KHOA HOC CONG NGHE
S6 0fr'2020
Xay dyng mo hinh tin hieu dieu khien cho thiet ke chuyen dong 3 true cua he thong mo phong hang hai
• PGS.TS.DtNH ANHTUAN;ThS.TRUCfNG C 6 N G MY;ThS. D O A N H U U K H A N H Trudng Dai hpc Hdng hdi Viit Nam
T Q M T A T : Trong bai bao, tmh dqng hpc ciia mo hinh chuyen ddng ba bac ty do co g i n buong lai t i u thiiy v i b i t chuoc chuyen ddng cira con tau dupc nghien cuu va gidi thieu mdt mo hinh tin hieu d i l u khien mdi Nghien ciru nay dua tren tiep can Stewart platform vdl ba b i c tu do (lie ngang, lie dqc va cao do). Sin buong lai dupc di chuyen bdi ba dpng servo c6 tich hop dieu khien tan so Mot cich de xuat mdi dupc xem xet de giai quyet van de nay, gpi la "phuong phap tinh toan mp hinh tm hieu dieu khien chinh xac". Tren co sd thuat gili I5p Newton-Raphspn, viec mo phing phuong phip niy dupc tien hinh, uu va nhupc diem ciia chung dupc SP sinh cu the, Ket q u i chi ra ring, vdi mo hinh tinh toan da c i i tien, khi dupc cung cap gia tri lap ban dau tdt chp thay da mo phdng chinh xac cac chuyen dpng phi tuyen cua cau true ba b i c tu do d i l u khien true song song dupc lya chpn TLf K H Q A : U P ph6ng hang hii, mo hinh chuyen d$ng, d i l u khien dpng cp servo
ABSTRACT- In this paper, the dynamics of a 3D0F motion platform which suppprls the bridge and imitates the motion of the ship is studied that introduces a new control signal model This research is based on a Stewart platform in three degrees of freedpm (rpll, pitch and heave) The platfprm deck IS moved by three frequency cpntrpiled servp drives A new approach is presented tp deal with this issue, namely "the evact cpntrol signal model estimation method" Base on Newton-Raphson iterative method, simulation of this approach is conducted, their demerits and merits are compared in detail U IS concluded that the improved estimatipn model, when providing good initial iteration values, shows the exact simulation of the nonlinear kinematics of the considered parallel mampulatpr 3DOF mption platform
KEYWORDS' Marine simulation, mption platform, servo cpntrpi
I.OATVANOI
He thdng md phdng t l u thiiy l i n h i m tao ra mdt b i n sao gidng h i t budng l i i eua mdt eon t l u h i l n d^i.
Trong b i i b i o niy, kich thudc ciia budng 111 dupe thilt k l l i 4x4m v i chieu eao l i 1,95m. Khdi lupng dii t l i ciia budng l i i kholng 1.500kg. Bin dieu khien, d c t h i l t bj nhu Radar/ARPA, ECDIS, Conning... v i ndi t h l t khie cung dupe trang bi. Budng l i i dupe g i n t r l n mdt s i n ehuyin ddng trong ba b i c t u do. Sin chuyen ddng dupe t h i l t k l t r l n nguyen t i c ciia Stewart platform. Thuc t l , vile ifng dung md hinh chuyen ddng ciia Stew/art platform cho d c he md phdng phUPng t i l n GTVT nhU m i y bay, t i u thiiy, d to.., rat da dang va phong phii. Trong cdng trinh niy, t i c g i l hudng den md hinh ba bic t u do k i l u d i l u khiln ba true song song dUa t r l n chuyin dpng quay ciia ddng CO servo vdi he tay quay ndi khdp tay ddn trung gian nhU Hinh 2.1b. Cd nhilu cdng trinh nghiin cifu xoay quanh k i l u d u triic tUong t u nay nhu eic edng trinh (1,3,4,5]
nghien cdu v l ddng hpc ngupc, thuan dang ba piston, cdng trinh [3J nghien cdu v l d i l u khiln dpng lUe hpc.
Tuy nhiln, chi cd d c cdng trinh [4,5] nghien ciru c l u true gidng vdl eau true ciia b i i b l o d l xuat. Cic cdng trinh niy deu cho phep tinh toan g i n dung gdc quay ddng CO servo o^, do dd khi dao ddng ciia m i t san md phdng kholng ±15^ g i n gidng thuc t l chuyin dpng eiia mdt eon t l u thi sai sd d i n 5%. D i l u n i y l i m g i l m tinh chinh xic trong md phdng ehuyen ddng tau thuy. Bii b i o s i t i p trung v i o vilc xay dUng each tinh chinh xle d l d i p dng eho md hinh d i l u khiln sau niy, ddng thdi t i l n h i n h d c md phdng de d i n h gia sai so dua tren md hinh ddng hpc t h u i n sd dung phuong p h i p Newton-Raphson.
2. MO HlNH MO P H O N G CHUYEN O O N G T A U THUYBABACTUDO
Mo hinh chuyin ddng Crng dung cho he thdng md phdng cabine budng III t i u thiiy dUpe d l xuit cd danq ba ble t u do t r l n cO sd c l u true cda Stewart platform Tuy nhiln, eO clu truyin ddng phd b i l n hien nay ciia d u triie n i y la dCing he d i n ddng k i l u piston ehuyin ddno t h i n g thdng qua true vit vd tan ndi true vdi ddng cothiiv luc, khf n l n hoic ddng co dien servo. Trong b i i b i o n i v
no
KHOA HOC CONG NGHE
S6 tX>/2026 t i c g i l nghiin cdu d u true cd dieu chinh, trong do 3 true
song thay b i n g 3 tay ddn dupe ndi khdp vdi 3 tay quay t n j y i n d^ng bdi 3 dpng cO servo nhu Hinh 2. /. Nhu vay, tin hilu d i l u khiln true t i l p chuyin ddng ciia sin cabine I I g i l tri gdc eua 3 tay quay: g = [«! az "i V. {!)
a) - Mil sin digin cabine buong Hi. b) - Khung tam giac truyin dpng t^nh 2.1: Hd hinh m6 phdng chuyin d^ng 3 b^c tudo sddung
ddng ca servo
Clu true hinh hpc ciJa md hinh n i y the h i l n d Hinh 2.2a, trong dd P,, P^, P, l i ba tren mat sin di ddng ndi khdp vdi d n h tay ddn; B,, B^, Bj l i 3 diem t i m true quay eua h i servo/hdp sd t r l n m i t sin ed dinh A^, A^, A^ l i ba k h i ^ ndi gida cinh tay ddn b v i a tay quay. Hai tam gilc d i u P,, P^, Pj v l B,, BJ, BJ ed kieh thudc b i n g nhau vdi dp dii mdi canh l i L = 1.255mm. d vi tri ban dau, mat sin dl d(^ng {P,, P^, Pj) cleh m i t sin cd dinh {B,, B^, B^} I I h^ = 458mm. Cabine budng III Hinh 2. la d i t cich mat san di dpng {P,, Pj, Pj) Hinh 2.lb 6 dp eao l i hQ= 458mm. Oilu ki|n v l kfch thude ciia 3 thdng sd a, b, h nhu sau:
b; = a_. + ftf, APrb = SOOmm; B/^=a = ZOhmm; 0^0 = h^
Hinh 2.2: a) Sa do hinh hoc cua md hinh 3D0F; b) Tay quay va tay ddn aia mot true
H I true g i n cd dinh t r l n mat phlng sin di ddng (P,, Py Pj) cd d c true X, y, z nhu t r l n Hinh 2.2. Vdi mat p h l n g niy c6 3 ehuyin ddng dupe tao ra bao gdm: ehuyen ddng quay quanh true y (lie ngang) l i (P; ehuyen ddng quay quanh true x (lie dpc) la 9 v l chuyin ddng trucrt dpe theo true t h i n g diimg l i z. Nhu viy, ta cd trang t h i i cua sin cd dang nhu sau:^ = [0 9 z ]^. De cd dupe vi tri ciia m i t sin di ddng theo vi tri cua t i u md phdng ta p h l i ehuyen ddi 3 true toa dp v l h i true tpa dp g i n t r l n mat sin cd djnh (B,, B^ B^) b i n g eic ma t r i n chuyin doi trye tpa d0.Theo t l i lieu [2] v l dpng lue hpc eua t i u ta cd hai ehuyin ddi chuyen ddng lie ngang 0 v i lie dpc 6 cua t i u theo t i m quay vcri hai phuong trinh ma t r i n quay I I [2} nhu sau:
T; K [COS cost 0 -sin sin Ip 0 1 0 slnsinip 0 cos cos ip ], T^ = 11000 cos cos $ - smsineO sinsme coi,
Tif [2] ta dupe ma t r i n chuyen ddi l i tfch TTp. Vdi g i l t h i l t ring, cabine budng l i i d i t ngay tai t i m quay ciia sin v l cich m i t sin mdt kholng each la h„= 0 .Ta cd tpa (2)
(3) dp cua ba d i l m P t r l n mat sin di ddng tai vi tn ban d i u :
'•izifO) = | i - ^ 0 ^ ^ - - ^ A„ ^ h« j
K i t hpp [2] v l [31 ta dUoc toa dp ciia ba d i l m t r l n m i t sin di ddng theo tpa dp ciia true t r l n m i t sin ed dinh s i I I TTp P.JiO). Chuyen ddi true thd ba chi l i trUot dpc theo true z , n l n ta ehi d n t h i m v i o tpa dp z eiia ba diem mdt gia tri nhu nhau z, l i thda man.
3. MO HlNH O O N G H O C N G U O C X A C DINH G O C QUAY D O N G CO SERVO
Md hinh hdng hpc ngupe rat quan trpng cho b i i t o l n d i l u khien 64 xac dinh gdc quay ciia mot trye dpng CO aji = 1,2.3) tif d d lieu dp nghiing, dp lie va dp cao tuong ddi tir md hinh md phdng 3D ciia con t i u I I vector T). Vdi dp cao ban d i u eiia t i m sin di ddng so vdi sin ed djnh I I h^ do dd, tam 0 eua sin cd cao do l i z, =h +z v l cd tpa dp: 0 = [OOhz -i-z]' trong mat phing c6 dinh. Kit hop vdi cle p h i p b i l n ddi true d i thuc h i l n d mue 2 ta dupc tpa dd cie diem P^^ s i cd dang nhu [4] sau day:
Phuang trinh [4] eho ta tpa dp eiia ba d i l m t r l n m i t sin di dpng k i t ndi khdp vdl ba thanh truyin ddng ehinh l i sin cabine budng Hi khi con t i u md phdng d mdt vj tri l i l n quan d i n toa dd ed i^nh. De tinh t o i n gdc quay d n thiet trong cdng thdc [1] ciia trye d i u ra ddng eO servo ta d n d c g i l tri z ciia ba d i l m k i t ndi n i y l i h i n g cudi ciing ciia ma t r i n [4]. Theo edng trinh [5] ta cd gdc quay ciia mdi true duoc tinh x I p xl nhu sau:
« - ( _ ^ ) _ ,3, Tuy nhiln, do cle han e h i ciia [3] nhu phan d i t v$n 64 d i n l u ra, phan t i l p theo ta se di tim mdt cdng thdc tinh t o i n a^ ehinh xic hon. TrUdc t i l n , t i / Hinh 2.2b ta cd toa dp diem B^ eua m i t san ed djnh v i diem A l i khdp ndi b i n l l dau true nhu [6] dudi day:
Bilt dupc tpa dp i^em P, tCr [41 v i B, tif [6] ta se tinh dupc dp d i i eie canh O^P v l BP,. Ap dyng dinh ly ham sd cos vdi eac tam gilc O^B P va B P A^ ta tinh dUpc cle gdc 6,f 6j. Td dd, ta tinh dupe chi'nh xie gdc a, nhu phuang trinh [7] sau diy:
Trong do:
- M ,
-;-(--J^)'-
m
. (8)
4 . K I £ M CHCTNG B A N G MO H I N H D O N G H O C T H U A N Xay dang mo hinh dong hoc thuan giup ta x^c dinh di/oc do nghieng, do 15c va do cao tuong doi thuc cua chuyen dong mo hinh t i / goc quay cua ba dong co a de
111
KHOA HOC CONG NGHE
so sinh vdi dCr l i l u dd nghting, do lie v i dd cao tir md phdng 3D l i vector r j . 04 xiy dung md hinh ddng hpe t h u i n ta sifdung phuong phap Newton-Raphson. Dd d i i A P = b, tir tpa dd eua A va P trong [4,61 ta tinh dUoe | AP p
= b ' v i d i t h i m f, cd dang l i f = [f,f f ] , trong dd cie an 0.
6, z I I chua bilt:
h = («^ -':»,)' * (>», - y*.y + ( f , - 'A.y - "* (9) Bdi vi f chifa nhilu hon mpt b i l n , dao h i m cua h i m f dupe sd dyng trong phuong p h i p Newrton-Raphson duoc tim b i n g cich lly dao h i m rieng cho moi b i l n ciia /]. J l i ma tran jacopian ciia ham f vdi b i l n rj dupe tinh nhu(10] dudi d i y :
•-s
'•I dii,Kl) la# dB »z d^ de ai a* OB dzl' '''""* ( 1 0 ) = 1.2,3 , Tddd. d e an sd trong q se dUpc tinh theo phucmg trinh:
!,"• = 5" - [/ [n")] ' f_{'f); vdi d i l u kien dau !!" = l*o"" ^n l'^.
Kit q u i thu duoe cua t h u l t gili lap n i y l i dii ehinh xac khi tham so dinh nghia dp chinh xie £ phli duoc xle djnh trude dii nhd: |/, [ri)\ < c Td [9,10) eudi eung ta cd luu dd t h u i t t o i n n h u H f n h 5 . r o ,
S.K^TQUAMOPHONG
Cic md phdng duoc thue h i l n bao gom d c kich b i n chi cd lie ngang, chi cd lie dpe, ehi ed truat t h i n g dimg v l chuyin ddng hdn hop (Hinh 5. lb). CIc tin h i l u d i p dng bao gdm ba gdc quay a, eiia ba servo (alphal, alpha2, alphaB); cie tin hieu dau v i o nhan duac tir p h i n md phdng 3D ciia t i u bao gdm ba chuyin ddng (roll,pitch,heave); eic sai l|ch gida tin hilu d i u v i o v i tin hi|u sau md hinh "Forward Model' (sum!, sum2, sum3) (Hin/J5.2a,6.c,d;
Hin/i S. l:a)- Thu^t toin Newton-Raphson; b) -So doi hi thong trin HatiabySimulink
dphdng
Hinh 5.2: Kit qui md phing khi: a) Chlcd lie ngang (9-rott):
b) Chi cd lie dqc (B-pltch); c) Chi cd trvpt dpc trye thing ddng (z-heave) vi d) Chuyin d6ng hSn hgp Vdi £ = W^ va chpn g i l trj l i p ban d i u 5° = [o o o T tif d e k i t q u i md phdng (Hinh 5.2a,b,c,d) ta t h i y sai sd vdl md hinh mdi n i y khdng vuot q u i 0,18717,5° = 1%, ddng thdi ta eung rut ra mpt k i t luan quan trpng cho kholng g i i tri gdc quay tdi Uu d l d i l u khien servo cdn n i m trong vung t u y l n tinh l i a, = ± 70° limg vdi gidi han eic ehuyin dpng roll: ±17.5", pitch: +15°, heave: ±190mm.
6. K^T L U A N
Cic k i t q u i md phdng trong myc 5 cho t h i y dd chinh xic khi lUa chon md hinh tin h i l u dieu khien phii hop, d i l u niy gdp p h i n v i o n h i l m vu p h i n i n h sU trung thuc trong md phdng ehuyin ddng eua con t i u , tao d m giae t h i t eho ngudi dupe huan luyen.Tuy nhien, phuong trinh [7,8] de tinh t o i n gdc a ciing phdc tap hon so vdi cic cdng trinh khic, d i l u n i y cd t h i dan d i n suy giim tinh thdi gian thUc eiia he thdng md phdng 3D. Vile d i n h g i i t i l u chi niy l i l n quan den q u i trinh tdng hpp t h u i t t o i n v i lUa chpn bd d i u k h i n ddng eO servo n l n d n p h i i nghiin cdu nd trong mdt edng trinh khie.
Tai lieu tham k h i o
[1]. Derek K. Brecht (2015), A 3-DOF Stewart Platform for Trenchless Pipeline Rehabilitation, Electronic Thesis and 0/sserfo(ion,The University of Vi/estern Ontario.
[2]. Thor I. Fossen (2002), Marine control systems - Guidance and Control of Ship, Rigs, Undenvater Vehicles, Marine Cydemet/cs, Trondheim, Norway.
[3]. Shailendra Shisode, Ganesh Shrigandhi (201A Design and Simulation of 3Degree of Freedom (DOT) Matbn Platform. International Journal of Curent Engineering and Technology.
[4] Xiaoyong Wu, Zhijlang Xie {2019), Fonfi/ard kinematics analysis ofa navel 3-DOF parallel manipulator.Sc^e^\t\a\ran\ca [5]. Webjom Rekdalsbakken (2015), Design and Apf^ication of a Motion Platform for a High-Speed Craft Simulator, IEEE Xplore.
Ngiy nhin b i i : 25/4/2020 Ngiy chip nhin d i n g : 11/5/2020 NgUdi phin biln: PGS.TS.Trin Anh DQng
PGS.TS.Olo Minh Quin
