BO BifeU

THIET KE BO BifeU KHIEN PHAN HOI TRANG THAI CHO HE CAU TRl^C

Trpih Luang Mien, Nguyin Vdn Tiem

Bp mdn Dicu khien hgc, Khoa Dign Di?n tir, Trudng Dgi hgc GTVT

r

Tdm tdt:

Bdi bdo dira ra md hinh todn ciia h? cdu true vd kit qud thiit ki bg diiu kliiin phdn hoi trgng thdi khi them thdnh phdn tich phdn nhdm tu dgng hod cdu true ddm bdo tri?t tieu sai lech tinh: vi trixe godng vd dao dgng tdi.

Summary:

This paper gives mathematical models of bridge crane and results of the state feedback controller with an additional integrator to operate automatically bridge crane with willingness reducing position error and swing of load as possible.

1. DAT

V A N D E

Cdu tryc Id thiet bj cdng nghiep dugc iirng dyng rdt rgng rai trong nhieu ITnh vyc nhu trong xdy dyng, trong nhd mdy hay tai cdc ben cdng, ... Nhung cau true ndy thudng van hanh bdng tay. Khi md kich thudc ciia cdu tryc trd nen Idn han vd yeu cau van chuyen nhanh hon thi qud tnnh dieu khien chiing se trd iien khd khdn neu khdng dugc ty dgng hod. Cau true di chuyen theo nhimg quy dao linh boat. Nhung nd hoat dgng dudi nhung dieu ki?n het sue khac nhiet vd mdt he thdng dieu khien kin Id thi'ch hgp nhdt.

Cdu tryc Id he rdt phirc tap. Trong sudt thdi gian qua da co khd nhilu cdc nghifin ciru [1-5] ve cdu tryc nhdm tim ra phuang phdp van hdnh nd mgt cdch higu qua. Trong so cac nghien ciiu do thi phuong phdp dilu khien cdu tryc dya vdo md hinh tuyin ti'nh da thu dirge mdt vdi kit qud khd quan [6-7]. Tuy nhien, van dk ton t^i Id cdc bg dieu khiln dugc thilt k^

chua triet tieu dugc sai lech tTnh. Do v^y, bdng cdch dua them khau U'ch phan vao bg dilu khien phdn hoi trang thdi se dam bdo sai l?ch tTnh cua h? thdng dugc triet tieu hodn toan va chdt lugng dieu khien dugc nang cao.

2.

M 6

HINH

T O A N

Hf CAN TRyC

Md hinh cdu tryc vdi he to? dg dugc chgn nhu md ta tr6n hinh I. True Ox ndm ngang dgc theo thanh rdm, tryc Oz thdng dung cd chilu hudng len tr€n. Xe godng di chuyin tren thanh rdm vdi vj tn dugc xdc djnh bdi x(t) Id khoang cdch do dugc tir goc O din dilm treo cua cap ndng tdi tren xe. Coi tdi nhu mgt chdt dilm cd khdi lugng mp, xe godng cd khdi lugn^

mt. Tdi trgng vd xe godng dugc ndi vdi nhau bdng mgt cap cimg cd khdi lugng khdng dangkS

vd cd chilu ddi /, sy ddi ra cua day cdp la khdng danh kl. Trong khi nang/ha tai hay di chuyin

xe thi tdi dao dgng trong m^t phdng thdng dung vdi gdc lech a(t). F^ la lye chuyin dgng xe

godng theo hudng x vd F| la lye nang tdi theo phuang /.

^ ^ ^ T r J i r-.'iny

iniita

T l i i r l i r.Vi

J

G K ) I I'an - - Moc tree-

'~~— B.'iny diL-L klm*n

, 7

0

i^i*] .

Thanh ram Tdi nang

- —K

nr

Xe goong (rrii)

X

^ A P i X p . Zp)

Hinh 1. Mo ta hf cau true trong hf tQa dq.

Phuong trinh chuyen dgng ciia he cdu tmc nhdn dugc tir phuang trinh can bdng ndng lugng Lagrange [I], [5]. [9]. Sau khi tfnh todn vd biln ddi, ta thu dugc phuang trinh dgng lye hoc md td he cau tmc nhu sau:

(m, + m^ )£&- m^ (sin a)^ mJ(cosa)SSt^ -2m ^ icosa)^+ niplisin a)(£c + F, m^ (sin a)S&- m^r^ m^ld& + m^g cos a+F,

(cosar)iBi»- /<»&= - 2 ^ - g sin a

(1)

Theo (1) ta da xdy dyng dugc phuong trinh md td chuyen ddng cdu tryc tdng qudt khi thyc hien chuyen ddng theo cd hai phuang x, /. Trong trudng hgp cd djnh cdp treo tdi, / = hang sd, ta cd A = P ^ O , liic ndy phuang trinh chuyen ddng cua he se dugc viet lai [9] nhu sau:

(m, + in^ )SA- mpl.{Scosa-d^ sin or) = F^

i&osQr+/dBg-^ sin a = 0

(2)

Md hinh tuyin ti'nh dimg cua he cau tryc thu dugc tur gid thilt gdc lech du nhd, liic nay ta cd sin or ~ a,cos a ~ I.

'(m,+m^)/fcm^/<jSfc=F, liSsr ga = -&.

He tuyin tfnh (3) cd thi bilu dien trong khdng gian trang thai [5] nhu sau:

J&=AX + 5M

y = Cx vdi

(3)

(4)

A =

x = [x

ro I

0 0 0 0 0 0

J&. a d^ u = 0 0' m,

0 1 m, +m„

--^-7^8 0 m,l

F/^

; B =

' 0 ' 1 m, 0 - 1

; C = "I 0 0 0

0 0 1 0 (5)

Thdng sd he cdu true dugc cho nhu sau: Khdi lugng xe m, = 2[kg]; Tdi trgng ban ddu mp = 0.2[kg]; Chilu dai cdp nang tdi l[m]; Khoang cdch di chuyin xe 0.2-l[m]; Gdc Idc dao dgng Idn nhat: a = 10° - 0.2 [rad].

3. Thiet kl bg dieu khien ,.x

Theo nguyen ly dilu khiln phdn hii trang thai [7], bg dilu khiln dugc chgn cho he (4) cd dang: u = F= -Kx ;v6i K = [K^, K^, K •pa K _(ia ; Ki hdng sd. (6)

Ta thay, ludt dilu khiln phdn hoi tr^ng thdi (6) dya tren nguyen ly ty le se tdn tai sai lech tinh [8]. Vi thyc chat, ludt (6) dugc tdng hgp theo md hinh tuyen tfnh tuong ddi (4), (5).

Do vay dl triet tieu sai lech tTnh, ta se them mgt khau tfch phan vao vdng phdn hdi vj tri cua xe godng, tire Id mgt biln x; dugc dua them vdo h? thdng [3], [7-8] nhu sau:

^=\x„+B„u l = C„x„

0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 -

K =

vdi jr„ =[xi X JSC a

0

(7)

0 0 m^g

m, 0 m, +m

0 0 0 1

•g 0 B„ =

0 _1_

' " /

0 - I L'^M

C = 0 1 0 0 0

0 0 0 I 0 (8)

m,/

Ludt dilu khiln phdn hdi trang thdi khi ndy cd dang:

u = F,=-K„x„ vaiK„=[K,, K^, K,^ K^„

Vdi bd dilu khiln (9) he kfn md rgng (8), (9) se nhu sau:

j8i.=Ax„-\- BM = (A„ - B„KJx„

—fl a—fl fl ^ et a fl'—fl

KJ.

⁽⁹⁾

(10)

0 * '

Nhu vay, neu cho tmdc cdc diem eye cua he ki'n md rgng Pi (i=I,5) thi cdc he so ciia bd dieu khien phdn hdi trang thdi Ka (9) se dugc xdc djnh tir viec so sinh nghiem cua phuong trinh det[sl (Aa-BaK,)] = 0 vdi pi.

det(5/-(A„-fl„/i:„)) = det 0

- I K.

0 - 1 K.

m, 0

m, 0

j + —=^

m, 0

0 0

-mp-\-K

0 0

pa K _da

m.

(m, +m^)g-K _pa

m, - I K

m.l m,l m,l m,l ^S--

Ma

m,l

= s' +

m,l m,l m,l m,l m,l Do dd, ta tfnh dugc cdc he so cua bg dieu khiln phan hoi trang thdi Ka (9) nhu sau:

K.,,={m,ip,P,P,PJ,)lg

K,. =[mmPiMA^MiPA ^PAM, ^M,PA^MyMs)V8

K„ =[-lK,+mM/3,/3, + AAy^4 +AAA + A/^jA + A A A +AA4A

+J3JJ, + A A A + AA4A + AA4A)]/5

⁽¹¹⁾

K„a = K^J + (,n,+ m^, )g -m,l{P,l3, + /3,/3, + /3,/3, +/3,fi, + fij, + j3J,

K,a = KJ -m,I(P, +P,+ P, +P,+Ps)

Cdu triic he thdng dieu khien cdu tmc dya tren nguyen ly phdn hdi trang thai nhu hinh 2. Bd dieu khien phdn hdi trang thai dugc dua them vao thdnh phdn tfch phdn nhdm triet tieu sai lech tTnh vi trf.

a.ret

^S-^Ehiih^m

Hinh 2. B9 dieu khiln phan hoi trang thai hf cliu true

Vdi thdng sd cua he cdu tryc nhu tren, tir (11) ta tfnh dugc he sd khulch dai cua bd dilu khien phdn hdi trang thdi nhu sau:

[Kix Kpx Kdx Kpa Kda]'^= [0.0100 1.5003 2.3833 -3.0465 -4.6255]"^ (12) Sa dd md phdng he thdng dilu khiln cdu tryc dugc xdy dyng tren Matlab/Simulink nhu hinh 3.

PHTT CraneXA

4-H

Hinh 3. Sff do mo phong he thing dieu khiin hf cau true tren Matlab

4. KET QUA M 6 PHONG

Trirdng hgp I: Khi xe di chuyin din vj trf ddt 1.0m

( a ) . D a p u n g \A tri x a goong

1 0 2 0 Tl-iol gian t (s)

3 0

0 . 0 4 0 . 0 2

- 0 . 0 2 - 0 . 0 4

-o.oe

( b ) . D a o d o n g tai ( I d - O . O I TAr)

3 0 Thoi g i a n i ( s )

Hinh 4. Ddp ung vj tri xe (a) vd dao d$ng tai (b) khi x<i =lm.

Ta thay bg dilu khiln cho chit lugng tdt, xe di chuySn den dung dfch trong thdi gian chap nhdn dugc (~10s), dd qud dilu chinh b6 (< 10%); tdi dao dgng vdi bien dg nhd (< 6*'), Truang hgrp 2: Cho xe di chuyen den vj tri" 0.4m rdi dimg, sau dd di chuyen tiep den vj tri Im.

( a ) . O a p u n g vl tri x e goong ( b ) . D a o d o n g tai ( 1 d - 0 . 0 1 7 4 r )

I

S

1 0 2 0 Thoi g i a n t (a)

3 0 10 a o

TTioi o<*ri t ( s )

3 0

Hinh 5. Dap irng vi tri xe (a) va dao d§ng tai (b) khi x^ =0.4m; Im.

Khi quy dao thay ddi, he thing dilu khiln van bdm dugc theo quy dao dat vdi ch5l lugng dilu khiln tdt.

Truang hgrp 3: Khi thay ddi khdi lugng tdi trgng mp

1.4 1.2 1

( a ) . D a p u n g vi tri x e g o o n g

z

8 0.8

5

^ 0.6 0.4 0.2

o

1 " ~)

/Sc". ' '

.1 1 . . - ^ d m p = ! 0 . S • nnp=l.o

I

10 2 0 Thoi g i a n t (s)

3 0

0 . 0 4

0 . 0 2

- 0 . 0 2

- 0 . 0 4

- 0 . 0 6

(b).Oao dong tai ( 1 d - 0 . 0 1 7 4 r )

" d m p = 0 . 2 m p = 0 . 5 n n p = i . o 10 2 0 Thoi g i a n t (s)

3 0

Hinh 6. Dap ung vj tri xe (a) va dao d^ng tai (b) khi thay doi nip.

Nhu vay, vdi bg dieu khien. phdn hoi trang thai chimg ta hoan todn cd the dieu khien cau tmc theo quy dao mong mudn. Su lien quan mat thiet giii'a cdc thanh phdn trong he cau tRic doi hdi chung ta phdi lya chgn cac diem cue hgp ly de tir dd tfnh dugc cac thong so bo dieu khien thfch hgp nhdm dam bao chdt lugng dieu khien he thdng nhu mong muon. Khi diem eye dugc chgn qua nho (< 0.5) thdi gian qua do se rdt lau; khi diem eye chgn qud Idn (

>10) do qua dieu chinh vugt ra ngodi viing cho phep. Diem eye hgp ly dugc chgn trong miln tir 1.0 den 5.0. De tdng do tdc dgng nhanh ta chgn diem eye ndm xa tryc do va do qud dilu chinh cang Idn khi diem eye ndm cdng xa tmc thyc.

V. KET LUAN VA KIEN NGHI

Nghien ciru dilu khien cau tmc Id mgt hudng iing dyng rdt thilt thyc vi su da dang va tfnh kinh te ciia nd. Bdi bdo da dua ra mdt phuang phdp ting hgp bg dilu khiln dan gidn nhung lai cho chdt lugng dieu khien tdt, dd Id phuang phdp tdng hgp bg dilu khien dya tren nguyen ly phdn hdi trang thai. Cdc ket qud md phdng cho thdy bd dilu khiln hodn todn ddp ling dugc yeu cdu ve dilu khien vd thyc tl van hdnh cdu tryc. Tuy nhien cdn phdi nghien ciiu them de dieu khien cdu tryc trong mdi tmdng cd nhieu, trong cdc dieu kien van hdnh khdc nhiet thyc te khdc nhu sy dnh hudng cua nhiet dg, dg dm cao, tdc dg thay doi gid,...

TAI LIEU THAM K H A O

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[2] Hahn Park, Dongkyoung Chwa, and Keum-Shik Hong: A Feedback Linearization Control of Container Cranes: Varying Rope Length, Intemational Journal of Control, Automation.

and Systems, vol. 5, no. 4, pp. 379-387, August 2007.

[3] Z.N. Masoud, A.H. Nayfeh, and N.A. Nayfeb, Sway reduction on quayside container cranes using delayed feedback controller: simulations and experiments, Journal of Vibration and Control 11, 1103-1122 (2005).

[4] R.J. Henry, Cargo pendulation reduction on ship-mounted cranes. Master's Thesis Virginia Polytechnic Institute and State University 1999.

[5] Lasse Eriksson, Modeling, simulation and control of laboratory-scale trolley crane system, Hamburg University of Technology, 1999.

[6] Yong-Seok Kim, Keum-Shik Hong, and Seung-Ki Sul, Anti-Sway Control of Container Cranes: Inclinometer, Observer, and State, Intemational Journal of Control, Automation, and Systems, vol. 2, no. 4, pp. 435-449, December 2004.

[7] Y. Hakamada i M. Nomura, Anti-Sway and Position Control of Crane System, Proceedings of AMC 2, 657-662, 1996.

[8] Nguyen Doan Phudc, Ly thuyit dieu khiin tuyin tinh, Nhd xudtt bdn KHKT, 2005.

[9] Trinh Luang Mien, lfng dung logic ma diiu khiin hi cdu true, Ludn vdn thac sT ky thudt, 2007.