夠提高導(dǎo)彈的突防與攻擊效果。
近年來,許多學(xué)者對(duì)多彈協(xié)同制導(dǎo)律進(jìn)行研究,取得一定成果。趙世鈺等[1]根據(jù)多彈協(xié)同攻擊要求提出一種雙層協(xié)同制導(dǎo)方法,底層導(dǎo)引由各導(dǎo)彈自身制導(dǎo)律實(shí)現(xiàn),上層導(dǎo)引通過分散式或集中式協(xié)調(diào)策略實(shí)現(xiàn),具有控制能量的次優(yōu)性。Zhao等[2]控制實(shí)彈跟蹤虛擬領(lǐng)彈,進(jìn)而實(shí)現(xiàn)時(shí)間協(xié)同。Harl等[3]基于滑模提出碰撞時(shí)間和角度約束制導(dǎo)律,利用反步設(shè)計(jì)二階滑??刂坡?,跟蹤期望視線率,保證在不確定條件下攔截目標(biāo)。Zhang等[4]利用偏置比例導(dǎo)引設(shè)計(jì)分布式協(xié)同制導(dǎo)律,保證在固定或者開關(guān)通迅網(wǎng)絡(luò)下時(shí)間協(xié)同攻擊目標(biāo)。Zhao等[5]分別利用比例導(dǎo)引和協(xié)調(diào)項(xiàng)保證目標(biāo)捕獲與同時(shí)到達(dá),進(jìn)而提出復(fù)合協(xié)同制導(dǎo)策略。針對(duì)三維協(xié)同攻擊情況,周銳等[6]提出一種基于網(wǎng)絡(luò)同步原理的分布式協(xié)同制導(dǎo)方法,保證多導(dǎo)彈完成協(xié)同攻擊任務(wù)。宋俊紅等[7]沿視線方向設(shè)計(jì)加速度,保證各導(dǎo)彈與目標(biāo)的相對(duì)距離在有限時(shí)間內(nèi)一致; 在法向上構(gòu)建視線角約束的導(dǎo)引律,保證各導(dǎo)彈以期望視線角攻擊目標(biāo)?;ㄎ娜A等[8]擴(kuò)展了適用于機(jī)動(dòng)目標(biāo)的剩余時(shí)間估計(jì)方法,并提出一種非奇異滑模制導(dǎo)律,保證多導(dǎo)彈以設(shè)定的飛行時(shí)間攻擊目標(biāo)。
導(dǎo)彈攻擊目標(biāo)過程由多個(gè)階段組成,每個(gè)階段均有自己的任務(wù)完成時(shí)間窗口。為了保證在規(guī)定時(shí)間內(nèi)完成任務(wù),有限/固定時(shí)間控制理論在導(dǎo)彈制導(dǎo)領(lǐng)域得到研究與應(yīng)用。郭正玉等[9]在文獻(xiàn)[7]的基礎(chǔ)上利用非奇異終端滑模設(shè)計(jì)視線法向制導(dǎo)律,迫使角速率在有限時(shí)間內(nèi)收斂到原點(diǎn)。Hou等[10]以漸近的方式提出三種有限時(shí)間控制律,解決了不同約束條件下多導(dǎo)彈協(xié)同制導(dǎo)問題,并通過仿真驗(yàn)證了算法的有效性。Song等[11]在視線徑向設(shè)計(jì)二階滑模導(dǎo)引律,保證多枚導(dǎo)彈同時(shí)到達(dá)目標(biāo),在視線法向上利用自適應(yīng)律與終端滑模建立有限時(shí)間制導(dǎo)律,迫使導(dǎo)彈以期望視線角攻擊目標(biāo)。有限時(shí)間控制系統(tǒng)狀態(tài)收斂時(shí)間依賴于初始值,而初始值通常難以獲得,因此,Jing等[12]在視線徑向與法向分別設(shè)計(jì)固定時(shí)間制導(dǎo)律,保證各導(dǎo)彈以期望視線角同時(shí)擊中目標(biāo)。Lin等[13]采用固定時(shí)間系統(tǒng)理論研究三維協(xié)同制導(dǎo)律,在視線方向上設(shè)計(jì)主從式控制方案驅(qū)使碰撞時(shí)間一致,在視線法向上提出固定時(shí)間終端滑模導(dǎo)引律, 保證各導(dǎo)彈在
規(guī)定時(shí)間內(nèi)調(diào)整自己方位角與高低角,并以期望角度攻擊目標(biāo),但該方法只針對(duì)固定目標(biāo)。
本文基于固定時(shí)間穩(wěn)定理論提出兩階系統(tǒng)狀態(tài)協(xié)同制導(dǎo)律,在規(guī)定的時(shí)間內(nèi)迫使每枚導(dǎo)彈與目標(biāo)的相對(duì)距離和相對(duì)速度保持一致,采用積分滑模抑制目標(biāo)的機(jī)動(dòng)性,選用自適應(yīng)律排除了導(dǎo)彈對(duì)目標(biāo)加速度上界的需求,具有較強(qiáng)的實(shí)用性。
3 仿真分析
為驗(yàn)證固定時(shí)間協(xié)同制導(dǎo)律的有效性與合理性,設(shè)計(jì)如下交戰(zhàn)場(chǎng)景: 3枚導(dǎo)彈協(xié)同攻擊1枚機(jī)動(dòng)目標(biāo),目標(biāo)的初始位置為(30 km,28 km),速度為500 m/s,初始航向角為120°,機(jī)動(dòng)過載3gsin(t)。3枚導(dǎo)彈的初始參數(shù)如表1所示,導(dǎo)彈最大可用過載30g。
3枚導(dǎo)彈之間的通信網(wǎng)絡(luò)如圖2所示,該通信網(wǎng)絡(luò)是連通的,各導(dǎo)彈之間通訊權(quán)系數(shù)矩陣A=[aij]為
A=010101010(23)
式中: Mi指編號(hào)為i的導(dǎo)彈。協(xié)同制導(dǎo)律參數(shù)為γ1=3/5,γ2=3/4,β1=19/17,β2=19/18,α=3,β=2,ε0=0.02。
根據(jù)交戰(zhàn)數(shù)學(xué)模型與初始條件,在軟件上進(jìn)行多導(dǎo)彈協(xié)同制導(dǎo)模擬仿真,結(jié)果如表 2和圖 3~7所示。
由表 2可知,3枚導(dǎo)彈都能擊中目標(biāo),脫靶量較小,制導(dǎo)時(shí)間一致,從而保證3枚導(dǎo)彈同時(shí)打擊目標(biāo), 協(xié)同時(shí)間與脫靶量差異分別為0.001 s和0.01 m。圖3為編隊(duì)協(xié)同攻擊蛇形機(jī)動(dòng)目標(biāo)的飛行軌跡,導(dǎo)彈在初始階段有較大的機(jī)動(dòng)調(diào)整,后段彈道變化趨于平緩。圖4為導(dǎo)彈與目標(biāo)的相對(duì)距離變化曲線,在2.85 s時(shí)各導(dǎo)彈和目標(biāo)相對(duì)距離趨于一致,并且在24.881 s時(shí)擊中目標(biāo)。圖5
為各導(dǎo)彈與目標(biāo)之間視線角隨時(shí)間變化曲線,結(jié)合圖3
軌跡曲線可知,各導(dǎo)彈從迎頭攔截到尾追,視線角逐漸變大,視線角速率并不收斂。由圖6可知,在法向加速度作用下,各導(dǎo)彈航向角在前2 s內(nèi)變化較大,保證相對(duì)距離趨于相同后趨于平滑。圖7為各導(dǎo)彈航向角與視線角差值,表明各導(dǎo)彈速度與相對(duì)距離之間有一定夾角,保證各導(dǎo)彈同時(shí)打擊目標(biāo)。
4 結(jié)? 論
與多數(shù)現(xiàn)存的一階協(xié)同制導(dǎo)律不同,本文提出兩階非線性協(xié)同導(dǎo)引律,能夠廣泛用于其他多智能體系統(tǒng)。今后將重點(diǎn)研究該領(lǐng)域亟待解決的問題: 分析各導(dǎo)彈協(xié)同攻擊目標(biāo)的力學(xué)與數(shù)學(xué)模型,探討制導(dǎo)律、加速度、速度與攻擊時(shí)間同步和期望視線角約束兩項(xiàng)任務(wù)之間關(guān)系,研究能夠?qū)崿F(xiàn)這兩種限制的魯棒協(xié)同制導(dǎo)律,并將其推廣應(yīng)用于空氣阻力作用下各導(dǎo)彈抗飽和協(xié)同攻擊目標(biāo)場(chǎng)景。
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Adaptive Fixed-Time Cooperative Guidance Law
Based on Integral Sliding Mode
Gao Jiwei1*,Zhang Jinpeng2,? 3,Gao Gang2,He Jingang2,Xu Xingyuan1
(1. Henan University of Science and Technology,Luoyang 471000,China;
2. China Airborne Missile Academy,Luoyang 471009,China;
3. Aviation Key Laboratory of Science and Technology on Airborne Guided Weapons,Luoyang 471009,China)
Abstract: For the problem of air-to-air missile cooperative attack on high-speed maneuvering target,? a multi-missile cooperative guidance law with consistent attack time is proposed. Firstly,? the geometric model of engagement between each missile and target is established in the longitudinal plane,? and the relationship between the radial and normal guidance laws of line of sight and the normal acceleration of velocity is analyzed. Then,the fixed time cooperative control law is designed, ?and based on the line of sight dynamic equation,? the robust cooperative guidance law with attack-time constraint is established by using adaptive law and integral sliding mode algorithm to ensure that multiple missiles hit the maneuvering target at the same time. Through numerical simulation,? the difference of cooperative time and miss distances are 0.001 s and 0.01 m respectively. The final results verify the effectiveness and rationality of the fixed-time cooperative guidance law.
Key words:?? cooperative guidance; cooperative control; adaptation; attack time consistency; integral sliding mode; communication topology;? missile