XAC DINH MIEN ON DINH NGAU NHIEN CHO HE BAM
T I T D O N GXAC D|NH TOA DO MUC TIEU TREN THIET BI BAY TlT DAN SlT DUNG TIEU CHUAN ON DINH HE DA CAU TRu'c
Nguyin Tdng Cudng Hgc vien Ky thugt Qudn sir Tdm tat:
Bdi bdo trinh bdy kit qud khdo sdt tinh dn dinh ciia hi bdm tu dgng xdc dmli tga do muc tieu tren thiit bi bay tu ddn trong diiu kiin xdy ra gidn dogn ngdu nhien thdng tin vi muc tieu ndy. Viec ddnh gid tinh dn dinh duac thuc hiin vdi su dung tieu chudn dn dinh cua hi da cdu tnic. Tieu chudn ndy ciing da duac tdc gid bdi bdo ndy di xudt vd cdng bd a tgp chi khoa hgc.
Dd xdc dinh duac miiii tham sd diiu khiin di ddm bdo h4 dn dinh vd miin cdc tham sd md hi mdt dn dinh.
Abstract:
The paper presents study results of stochastic stability for automatic coordinate finding systems of self-tracking flight control systems executed in tracking conditions with discontinuity of target information. The stability study based on using the stability criterion for multistructural control systems. This stability criterion proposed by author and published in scientific journal. This paper presents stability area and non-stability area for tracking system parameters.
I. DAT VAN DE
Trong he thdng thilt bj bay ty ddn, he xdc djnh tga do gdc muc tieu cd nhiem vy cung cdp thdng tin cdc tga do gdc vd cdc dao ham ciia chiing. Cd hai dang he xdc djnh toa do gdc:
he xac dinh toa do vdi so sdnh tfn hieu ddng thdi vd he xdc djnh toa do vdi so sdnh tfn hieu Idn lugt. Trong he xdc djnh toa do vdi so sdnh tfn hieu ddng thdi, toa do gdc myc tieu vd dao hdm cua chdng dugc xdc djnh theo kit qud so sdnh cac tham sd ciia tfn hieu (bien do, pha, tdn sd) thu dugc ddng thdi tii cdc dng ten. Trong he xdc djnh toa do vdi so sdnh tfn hieu Ian lugt, sy thu tfn hieu myc tieu trong moi khodng thdi gian dugc tien hanh d mdt dng ten, toa do myc tieu dugc xdc djnh tren cd sd so sdnh dudng bao cua tfn hieu nhdn dugc vdi tfn hieu chuan.
Dudi day, bdi bdo tiln hdnh khdo sdt xdc djnh mien dn djnh cdc tham sd ciia he xdc djnh tga do trong dilu kien gidn doan ngdu nhien thdng tin ve toa do muc tieu.
IL PHAN TICH CAC KHA NANG GIAN DOAN T H O N G TIN TRONG HE XAC DINH TOA DO G 6 C MUC TIEU
Cdc tinh hudng dan din sy gidn doan thdng tin vl toa do gdc myc tieu trong cdc ddu ty dan rada don xung dugc xem xet tren co sd thyc tl ciia cdc phuang phdp chong lai he thdng tu ddn. Cdc phuang phdp chdng lai he thdng ty ddn cua ten lua gdm:
Bay theo top.
Bay thdp.
Tao nhieu nhdp nhdy tir hai hay nhilu dilm trong khdng gian.
- Tao nhilu vdi sy dao ddng theo tdn sd tir hai hay nhilu dilm trong khdng gian.
- Tdng hinh.
Myc tieu bay theo tdp se lam gidm khd ndng phdn biet ciia ddu ty dan rada. Khi tfn hi|u phan xa tir cdc myc tieu cd cudng do nhu nhau, hudng can bdng tfn hieu cua rada ddu ty dan se xac lap theo hudng trung gian giiia cdc myc tieu. Neu cdc tfn hieu phdn xa tir cdc myc tieu CO cudng do khdc nhau thi dng ten ciia he xdc djnh toa do se djch chuyen tuong ung vdi sy thay ddi miic cua cdc tfn hieu tir myc tieu ndy so vdi myc tieu kia. Vdkhi dd cd khd ndng bdt
muc tieu mdi ndm d hudng khac so vdi hirdng cua muc tieu bam sat trudc do ddn den djnh hudn? lai dng ten va gay ra sai so goc.
^NIU iron" khdng gian dai cac may phat nhieu rieng biet dong ma theo chuang tnnh hoac theo quy fuat no{\u nhien, dfiu lir ddn rada bam theo nguon gay^nhieu se huong toi bam sat'khi thi muc tieu nay khi thi muc tieu kia va dng ten ciia dau ty dan bi nhay theo goc theo su chuyin mach ciia nhiiu. G6c phan biet khi co tac dgng ciia nhieu nhap nhay se tang len.
Khi ddn ten lira din muc tieu kep lam tdng gdc tdi ban de phan biet cac myc tieu dan tai tan^ do tiii'gt ciia ten lira. . , , , • • •- . v , x Khi eo hai hay nhilu dilm nhieu quel theo tan sd dan den nhu the dau tu dan nhin thay cac muc tieu khac nhau. Cac muc tieu ndy xudt hien trong trinh ty Idn lugt nhanh theo miic ailng nhu khi tdn s6 ciia may phat nhieu Idn lugt roi vao ddi thdng cua may thu dau tu dan.
Khi tac chiln vdi cac may bay tang hinh, tin hieu cd the bi hdp thu hodc tnet tieu hoac cd luc cd, luc khdng.
Vdi nhung tinh hulng nhu vay, he tu dan cd the khdng thu dugc thdng tin ve myc heu mgt cdch lien tuc, thdm chf mdt hdn thdn^ tin.
Dl tang khd nang phdn biet ciia dau tu dan rada cd the thu hep cdnh sdng dmh hudng cua dnten, nhung nhu vay se 1dm tang kfch thudc va trgng lugng cua dng ten. Vi vay, can quan tam din giai phdp so dd mach. Cac phuang phdp bao ve dugc dya tren co sd phuang phdp chgn^^theo gdc. Thuc hien phuang phap ndy lam gidm khd ndng ty ddn d mdt trong cac hudng va clan din gian doan cac thong tin cd fch trong qua trinh dan.
HI. xAC DINH MIEN ON DINH CUA HE BAM T l / D O N G XAC DINH TQA BQ MUC TIEU
3.1. Phat bieu tieu chudn In djnh ngau nhien ciia he da cau tnic [2]
X ^ he dilu khiln tuyin tfnh da cdu true dugc md ta bdi he cdc phuang trinh vi phdn ngdu nhien tuyen tfnh sau day :
^''\t) = d''\i) + D('^(t)X(*^(t) + H('>(t) ^^'^t) ^^^
i = iCs
Trong dd:
X^'^ (t) -vec ta n chilu cd cdc thdnh phan Id cdc toa do pha ciia he tai trang thdi i;
C^'\t) - vec to n chieu ciia hdm tien djnh;
D^'^(t) - ma trdn ( n x n ) chieu cua cdc he sd tien djnh thay ddi theo thdi gian;
H^'^(t) - ma trdn ( n x m ) chilu cua cdc be sd tien djnh thay ddi theo thdi gian;
I, ^'\t) - tap trdng tmng tam m chilu vdi ma trdn cudng do ddi xung G''^(t).
Cdc vec to vd ma trdn neu tren dugc gid thiet sao cho qud trinh X^'^(t) la qua trinh ngdu nhien Marcov- dieu nay cd dugc khi thda mdn dang cdc dieu kien Lipshitz. Trinh ty thay ddi cdc chi sd trang thdi (i = 1,S) la qud trinh Marcov gidn doan vdi cudng do chuyen doi trang thai Vij(t) (i,j = l,S ; i ^ j ) .
O ddy ta ^idi ban chi xet he dieu khien tuyen tfnh da cdu tnic vdi phan bd xdc sudt chuyen ddc lap vd dieu kien khdi phyc cd djnh, khi dd phuong trinh ciia ky vgng toan hpc
m^'^'^(t) = (m5'\t), m^2'^ ' mi,'^(t))cho qud trinh ngdu nhien X^'^(t) d trang thai iseld [I]:
S
idf'^(t) = Pi(t)d'^(t) + D^'\t)m('\t)-Vi(t).m('\t)+ £v^i(t)m<J>(t),
j=l^i
(i = l,S) (2) Trong do: pj (t) - xdc suat trang thai de he thudc cau true i:
S
Vi(t)^ Zvij(t) (3) CJ trang thdi cau true i, phuang trinh ddi vdi ma trdn cdc moment ban ddu bdc hai
M('\t) = (M(iJ)„><„;vdiM('q)=j.,.q, JxrX, a)^'^(X,t) dX ; r, q = Ln .(') K*('Ht) = D('>(t)M(')(t) + M^'^(t)D(')'^ + Pi(t)B(')(t)-Vi(t)M('\t)-
S
+ E v j i ( t ) M^J^(t)-hm^'^(t)C(')'^(t) + C('\t)m^'^'f'(t), j=l;^i
(4)
(5) (i = l.S)
Trong d6: B^'\t) - ma trdn cdc he s6 khuylch tdn.
Sii dyng cdc ky hieu:
scM^'^t) - vdc ta n"^ chieu, cd cgt tao nen tir cdc cgt cua ma trdn M^'^(t).
M*(t)-vecta sx n" chieu, cd cdt tao nen tir cdc vec to scM^'^(t) vdi i = l,s.
m*(t)- vec to s x n chilu, cd cdt tao nen tir cdc vec to m^'^(t), i = l,s.
Tir (2), (3) vd (5) cd the vilt cdc phuang trinh thudn nhdt ddi vdi vec to m*(t) va vecto M,(t)
n&(t) = Di(t)m*(t) Hl*(t) = D2(t)M*(t)
Oday: Di(t)- ma tran ( n s x n s ) chieu
(6) (7)
Di(t) =
D « - V i l V12I visl
V21I D(2)-V2l
V2sl
vsil VS2l b ( S ) - v s i _
(8)
2 2 '
D2(t)-matrdn (sn x s n ) chieu
D2(t) =
D^xD^^^'^-ViI V21I
V12I D ( 2 ) X D ( 2 ) T
A
VisI V2sl -
A Vsil V2I A Vs2l
A A A
A D ( S ) X D ( S ) T . -Vgl
(9)
(10) I - ma trdn don vj cd kfch thudc tuong iing ;
DCOXD^'^'^ =I@D(i)+D^i)@I
Trong dd: ky hieu © Id phep lay tfch Kroneker cdc ma tran.
Xet tmdng hgp he thdng cd cdc he sd d^^'^ , (i = l,s , k, r = l,n) cua ma trdn D^'^t);
Vi va Vji Id cdc hdng so. De he thdng (1) dn djnh tiem can theo moment bdc nhdt thi dieu kien cdn vd dii Id mgi nghiem cua phuong tnnh ddc trung | XI-D^j = 0 cd phdn thyc dm [2].
E)e he (1) dn djnh tiem can quan phuang thi dieu kien can va du la mgi nghiem phuong trinh (11) sau day cd phan thyc dm :
| X I - D 2 | = 0 (11) Djnh ly 1.
Xet he tuyen tfnh dirng da eau true thay ddi ngau nhien dugc md ta bdi phuang trinh:
> ^ ' \ t ) = C<'^+D('' X<'V) + n " ' ^ ^ ' ^ ( t ) , (12) Trong do:
j,i = l,S ; C^'^ = const , D^" = const ; Vjj = const; H^'^ = const,
Dieu kien can va dii de he thong dugc md ta bdi dang (12) dn djnh tiem can quan phuang, la phai dam bao thoa man mgt trong cdc ngi dung sau:
1/Tat ca cac dinh thirc Huiwitz cua phuang trinh ddc tmng (11) phdi duang.
2/ Tat ca cac phan tir tren cgt thir nhat cua ma trdn Routh tuong iing vdi phuang trinh (11) phai duong.
T
3/ Phuang trinh ma trdn D2 U + UD2 = - W cd nghiem U xdc djnh duong vdi ma tran W duong bat ky (trong dd, D2 dugc xdc djnh theo cdng thiic (9)).
3.2. Xac djnh mien on djnh cua he bam tu dgng xac djnh tga dg muc tieu
X6t so do cau triic tdng qudt ciia he bam ty dgng \^c djnh toa dg gdc (Hinh 1) vdi cac K ' '
thanh phan : K(P) = ; he sd truyen khdu phan lap Id Kd (tmdng hgp tuyin tfnh)
Hinh 1. So" do cau true hf xac djnh tpa dg goc
Xet phuang trinh vi phan tuong img md td he bdm xdc djnh toa dg bdm khi co thdng tin ve myc tieu (tuong img ddng kfn ky hieu KH qui udc trang thdi i = 1)
?^"(t) = X<»(.)
Phuong trinh vi phan md td he xdc djnh toa dg khi gidn doan thdng tin vl muc tieu (tuong irng hd ky hieu KH vd Kd = 0 - Qui udc trang thdi i = 2 )
^ ' ^ ( t ) = x(/)(t)
(14) 4^>(t) = - l . x ( 2 ) ( t ) - ^ V ( t ) .
Tir(13)vd(14)vddjnhly L t a c d : fO I ) fO I D'" = KKd _I
TJ
; D'^' = 1 0 - -
TJ
(15)
D9 =
- V p KKd
0 1
T - ; r - v i 2 I T
V21 0 0 V21 0
V12 0 0
2KKd 0
V12 0
T 0 0
0
- V 2 1 2
0
0 0
V21 0 - ^ - ^ 2 1 1 1
'12 0 0 - ^ " ^ 2 1
(16)
Trong do v,^, V21 '^ ^^^ 8'^ ^'i cudng dg chuyen ddi trang thdi (cudng do chuyin ddi ddng - m d khod K H tren Hinh 1).
Theo djnh ly 1, de he xdc djnh tga dg dn djnh trung binh qudn phuang, cdn vd du d l Id ma trdn D2 phdi dn djnh. Vf dy dp dyng tiSu chudn Hurwitz cho ma trdn D2 ta se cd dugc cdc dieu kien dn djnh cho he xdc djnh toa dg tren ddy. Cd the bieu dien mien dn djnh cua he tren mat phdng cdc tham sd cua he nhu sau vdi ky hieu: Q = v,2 / Vzi; P = I/TV21 (Hinh 2).
So sdnh vdi phuong phdp tmdc day xdc djnh tfnh dn djnh cua he dgng hgc ngdu nhien, cd the nhdn xet each tiep can de xudt trong bdi bdo cd dieu khdc biet Id: tien hdnh khdo sdt tfnh dn djnh tryc tiep theo ma tran D 2 , md khdng can phdi gidi phuang trinh ma trdn phuong sai (trong nhieu t m d n g h g p dieu ndy se thudn tien ban so vdi gidi he phuang trinh ma trdn phuang sai).
1
4
J
2
1 0,5
P
Q=l,8 Q-0,5 /
/ / /
/ /
/ Q=o,3 / Q=o,2
Ah
Q = o , i /
ien khdng dndinh
KdKT
20 40 60 80 100
.\ X
Ifinh 2. Mien on djnh ciia hf tga dp
IV.KETLUAN
Tir d l Ihi (Hinh 2), co the kei luan ve anh hirdng ciia viec gian doan thdng tin dii vdi tfnh on dinh cua he xac dinh toa do. Khi thong tin dugc cap lien tuc (khdng gian doan), he xac dinh toa do ludn on dinh vdi moi gia Iri cac he so Kd.K vii T Song khi cd gian doan thdng tin vdi cudng do v^^, v,, thi tfnh dn dinh ciia he xac dinh toa dg bi anh hudng kem di rd ret.
Ro rang dieu nay phu hgp ve mai y nghTa vat ly,vi khoang thdi gian gidn doan thdng tin cang Idn so vdi khoang thdi gian c6 thdng tin (tham sd Q Idn) thi mien dn djnh cdng bj thu nho lai.
TAI LIEU THAM KHAO
[1]. ApTCMbCB. B. M. ''VnpaejieHue e cucmcMax cpasdenenueM epcMenu" MHHCK, BbimeHmaH mK0.ria, 1987
[2]. Nguyen Tdiig Cudng."Ke xdy dung mdt sd tieu chudn dn djnh ngdu nhiin cho he diiu khiin da cdu triic" Tap chf "Tin Hgc & Dilu Khiln Hgc" Vi?n Khoa hoc vd Cdng nghe Viet Nam, Noll, 2010.
