SU'DUNG BO DIEU KHIfiN GIAM SAT Md S O M PHA TRONG MIEN TlTONG Tir DIEU KHIEN PHI TUYEN HE THONG NANG
VAT TRONG TU" TRITONG
re. Nguyin Hm Chan Thanh Khoa Dien - Dien lir vien thong Tom tdt: Bai bao trinh bay rngt bo dieu khien ma luang tit ap dung dieu khien he ndng vat Irong tit trttdng. He nang vgt trong lir trudng la he thong phi tuyen vd phitc tgp, nen rdl khd mo hinh hoa bai cac phuang Irinh todn hoc chinh xdc. Nhdm cai thien dac tinh dieu khien, bai bao sir dung mot bg diiu khien gidm sdt ma sam pha trong mien tttang lu, kel qud dieu khien duac mo phdng vai MATLAB- SIMULINK vd dp dimg vdo he thong thttc vai gidi thuat dieu khien duac nhung vao vi dieu khiin PIC I8F4550.
Abstract: This paper presents an analog fuzzy logic based controller applied to a magnetic levitation system. This system is nonlinear and complex, so it is difficult lo obtain exact mathematical model. To improve control performance, an analog fuzzy supervisory lead phase controller has been used. The proposed controllers for magnetic levitation system is simulated by using MATLAB- SIMULINK and implemented on an experimental system using a PIC I8F4550 microcontroller.
Keywords: Magnetic levitation system, phase lead compensation, analog fuzzy supervisory control.
1. Gioi thieu
He thong nang tir truong dugc ling dyng rgng rai trong cong nghiep nhu nang tir truong trong he thong xe lua dien sieu tic, che t^o bac dan khong ma sat, va ban dao dgng each ly trong cong nghi$p san xult ban dan... He thing nang bjng tit truong (MLS) la h? thing phi niyin va vong hg khong I n djnh, do do he MLS la h^ thing ly tuong dl kilm nghiem cac thujt toan dilu khiln phi hiyen khac nhau.
Trong nhimg nam gin day, biln h o dieu khien s i (DCP) da dugc nghien cuu va san xuat rgng rSi. Kit hgp DCP va vi dilu khien se cung d p cho chung ta giai phap re tien va linh hoat d l dilu khiln cac h$ thing tuong HI ma khong cin phai chuyln dli sang mien thoi gian roi rac, cung nhu khong cin sir dtmg cac bo dilu khiln xii ly tin hieu s i gia thanh cao.
Qua tiinh thilt kl mang tinh moi va dgn gian dua ti^n phuong phap In dinh blng bg bil sdm pha dugc gidi thi?u tt-gng bai bao niy. Bg dieu khiln nay rlt dl dang hieu chinh tham chi khi cac thong s6 he thing khong dugc bilt chinh xac. Bai bao tiip trung phan tich h? thing trong miln thoi gian lien ttie va thiet ke bg dilu khiln giam sat mg
Cong hien khac cua bai bao la thilt kl he nhung dua tren vi dilu khiln PIC 18F4550 the hien thu$t toan dilu khiln, giiip cho he MLS co thi ho^t dong dgc lap.
2. Ket cau vd mo hinh toan hgc ciia he M L S
il. Ket c l u ciia he M L S Kit clu vat ly e i a he MLS dugc thi hi$n trong hinh 1 va so d l khii giai thich bp dieu khien giam sat mg sgm pha trong miln tuong tu dugc cung d p a hmh 2. Dli tugng nang la vien bi kim loai co trgng lugng 35.2901 gram, bg khung cua h$ thing lam bang go.
Nhu hinh 1 t h i hien, mgt c j p LED phat v4 thu hong ngoji dugc sii dung d l cam nh jn s.\f thay d l i vi h-i e i a vien bi quanh dilm can bang. Tin hieu tuong iing 6 ngo ra nlm trong khoang 8.5 din 9.3V, phu thuoc vao cuong do anh sang ma LED thu hong ngoJli nhan dugc. Khi dinh cua vien bi nSm chinh xac ngay tam cua LED thu, dien ap ngO ra ciia sensor la 8.9V. Khoang each tit cue tit din dinh vien bi la 4mm, dong dien d n thilt dl can bang voi trgng lire la 1.023A.
Chi tilt he thing dilu khiln h$ MLS va phan hoi dO li$u v l may tinh hiln thi dugc the hien o hinh 3. Thong s i vat ly h? thing
Bang 1. Thong s6 vat ly ciia he thdng thirc Symbol Description Value Unit
(a)
Hinh 1. Mo hinh Ihifc te h4 MLS (a) He cdn bdng khi khdng co nliieu tdc dgng
(b) H4 cdn bdng khi co nhieu tdc dong
lef X
1
Fuzzy Supenisory
y • Gr(s)
>
G(slI-I -
1 ^
! • • . . — =
X . m R L Io
p
y g
Nominal operation position Mass of metal ball
Coil's resistance Coil's inductance Nominal operation
current Voltage to ampere convert coefficient Meter to voltage convert coefficient Gravity acceleration
4 35.2901
5.2 0.02045
1.023 0.55 24.55 9.8
mm gram
n
H A A/V
V/m m/s'
Ka qua di^u khi^n dugc giri lai MATLAB SIMULINK dk quan sat thong qua card DAC NI USB 6008. Tin hieu tuong tu cua Xo va X cung cap true tiep den ngo vao tuomg tu ciia USB 6008.
b. Mo hinh toan hQC cua he MLS TiJ hinh 4 phuong trinh can bang lire tu va trpng lire [6] mo ta chuyen dong eua vien bi theo dinh luat 2 Newton :
ElttnoimtKti
Hmh 2. Sa dd khdi he thing dieu khien hi MLS He thdng di6u khiln sir dung PIC 18F4550, PIC doe gia hi vj tri tham chi6u Xo va vi tri hien tai ciia vien bi X, sau do thuc hien thu^t giai di8u khien tinh toan thong s6 R ciia m^eh bii som pha, cung cap cho bien tra s6 thong qua kenh giao ti8p SPL Thai gian l4y miu ciia he dieu khien duoc chgn la 1ms.
= mg-F = mg-C- (1) Hinh 4. Mo hinh cdn bang l^rc cua he MLS
m—r = d'x dt-
Vai m la khoi lugng vien bi, g la gia toe trgng truong, x la khoang each giiia vien bi va cue tir, i la dong dien trong cuon day va C la hSng so lire :
C = mg (2)
Hmh 3. Chi tiit hi thong diiu khien hi MLS
Xo la vi tri can bang mong mu6n, Io la dong dien can thiet tao ra lire tir can bing trpng lire, tuong ung voi Xo.
Ap dung khai trien Taylor mo rgng [5]
cho lire F tai (Xo, Io):
65
(3)
F = cJ^Ax-X„)Ai-h)
xl dt dl + high _ order _ terms
+ high _ order __ terms B6 qua cac thanh phan bac cao vi gia tri chiing rdt nho, k6t hgp (1) (2) \h (3):
$ . | ( . - ^ ) - ^ , i - . „ ,
(4) Vj tri vien bi dugc phan hoi boi dien ap cua LED thu hong ngoai:K^., = -r(.^-Xo) (5)
H? so tuyen tinh chuyen doi vi tri va di?n ap xap xi boi -y (volt/m).
<^ l^K,^ =-y'^ (6) Moi quan he giira dien ap dieu khien va
dong di?n qua cuon day theo he thiic :
i = Pu + Ia (7) Voi P (ampere/volt) la he s i chuyln
doi di?n ap sang dong dien.
<=> Al = fiAu (8) Kit hgp (4) (6) va (8) :
r rx„ '^ i„
o A l ' = ^ A K + y 5 ^ A i ,
Xo I„ 0)
Ham truyin tuyln tinh he MLS thu dugc khi chuyln dli Laplace phuong trinh (9):
GW = -
AM(i) (10)
Voi:
Tir (10) va thong s i vat ly ciia he MLS
-Pi = ^0 = = 70 (11) 3. T h i l t ke b o diia k h i l n on dinh he M L S
a. Tai vi tri co dinh Xo=4mm Phuong trinh (11) the hien he MLS co 1 cue on djnh va 1 cue khong on djnh, do do he MLS khong the can bang khi thay dli dp Igi ciia h$. Cach dgn gian de giOp he MLS can bang la su dung bg dieu khien bii som pha keo quy tich nghiem ve mien trai mat phang phiic. Zero ciia bg bii sgm pha dugc thilt ke nam giiia cue dau tien ben trai mat phang phiic va ggc tga do. Cue ciia bg bit dugc thiet kS nam sSu ve mien trai mat phing phiic, giiip giam toi thieu su dnh huong ciia cue bg bil sgm pha vao quy tich nghiem toan he thong.
Ham truyen cua bg dieu khien bii sgm p h a :
Gc(^) = K, " 1 ' / ^ (0<a<l) (12) s + l/(aT)
Thanh phan 1/T trong phuong trinh (12) dugc chgn blng 66.67. Ap dyng dinh luat Thumb, thanh phln l/(aT) xIp xi 10 lan thanh phln 1/T. Tir thong s6 he thing thirc o bang 1, thong so thiet ke cua a va T lln lugt la 0.1007 va 0.015. D l tinh toan Kc, d n su dung tieu chuan on dinh Rooth-Hurwitz kilm tra ham truyin vong kin trong hinh 2 nhu sau:
l + G(i)Gc(j) = l + - r^c s + i / r (13) i -io„ s + l/(aT) Hiln nhien, he thing I n dinh khi Kc>0.
Dieu nay the hien he MLS co thi can blng voi bit ky trgng lugng vien bi khac. Trong he thing MLS thuc t l , Kc duoc thilt k l blng 206.55.
Boi vi mo hinh toan hgc chi la xip xi tuyen tinh cua he phi tuyln, rlt kho ap dung cae ly thuyit In dinh tuyln tinh vao he MLS, dan din he khong t h i can blng. D l he dilu khien dat dugc tinh b i n vihig khi mo hinh toan hgc khong chinh xac tuy?t d l i , zerg cua bg bil som pha dugc thilt k l blng -66.67,
dugc thilt k l x i p xi voi gia hi la 666.7.
Jii hinh 5a, bg dieu khien bu som pha CO the keo quy dao nghiem chua bu trong mien phai mat phing phuc v l miln trai, dilu n4y chi ro he MLS djlt dugc su can blng.
b . T a i vj tri Xo thay d l i
He MLS la h$ phi tuyln do dac tinh ciia luc tir. Bg dilu khiln bit som pha 6 phln 3a chi I n dinh dugc khi vi tri tham chilu ciia vien bi c6 dinh. N l u trgng lugng vien bi hoac vi tri tham chilu thay d l i he MLS se roi vag
trang thai bit In dinh nhu hinh (5b) vgi Xo=5mm va lo=1.445A.
Be he MLS co the can blng trgng day rgng cua vi tri viSn bi, bai bao su dung bo dilu khiln giam sat mg som pha trong miln tuong tu nhu hinh 6.
Tir hlnh (6), neu gia tri ciia RMCP4IIOO va RMCP4IOIO thay d o i ; T, a va Kc cua bg dieu khien bii som pha se thay d l i tucmg ling:
^ ' - < 1
•'^i •'"•"Mcpaiioo • ' • - ' 4
( « 1 + liMCpti] \oo)-C (14) Kr=l-i-
li^+K
i:
(b)
Hinh 5. Quy tich nghiem cua he MLS khi dieu khien bdng bg bu sdm pha
(a) Xd=4mmvdld-}.023A (b) Xd=5mmvdld-I.445A
-*• PIC1SF45;0 ! RZZV Sl,TEH\ 1S0R^
A...
« ; *"" ;
7 7<
• • '^-.™:
: ' • ] «
Hmh 6. BQ diiu khiin gidm sal md s&m pha trong mien tucmg tu
Tap mo dugc dinh nghia : X^ = {5mm,4.5mm,4mm} = {L,M,H) X = {5mm,4.5mm,4mm} = {L,M,H}
R^p,^^^={50K,6^K,15K,%%K,\00K}
R^p^^^^ = {\K,\.2K,\.4K,\.eK,\.%K}
Lugng tir hoa mo the hien trong hinh (7) va lu3t hgp thanh m o dugc cung cap trong bang (2).
Ket qua mo phong ap dung bg dieu khien giam sat m o som pha trong mien tuang tu vao he MLS the hien trong hinh (8).
Khi vi tri tham chieu Xo thay doi trong khoang [4mm, 5mm], vi tri vien bi X thay doi tuong ung voi gia tri tham chieu. Bg dieu khien giam sat mo som pha co the giii:
he MLS on dinh khi vi tri tham chieu thay doi.
50K 68K 75K 88K lOOK RMCPIIIM IK 1.2K 1.4K 1.6K I.8K RMCPJIOIO
(b)
Hmh 7. Lugng tu hoa md su dung hdm thuoc tinh tam gidc
(a) Md hda vi tri vien bi X vd vi tri tham chieu Xo
(b) Md hda gid tri dien trd cua DCP RMCP^IIOO vd DCP RMCP4IOIO
67
Hinh 8. Kit qud mo phong h? MLS vai bg diiu khien gidm sdt md sam pha Bdng 2. LuathcfpthanhinacuaRMCp4itoo vaRwcp^ioii
R M C P 4 1 100.
R M C P 4 I 0 I 1 )
X H M L
Xo H M7JKi t*! 4K MBBK. M I 2 K tllOOK. f^lK
M M6!(K> ^ 1 6K M7JKi 1^1 JK M88K. Ml 2H
L MiOK' Ml 8K H6aK7 Ml 6K M75K» Ml4K
x« 1.
0.1007
Kc
(a)
\tr~-^^^ ^ ^ > . v . » ~ ' — ~ . i - -
• ' • • ' • • -
\.——"-rrv>r-•;-:••.. j
itfc..
-. ^ TlV'|i''f«iy-1(b)
4. K^t qua di^u khiln th^c te Ket qua dieu khien th\rc te the hi?n o hlnh (9) chiing to bo dieu khien giam sat mo som pha trong mien tuong tu co kha nang giii can bang va duy tri vi tri vien bi nhu hinh (9a), thgm chi voi su tac dgng nhieu loan nhu hinh (9b).
Bg digu khien da the hi?n tinh b^n viing khi dieu khien h? MLS khi vj tri tham chi6u vien bi thay doi trong khoang 4mm den 5mm nhu hlnh {9c).
Thong so kinh nghiem tir di6u khiln m6 hinh Ihi^c dugc cung cSp trong bang (3).
5. K^tluan
Dong gop chinh cua bai bao la t h i a kg mgt bg dieu khiSn giam sat mo s6m pha trong mi8n tuong tu co kha nang di6u chinh thong s6 d i k khiSn T, a va Kc giup he thich nghi khi trgng lugng hoac vi tri tham chiSu thay doi.
Ket qua cua bai bao nay co thg phuc vu cho cac nghien cihi lien quan Uong tuong lai, hay su dyng cho cac huong dan hoc thuat]
truyen cam hung khoa hgc va giai tri.
Bing 3. Cac thong s6 kinh nghi?m
(c)
Hmh 9. Kit qud dieu khien tren md hinh MLS phdn hdi ve MATLAB Simulink (a) Can bdng lai vi tri tham chiiu Xg=4mm (b) Cdn bang tai vi tri (ham chieu Xo=4mm vdi nhieu loan tdc dgng lai thdi diem 0.6s (c) Cdn bdng khi vi tri tham chieu Xg thay doi
tir 4mm den 5mm Tai lieu tham khao:
[1] Li, J.-H, "Fuzzy Supervisory Control Of A DSP-Based Magnetic Levitation System," Proceeding of the 4?"' IEEE conference on decision and control, Mexico, pp. 2606 - 2611, 2008.
[2] Li, J.-H, "An Undergraduate Digital Control Project: A Digital Signal Processor (DSP)-Based Magnetic Levitation System,"
World Transactions On Engineering And Technology Education, vol. 5, No. 1, pp.
207-210, March 2006.
[3] Li, J.-H, "DSP-Based Control Of A PWM-driven Magnetic Levitation System,"
IEEE ICSS Intemational Conference On System And Signals, pp. 483-487, 2005.
Ng^y nh$n b^i: 15/12/2013 Ngiy ch^p nhSn dang: 31/12/2013 Phan bien: TS. Vo Cong Phinmg
