'Dgi hoc Bach Khoa Hd NQI TOM T A T Bai bio gidi thi?u m6t phucmg phap thiet ke bo di§u khiln du bao phan hoi trang th^i dk diku khien bam on dinh h6 truyen dong qua banh r5ng c6 cac
Trang 1DIEU KHIEN BAM HE TRUYEN D Q N G BANH RANG
V 6 l BQ OIEU KHIEN DlT BAO C O RANG B U O C
Le Thi Thu Ha', B6 Thj Tu Anh^
Trudng Dgi hoc Ky ihuat Cong nghiep - DH Thai Nguyen
'Dgi hoc Bach Khoa Hd NQI
TOM T A T
Bai bio gidi thi?u m6t phucmg phap thiet ke bo di§u khiln du bao phan hoi trang th^i dk diku
khien bam on dinh h6 truyen dong qua banh r5ng c6 cac dieu kien rang buoc Bo dieu khiln du bdo ciia bdi bdo sir dung mo hinh xap xi tuyln tinh ciia he truySn dong banh rang va sir dung ham
thdnh bai todn khong rang buoc Do sir dung nguyen ly toi uu sai lech bdm la nho nhat nen mdc dii i\s
dyng mo hinh xap xi tuyen tinh, song bp dieu khien van cho thay dupe chat lupng bdm tot
Td' khda: Dieu khien du bdo; Hi truyen dong banh rdng; Toi uu hoa co rdng bugc
DAT VAN DE
H? truyen dgng qua banh rang (hinh 1) la mot
trong so cac he truyen dgng dugc sir dung
rgng rai nhat trong cong nghiep, vi vay van de
chSl lugng di8u khi6n he IruySn dgng qua
banh r5ng ciing giO" mgi vai tro khong nho
trong chSl lugng he thong di6u khien qua
trinh noi chung Tu ly do do ma viec nang cao
ehSt lugng dilu khiln h? truyin dong qua
banh rang luon mang tinh thoi su va nhan
dugc su quan tam d^c bi?t ctia cac nha thilt
ke he thdng dilu khiln qua trinh
Bai loan dieu khien he truyen dgng qua banh
rang dugc quan tam trong bai bao nay la phai
xac djnh dugc quy luat thay doi moment dan
dgng tao ra tiJ dpng co dSn dong de he co
dugc toe d^ goc ciia tai dau ra luon bam on
dinh dugc theo mgt quy dao dat truoc va dieu
nay phai khong dugc phu thuoc vao cac tac
dgng khong mong muon vao he Tat nhien de
dieu khien dugc he truyen dgng voi chat
lugng cao can phai co mo hinh toan mo ta
chinh xac he truyen dgng Tai lieu [5] da gioi
thieu mpt mo hinh nhu vay, trong do no chua
dung gan nhu day dii tat ca nhung thanh phan
phi tuyen rat kho xac dinh dugc mgt each
chinh xac, song lai giu vai tro khong nho toi
ch5t lugng truyin dong cua he Do la cac
thanh phan nhu nhung luc ma sat khac nhau,
khe ho giira cac banh rang, dp cung vDng cua vat lieu
Tuy nhien mo hinh cang chinh xac, cau true phi luyen ciia mo hinh cang rac roi, keo theo phuong phap dieu khien cung nhu bg dieu khien sau nay cang phuc lap va linh lin c|y cung nhu tinh ben vung cua be dieu khien cang giam Bdi vay Irong thuc te nguoi ta thudng chi can den mpt mo hinh loan vira
du chinh xae sao eho van co the dam bao dugc chat lugng dieu khien dat ra, ma lai khong lam phiic tap cau true ciia bp dieu khien sau nay
|BilnllnP~
Emad- hahienI977@gmad com
Hinh 1: Dieu khien he truyen dgng qua banh rdng
Phucmg phap dieu khiln don gian nhat thuong dugc ap dung la dieu khien PID [2] Day la phuong phap nay doi hoi mo hinh loan
he truyen dgng phai xap xi dugc ve dang tuyen tinh Song nlu x4p xi ve dang tuyen tinh nhu vay ta da phai gia thiet la Irong he truyen dgng khong co khe ho, ma sal va khong CO moment xoan (vat lieu la tuyet doi cung) Dieu nay da v6 tinh lam giam chat
Trang 2Le Thi Thu Hd vd Dtg Tap chi KHOA HQC & CONG NGHE
lugng he thdng dilu khien, vi eac gia thiet
neu tren rat de bi pha vo trong thuc te
Nhu vay, mu6n nang cao ch§t lugng he thong
ta phai sir dung mo hinh phi tuyen cua no,
Tuy nhien khi sir dung mo hinh phi tuyen
cimg voi phuong phap dilu khiln tuyen tinh
ta phai tuyen linh hoa xap xi mo hinh phi
tuyen cita no xung quanh cac diem lam viec
Cac phuong phap da dugc gioi thieu o tai lieu
[7],[10] la nhiTng vi du vl nhom phuong phap
dieu khien nay
Song viec luyin tinh hoa xung quanh diem
lam viec ma khong phai tra gia cho su sut
giam chat lugng dilu khien khong phai luc
nao ciing thuc hien duoc, dac biet la khi co sir
Iham gia ciia cac thanh phan phi tuyen manh
nhu ma sat, khe ho, do cirng vUng ciia vat
lieu Do do, dl v5n khong lam giam chat
lugng he thdng khi phai tuyen tinh hoa ngucfi
ta da SIX dung them cac co cau nhan dang ma
sat, khe ho hay do cung vimg cua vat lieu de
dilu khiln bii su anh huong ciia chung tdi
thanh phin dgng hpc tuyIn tinh trong md
hinh, trudc khi sir dung bd dilu khien luyen
tinh Mpt sd tai lieu nhu [3], [12], [17] da
cdng bo cac ket qua dieu khien di theo huong
giai quyet nay Tat nhien vdi hudng giai
quyet bang each bd sung them eac co cau dieu
khien bii do, cau true bd dieu khien se cang
phuc tap them, keo theo do tin cay va tinh ben
virng ciia chat lugng dieu khien cang giam
Bdi vay, cudi ciing xu hudng thiet ke bp dieu
khien true tiep tren nen md hmh phi tuyen cua
he truyen ddng la mdt giai phap dung dan Nd
hua hen se khdng lam lang them tinh phirc lap
cLia cau trite he dieu khien ma van dam bao
dugc chat lugng dieu khien dat ra ban dau
Cac tai lieu [6], [8], [13], [14] da cdng bd mdt
so ket qua ve xu hudng dieu khien thich nghi
ben vGng phi tuyen nay,
Mac dii vay lat ca cac phuong phap dieu
khien neu tren, ke ca phuong phap dieu khiln
thich nghi ben virng phi luyen, se van bj ban
che nlu nhu trong yeu cau chat lugng dieu
khiln dat ra ban dau cd them gia thilt ve tinh
bi chan cua tin hieu dilu khien, d day dugc hieu la moment dat d banh rang chii d^ng, hoac khoang gia tri biin thien cho phep ciia eac trang thai trong he, chang ban nhu cac gidi ban vl toe do, gia tdc cua cac banh rang, Nhirng gia thilt nay, tir yeu clu vl linh bin vung cua he thdng, ludn phai dugc thda man, ,nham cd the dam bao dugc vat lieu ciia he banh rang khdng qua bj mdi trong thdi gian lam viec
Mpt trong cac bg dilu khiln dugc xay dung tir md hinh phi tuyen ciia ddi tugng dieu khiln ma vin thda man cac dilu kien bi ch|n
vl dai biin thien gia tri ciia cac tin hieu dilu khiln va Irang thai ciia he la bg dieu khien dy bao theo md hinh, dugc vill tat thanh MPC (model predictive controller)
Bai bao nay se trinh bay phuong phap Ihiet kl
bg dilu khien du bao eho he truyen ddng qua banh rang, cd md hinh phi tuyen chiia dSy du cac thanh phSn luc ma sat, khe hd va dp khdng cihig virng cua vat lieu ben trong la [5]:
'jsA=^i ~^m , -d(.t)rQ,iF,+D,)
•^Sr+\'Pr+i =(^l+\ +^m.il+\))- ( 0
-d(i)ro.,.,l(F,^,+A+,) trong do, d (I) ta da bo qua hien tugng va dap banh rang [5], Viec bd qua nay la hgp ly vi vdi bai toan dilu khiln thi khoang thdi gian xay ra qua trinh va dap banh rang la v6 ciing nhd so vdi oua trinh qua do, nen cd the xem nhu xap xi bang 0 Ngoai ra:
- d{t) la ham md ta khe ho,
- Mj„„ la tdng cac moment ma sat tai cap
banh rang thu" i,
A^,,M,+] la cac moment vao va ra d banh
rang thir J cd M, - M,i la moment dai d dau
vao, dugc lao bdi dgng ca, (Fi+D,) la luc bien dang dan hoi va luc giam chan giira hai banh rang trong cap banh
rang thu i dugc xac dinh theo cdng thirc:
(F, + DJ = q% cos^ tti(p, + J,_,+iP,+i) (2)
vdi To,, ^,, i,,+i, c, ISn lugt la ban kinh vdng
Iron CO sd, gdc quay, ty sd cac rang giira hai banh rang va do cung virng vat lieu cua cap
banh rang thir i
Trang 3Nhiem vu dieu khien bam dn dinh ben vihig
cho he truyin dpng banh rang (I) dugc dat ra
d day cho bai bao la phai thilt ke dugc bg
dieu khien MPC phan hoi tr^ng thai de he
truyin dgng gdm n cap banh rang cd gdc
quay dau ra ^!9„ bam theo dugc quy dao mong
mudn Pj^j
<P„ ->*',<./
ddng thdi tin hieu dieu khien va cac bien
Irang thai phai cd gia trj bien thien trong dai
cho phep la:
KN^^max- k | < < I ' „ ^ = l,2, ,n (3)
vdi A/n,3^,<P,, 1 = 1,2, ,n la nhiing hang so
duong cho trudc,
THIET KE BO DIEU KHIEN DU BAO
CH9 HE TRUYEN D O N G BANH R A N G
Thiet ke bg dieu khien MPC co dieu kien rdng
bugc nha hdm muc tieu tham so bien ddi
Hinh 2a) bieu dien cau triic co ban eua he
dieu khien du bao ddi tugng phi tuyen, gdm 2
thanh phan la [1],[4]:
- Khoi md hinh khdng lien tuc ciia ddi tugng:
a = / ( ^ * ' l i O ' !it=^(^i) (4)
cd tac dung du bao cae vector trang thai ciia
be dugc tinh lir thdi dilm k hien tai, trong dd
X) la vector trang thai va w^ la vector cac tin
hieu dieu khien ddi tugng (lin hieu dau vao),
Cac gia tri trang thai i^.^^, 0 < i < TV dugc du
bao trong khoang cua sd du bao [A:,A: + N']
trong khoang thdi gian tuong lai, tinh tir thdi
diem hien tai i nhu md ta d hinh 2b) se la:
5 u =/(a-+i-i'?^fe4-,-i)
= /(/(^(+,-2.yjL-+,-2)'yi+,-l)
= /(/( 7(5(,a-)'^t4-i)' ••• )'a-+,-i)
Tir cac gia tri trang thai x^ ,.;, 0<i<N du
bao dugc trong ciira sd du bao hien tai [A;,/i:+Af] ta cung se cd cac gia tri dau ra du bao trong cua sd du bao do la:
= 5(/-(^t,yt.Mi-+h - 'ytk+i-]))
!-!?,(^t'?^t'Mt+i' ••• Mi+,-|) (5) Khdi tdi uu hda, cd nhiem vu xac dinh lin
hieu dieu khiln tdi uu ul Khdi nay chira
dung Irong nd 2 khdi con gdm ham muc tieu
va thuat loan Idi uu xac djnh nghiem ciia ham muc lieu dd
Ham muc lieu tuong ung trong khdi nay duoc xay dung tir chi tieu chat luong dat ra cho he thdng Vdi chi lieu chat lugng dai ra la tin
hieu dau ra y phai bam dn dinh theo dugc lin hieu dat w,., Ihi mdt trong cac ham muc
lieu thda man dugc chi lieu chat lugng do la
^ = i:((Hi+,,-j/,^,)^Q,(ii^t- JK
vdi Q,, /£, la nhiing ma tran ddi xiing xac dinh duong tiiy chpn va 0<N^,N2<N cung la hai
sd duong liiy chpn [16] Rd rang, khi sir dung kel qua du bao (5) cung nhu do z^ la da cd,
thi khi chpn N^-\ = N2 =N, ham muc tieu J
se Ird thanh ham ciia cac tin hieu dieu khien can tim:
%=col(Uj^,u^.^,, ,Mfc+jv)
Dieu khiindirbao
Mo hinh
doi tUdng
Toi Uu
hoa
Goi tUi^ng di«u Ichien
tr
Trang 4tLrc la J = J(Wj ), luc nay dugc viet lai thanh:
trong do:
Kh6i con thu hai la khoi thuat toan t6i uu dS
tim nghiem bai toan toi uu:
= arg min /(W^,)
trong do U d R ' " la dieu kien rang budc ciia
vector lin hieu dieu khien uj dugc suy ra til'
(3) Thuat loan tim W^ thudng dugc sit dung
laSQP[ll]
Tuy nhien, khi su dung cac phuong phap tdi
uu hda de lim nghiem bai toan tdi uu c6 rang
budc (7)thi rat cd the ta chi thu dugc nghiem
dja phuong, Ndi each khac nd £^ tim dugc
CO the chi mdi la diem cue In eua /(W;.), chu
chua phai nghiem ciia (7), De lim nghiem
loan cue ciia (6), la can tdi phuong phap dieu
khien tdi uu, chang han nhu phuong phap
bien phan, hoac quy hoach ddng ciia Bellman,
song cac cdng thuc ludng minh xac djnh
Uj-Iheo phuong phap dieu khien tdi uu nay lai
mdi chi dirng lai cho Iru'dng hgp khdng rang
huge, do do khdng the ap dung dugc khi bai
loan dieu khien du bao cd them cac dieu kien
rang bugc nhu d cdng thii'c (3),
Mac dii vay, neu nhin lai va phan tich cau true
ham muc lieu (6) ciia bai loan tdi uu (7) ta se
thay:
- Khi ||72.|[ cang Idn, su tham gia ciia thanh
phan Uj^ T^lii trong ham muc tieu (7) cang
cao, keo Iheo khi cd dugc ^(W^)-> min, gia
tri eiia ||i^J| se cang giam Dieu dd ddng
nghTa vdi viec cang tang ||7?.|], dieu kien rang
bugc (3) cang de dugc thda man
- Nhung neu cang lang ||7?-||, gian tiep se cang
lam cho su tham gia ciia thanh phan thir hai la
^L Q^k- 'rong (6) lai cang giam, keo theo
cang khd cd dugc \\s^ | -> 0, lire la chat lugng
Tat nhien ta cang khdng thi vira tang pl\\
vua tang | | Q | , vi nhu vay tuong quan vl sy
tham gia cua hai thanh phdn uj.'^y.k ^^
^I^^k ''•°"8 -^(^fe) se khdng thay ddi
Bdi vay mdt y tudng dung hda xuat hien d
day la ngay ban dau (khi k nhd) la chpn ||7?.||
dii Idn dl cd llw^ 11 dii nhd sao cho vdi nd co dugc dilu kien rang budc (3) Khi dieu kien rang bugc (3) da dugc thda man, ta se giam
||7?.|| dk thdng qua dd lam tang them su Iham gia eiia thanh phan sai lech bam £^Q£_i trong
•KKk) nham lam giam sai lech bam sau nay,
Tuong tu ta cung cd thi chon ||Q|| dii nhd ban
dau, sau dd tang dan j|QJ| theo k Vdi hai,trudng hpp thay ddi hai ma Iran "R hay Q Iheo thdi gian k nhu tren, ham muc
lieu gdc ban dau (6) trd Ihanh:
JiiLk) = fkQi.^k^ui'^kllk (8)
va tuong img, bai loan Idi uu cd rang budc (7) trd thanh bai loan khdng rang budc:
ul =argminJ(Wj) (9) Sau khi da cd nghiem tdi uu U ciia (9), phan
lir dau tien cua Z^ la u^ se dugc dua vao
dilu khiln ddi tugng Irong khoang thdi gian
giira hai lan trich mau kT•<t<{k + \)T, trong
do T la chu ky trich mau Nhu vay bg dieu
khien du bao lam viec theo nguyen ly lap vdi cac budc sau:
1) Chgn W>O.Gan k-.= Q 2) Do Irang thai x^ va tim nghiem tdi uu U^
cua bai toan tdi uu cd rang bugc (9), 3) Xuat u J = ( / , 0 , ,0)W* de dilu khiln ddi lugng trong khoang thdi gian
kT<t<{k-i-\)T roi gan k:=k + \ va quay
ve 2,
Xdy dung mo hinh du bdo
Theo nguyen t k dieu khiln du bao vira trinh bay, dl cd dugc bd dieu khiln du bao cho he truyin ddng banh rang, thi tir md hinh (1) da
cd ciia he truyen dpng banh rang ta phai xay dung md hinh khdng lien tuc dgng (4) lam mo
Trang 5Tir (1), tai lieu [9] da d u a ra md hinh t u o n g
u n g cho h e t u o n g u n g cd mdt c a p banh rang
n h u sau:
l 7 | ^ + c j i | C o s a i , ( ( ? , + % ^ ) = M , ; - M „ „
(10)
[Jlipi -CTij'^os ai{(p2+iQ_m) = -M,, -M„,,2
trong đ:
- ai gdc an k h d p c u a hai banh rang, va
cung la dai l u g n g d a n h gia khe hd giúa
cac banh rang, Khi hai banh rang tieu
chuan va khdng cd dp djch l a m , thi gdc
an k h d p or^ = a = 20° , Vdi he cd khe b d
thi \%°<a,<2S°,
- c la dai l u g n g d a n h gia do c u n g eiia banh
rang, G i a tri c cang nhd, dp mem deo
ciia banh rang cang Idn va
\c h che do an kh6p
[0 d c h e dp k b e h P
- J,h'^]'J2 ' ^ " ''J'9^ ' ^ m o m e n t quan linh
ciia d g n g c o , banh rang 1 va banh rang 2
va J^ = J ^ + J ] ,
~ M,, la m o m e n t can, bao gdm ca m o m e n t
tai,
- M„,,;|, M,„,(2 ' ^ m o m e n t ma sat trong cac 6
true banh rang,
ru, ri2 la ban kinh lan t u o n g iing cua hai
banh rang (ban kinh ngoai),
(Ol =g)i, 0)2=^ la van tdc gdc l u o n g u n g ciia
hai banh rang,
i|2 la ty sd truyen tií banh rang 1 sang
banh rang 2, tiic la (^2 = V2\^ •
N h u vay, gidng n h u (1), md hinh (10) nay ciia
he mdt cap banh rang c u n g chiira d u n g Irong
nd tat ca nhiJng thanh phan bat djnh khdng
the x a c djnh d u g c mgt each chinh x a c trong
nd, bao gdm m o m e n t can M,,, gdc k h d p hai
rang ai, chi sd d o d o cirng vu"ng ciia vat lieu
lam banh rang c , cac m o m e n t ma sat cOa hai
banh rang M ^ , | , M.^^2 •
Tat nhien vdi nhieu t h a n h phan bat dinh Irong
md hinh n h u vay, c d n g thiie (10) khdng t h i
sii d u n g d u g c lam m d hinh d y baọ D o đ la
cSn phai xSp xi nd va chap nhan rang trong
md hinh xap xi khdng cdn chira thanh phan
bat dinh nay Idn lai mdt sai lech md hinh
M a c dii cd sai lech m d hinh, luy nhien n h d linh tdi uu cua bd dieu khien d u bao sau nay
ma s u anh h u d n g ciia sai lech md hinh đ tdi chat l u g n g he thdng se d u g c giam thieu
T r u d c lien la xap thanh phan m o m e n t ma sat đng, bd qua ma sat Imh:
cung n h u cac he sd xap xi hang 0:
^1 - c r / i c o s ^ t r ^ , 6*^' -crljcos^ai
Ihi (10) chuyen ve d u g c thanh:
pi9\ +i9|(9)i +ii2¥2) = ^d -h9\
\j2ip2 -62^{<Pi+H29\) = -hh
Tir p h u o n g trinh I h i i h a i Irong (1 l ) c d :
9\ =^2\f2{J29l+h92)-<P2\
= 0^ip2+9i(P2-h2<P2
vdi
^ 3 = ^ 2 ' ^4=^12^2^2 Suy ra
q\=9^<p'-^^ +ế(P2-lx2<P2
T h a y vao p h u o n g Irinb Ihu nhat ciia (11)
d u g c :
(11)
M j = j , « 3 ? i ' » + ( j , e 4 + 6|fl3)^2 +
+ [\0, +9,^3 - J|I,2)?*2 +(91^4 -l>\\l)<h
hay:
Xj; - X;^+| khi 1 < ^ < 3
[ i 4 = f l j i + 9 , i (12)
V = il
trong do:
H = « ^ ^2 ='Pị'^i=<h-H=<h a: = CO1(:E2 ,3:3,2:4 ), u = M,;
•' J.ffj - ' J|93
«1»4-''|'|2_
61^4 +51^3 -J[l\2
1 ^4 ^"\^i
-a,
0 2 O3
Do chi quan tam tdi tdc do x^-ipi ii^i ^^ cd the bd bdt di bien Irang thai x\=(p2 trong md
hinh (12), Khi d o m d hinh he truyen d d n g q u a mdt c a p banh rang se la:
= Ax + ^ u va j/ = c ^ z (13)
Trang 6Le Thi Thu Ha va Dig Tap chi KHOA HOC & CONG NGHE
i =
0 1 o"!
0 0 1 , £ =
G] (22 '^3 J
ó
0 ,«.y
,
£.-n
0
oJ
Tir day, va voi chu ky trich mau T chon
truoc, co:
(iị+l ='*&+»%
la = / a
trong do
 ế^.b^lếbdi
W^A"*')
A =
c'b 0 0 )
c^'Ab c^b ••• 0
, r , « i ,T.«-I
WA"b c'A"-'b c ' t ;
Wj=COl(»,.,lli+,, ,ut+„)
Suy ra, ham muc tieu (8) t6ng quat trcr thanh:
Qi,'
(14)
va ta se sir dung mo hinh (14) nay lam mo
hinh du bao cac trang thai 5^,^,, 0<i<N
trong cira so du bao hien taị
Xdy dimg khoi loi im boa
Vai mo hinh du bao (14) cho he truyen dpng
mpt cap banh rang, cong thuc du bao dau ra
t6ng quat (5)bay gia tra thanh;
= £'''4^il+,-2+£''''^"t+.-2+^''H+.-l
'C^Áxi + ( / ^ ' " ' 4 , c^Á^'b , , c'^iW,
trong do:
^;=™l(«t."l+ %+.-l)
Boi vay, neu ky hieu vector sai lech dau ra
tuang lai trong taan bp cOra so du bao
[t.t+W] la:
£ = <:»l('»l+l-Sui, ••• n+iV+l-i/J+iV+l)
ta se dugc:
trong do:
(15)
(16)
3*., 0 - 0
0 0 ••• Oi+jv+i
Rt 0 ••• 0
0 Rt^i •• 0
0 0 ••• Rt^f,)
N6u nhu cac ma tran £?;:+,,flfc+, doi xiing xac djnh duang dugc chpn sao cho nghiem toi uu
ul cua (9) luon thoa man dieu kien bi chfin
(3) ma cu the 6 day la:
Kl^^max- 1^,1 < 0 , , j = 1,2,3 (17)
thi bai loan tdi uu bj rang budc (7) se trd thanh bai loan khdng cd rang budc (9) Trong trudng hgp nhu vay ta cd ngay:
Uf^ =aigminJ(li,)
= aiBmin[i/(Á'q.A+9J,)i4 - 2 / ^ 4 4 ]
.[Âa,A*-R,]" ÂQ^a (18)
va cudi cimg la:
4 ={1,0 .,Q)l^ (19)
Hai cdng thiirc (18), (19) tren mgt ISn núa
khang djnh rang vdi Qi;+.,,Rk-vi ^^rgc chgn
sao cho Q va 7?.^, cd |Q|1.|| cang nhd hoac
LA Qic^t + Tii *^^ng Idn thi \uf\ se cang
nhd
Thudt todn dieu khien dir bdo he truyen dgng banh rdng co dieu kien rdng bugc
Tir eac cdng thirc (15), (16), (18) va (19) ta c6 dugc thuat toan dieu khien dy bao cho he truyin đng banh rang (12) gdm cac budc sau:
1) Chgn W>0 va cac ma tran (3t+,,ftt+, tuong iimg vdi dilu kien rang bupc (17) Xac
dinh ma tran Ạ theo (15) Gan jt:=0 2) Do trang thai x,^ va xac dinh u Iheo (15)
Trang 73) Xay dung cac ma Iran ^,'^k theo (16)
4) Tinh l£ theo (18) va tir dd la uj theo (19)
5) Xuat u^ de dieu khien ddi tugng trong
khoang thdi gian kT<t<(k + \)T rdi gan
k:=k + l vaquay ve2
KET QUA MO PHONG
De minh hga phuong phap, la xet he truyen
ddng banh rang cd md hinh tuyen tinh xap xi
dang (13) trong dd:
/ 0
0
- t )
1
0
-n
"1
•
- 6 J
6 =
("]
a
^-fi
0
0
Ta se ap dung thugt toan dieu khien du bao de
he thdng nay bam dugc tin hieu dat
Wj^ =1, Vfc va thda man dieu kien rang budc
cua tin hieu dieu khien |u^.|<30 Chpn ehu
ky trich mau T = 0.2 , eiia sd du bao N = 5 va
cac ma triin g^ = S = 10/, 7^^.-O.Ol(^) /
vdi I la ma tran don vj cd kich thudc phii
hgp Viec chgn 72.^ giam dan theo thdi gian
nhu tren xuat phat tir lap luan nhu sau Tii cau
true ham muc tieu (8) ta thiy khi 7^^ cang
nhd thi tin hieu dieu khien % se cang Idn Do
dd, d thdi diem ban dau, sai lech bam giira lin
hieu ra va tin hieu dat la Idn nhSt nen Ttj can
dii Idn de uj khdng vi pham dieu kien rang
bugc Sau dd, khi sai lech bam giam dan thi
do Uf cung cd xu hudng giam nen de nang
cao kha nang bam lin hieu dat, ta lai cd the
giam dan Tt/ nham tang u^ ma van dam bao
thda man dieu kien rang bugc Lap luan nay
se dugc kilm chiing d phSn md phdng qua so
sanh vdi trudng hgp ma tran nay khdng thay
ddi, tuc la khi 7^^ = 7^ = 0.003
Hinh 4: Tin hieu dieu khien u
Hinh 3 va hinh 4 minh hga cho tin hieu ra va tin hieu dieu khien eiia h? thdng Trong trudng hgp "K.^ giam dan (dudng net lien), ta thay tin hieu ra bam dugc theo tin hieu dat ma van dam bao thda man dieu kien rang budc
ctia tin hieu dieu khien \ui, | < 30 Trong khi dd neu giiJ nguyen TZ.j-='Tl (dudng net dirt) thi
Tt phai dugc chgn dii nhd nham tao ra tin
hieu dieu khien du Idn mdi cd thi dua he thdng bam dugc tin hieu dat Dieu nay dan den viec d nhirng thdi diem dau lien, dieu kien rang budc ciia u/ bi vi pham Ngoai ra, uu diem ciia viec sir dung ham muc lieu cd tham sd bien ddi so vdi ham muc tieu
cd tham sd cd djnh cdn dugc the hien qua ket qua md phdng d cac hinh 5 va hinh 6, De khdng vi pham dieu kien rang budc cua u^ thi viec gio- nguyen 72.^ = 72 = 0.01 lai khdng the dem lai chat lugng bam tdt, kl ca khi tang cira
sd dy bao Cu the ban, sai lech bam cDa he thdng img vdi ^ = 5 0 (dudng cham gach)
nhd hon so vdi sai lech bam irng vdi N = 5
(dudng net gach) Tuy nhien, A'' cang Idn thi khdi lugng linh loan ciing cang Idn Trong khi
do ta cd the dat dugc sai lech bam bang khdng vdi 7J.^=0.0lf^J / va A' = 5 (dudng net liln)
Trang 8Hinh 6: Tin hieu diiu khien u
K E T L U A N
Bai bao da xay d u n g d u g c mdt p h u o n g p h a p
t h i l l k l bg d i l u khien d y bao cd rang budc
cho he thdng phi tuyen voi md hinh xap xi
d u g c ve dang tuyen linh lien tuc (13), T h d n g
qua viec sir d u n g ham m u c lieu cd tham sd
b i i n ddi, bg dieu khien d u bao phan hdi Irang
thai trong bai bao cd the lam tin hieu ra cua
he Ihdng bam d u g c t h e o tin hieu dat ddng thdi
thda man cac dieu kien rang bugc ciia vector
trang thai va tin hieu dieu khien Ket q u a md
phdng tren Matlab cho thay ro anh h u d n g ciia
viec thay ddi cac tham sd ciia ham m u c lieu
nay tdi chat lugng bam c u a be truyen d d n g
banh rang cd rang b u d c Viec phan tich linh
dn dinh bam cua h e t h d n g dieu khien d u bao
nay se la van d e nghien ciru tiep theo cua
chiing tdi
TAI LIEU T H A M K H A O
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predictive control Springer
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Electro-mechanical Systems Elservier GB
3 Deur,J and Peric,N (1999): Analysis of Speed
Control for Electrical Drivers with Elastic
Transmission IEEE Intemaltional Symposium on
Industrial Electronics Bled, Slovenia, pp 624-630
4 Griine, L and Pannek, J (2010): Nonlinear
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banh rdng Tap chi Khoa hpc va Cong nghe Dai hoc
Thai Nguyen, tap 118, so 4,2014, Uang 67-78
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ve diiu khiin du bdo Phan I: He tuyen linh
Tuyen tap bdo cao hoi nghi khoa hpc Khoa Dien tit, Trucmg Dai hpc ky thu$t cong nghiep Thai Nguyen, t r l 2 9 - l 3 8
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Trang 9S U M M A R Y
T R A C K I N G C O N T R O L O F G E A R I N G T R A N S M I S S I O N S Y S T E M S
V I A C O N S T R A I N E D M O D E L P R E D I C T I V E C O N T R O L L E R
Le Thi Thu Ha'", Do Thi Tu Anh^
'College ofTechnology - TNU, 'Hanoi University of Science and Technology
This paper introduces a method to design feedback predictive controller for stable uacking control
of gear transmission system with boundary conditions The predictive controller of this paper uses form with parameters shift, hence, control problem with constrains is always being non-constrain problems Since the optimized principle with tracking error used is smallest, thus, despite of using linear approximate model, the performance of controller still recorded high tracking quality
Keywords: Model Predictive Control; Gear transmission system; Optimization with constrain
Ngdy nhdn bdi:01/10/2014; Ngdy phdn blen-03/11/2014; Ngdy duyet ddng 25/11/2014
Phan bien khoa hoc: PGS TS Lai Khac Lai - Dgi hoc Thdi Nguyen