cach su dung matlab

Th.s. NGUYN CH NGN

Th nghim CAD(Computer-Aided Design)c bin son trong khun kh d n ASVIET002CNTT Tng cng hiu qu o to v nng lc t o to ca sinh vin khoa Cng ngh Thng tin - i hc Cn th

I HC CN TH - 12/2003

Gio trnh th nghim CAD

Li ni uCng vi s pht trin nhanh chng ca my tnh, CAD (Computer-Aided Desgin) c xy dng ngy cng hon thin v ng dng trong hu ht cc lnh vc khoa hc k thut. i vi chuyn ngnh in t, nhiu phn mm CAD cho php thit k mch, m phng v v mch in mt cch nhanh chng v hiu qu nh OrCAD/Pspice, Multisim (Electronics WorkBench), MicroSim, ExpeditionPCB, Tuy nhin, y l cc phn mm ng gi ch c ng dng trong chuyn mn hp l in t, n khng cho php lp trnh m phng cc h thng ng (Dynamic systems) bt k khc. V vy, chng trnh o to mn CAD cho sinh vin in t chuyn ngnh Vin thng v T ng ha hng ti phn mm Matlab. y l mt ngn ng lp trnh cp cao dng ngun m, n h tr rt nhiu th vin chc nng chuyn bit t Ton hc, Kinh t, Logic m, Truyn thng, iu khin t ng, n iu khin phn cng cho cc thit b. ng thi, n cho php ngi s dng b sung cc cng c t to lm phong ph thm kh nng phn tch, thit k v m phng cc h thng ng lin tc v ri rc, tuyn tnh v phi tuyn bt k. Vi nhng u im ni bc ca mnh, Matlab c nhiu trng i hc hng u trn th gii p dng v ging dy. Tham vng th nhiu nhng trong phm vi 30 tit thc hnh, chng ta ch c th cp n nhng vn c bn nht. Hy vng t sinh vin t nghin cu, hc hi c th thit k v m phng cc m hnh H thng Vin thng hay cc H iu khin t ng. ng thi cng nm s lc v cc phn mm m phng mch v v mch in nh Multisim, OrCad, Gio trnh ny gm 7 bi, mi bi 5 tit. Sinh vin chn 6 bi thc tp:1. Thao tc trong ca s lnh ca Matlab. 2. Hm v Script files. 3. Symbolic v Simulink. 4. M hnh h thng Vin thng. (sinh vin chuyn ngnh VT) 5. M hnh h thng iu khin t ng. (sinh vin chuyn ngnh KT) 6. To giao din trong Matlab. 7. Thit k - M phng v v mch in (cc sinh vin khng chn bi 4 hoc 5)

Mc d ht sc c gng, song do trnh hn ch ca ngi vit m nhiu vn chc cha c trnh by tt cng nh cha b cc hp l. Xin chn thnh cm n mi kin ng gp ca sinh vin v cc bn ng nghip. TcAD, thng 11 nm 2003Nguyn Ch Ngn a ch lin h:

B mn Vin thng v T ng ha Khoa Cng ngh Thng tin, i hc Cn th 01 L T Trng, Tp. Cn th, tnh Cn th Tel: (71) 831301 Fax: (71) 830841 Email: [email protected] URL: http://www.cit.ctu.edu.vn/department/ac/ncngon.html TcAD - 20032


Mc lcLi ni u Mc lc BI 1: THAO TC TRONG CA S LNH CA MATLAB 2 3 5

I. Mc tiu....................................................................................................................5 II. Tham kho...............................................................................................................5 III. Thc hnh ..............................................................................................................5 III.1 Ma trn ..........................................................................................................5 III.2 Vect .............................................................................................................6 III.3 Cc a thc....................................................................................................7 III.4 ha ...........................................................................................................7 IV. T chn................................................................................................................12 BI 2: HM V SCRIPT FILES 13 I. Mc tiu..................................................................................................................13 II. Tham kho.............................................................................................................13 III. Thc hnh ............................................................................................................13 III.1 Script files ...................................................................................................13 III.2 S dng cc hm xy dng sn...................................................................15 III.3 Xy dng hm.............................................................................................17 IV. T chn................................................................................................................21 BI 3: SYMBOLIC V SIMULINK 22 I. Mc tiu..................................................................................................................22 II. Tham kho.............................................................................................................22 III. Thc hnh ............................................................................................................22 III.1 Symbolic ......................................................................................................22 III.2 Simulink.......................................................................................................24 IV. T chn................................................................................................................30 BI 4: M HNH H THNG VIN THNG 32 I. Mc tiu..................................................................................................................32 II. Tham kho.............................................................................................................32 III. Thc hnh ............................................................................................................32 III.1 H thng thng tin lin tc (Analog Communications) ..............................34 TcAD - 20033


III.2 H thng thng tin ri rc (Digital Communications).................................36 IV. T chn................................................................................................................37 BI 5: M HNH H THNG IU KHIN T NG 38 I. Mc tiu..................................................................................................................38 II. Tham kho.............................................................................................................38 III. Thc hnh ............................................................................................................38 III.1 Hm truyn v phng trnh trng thi ca h thng ..................................39 III.2 B iu khin PID........................................................................................42 III.3 Hiu chnh thng s ca b iu khin PID ................................................45 IV. T chn................................................................................................................47 BI 6: TO GIAO DIN TRONG MATLAB 49 I. Mc tiu..................................................................................................................49 II. Tham kho.............................................................................................................49 III. Thc hnh ............................................................................................................49 IV. T chn................................................................................................................55 BI 7: THIT K M PHNG MCH V V MCH IN 57 I. Mc tiu..................................................................................................................57 II. Tham kho.............................................................................................................57 III. Thc hnh ............................................................................................................57 III.1 Multisim.......................................................................................................57 III.2 OrCAD.........................................................................................................59 IV. T chn................................................................................................................64

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BI 1 THAO TC TRONG CA S LNH CA MATLABI. Mc tiuBi th nghim ny gip sinh vin lm quen nhanh vi Matlab 6.5 bng cc thao tc n gin trn ma trn, vect, biu thc ton hc, cc lnh ha, , thc hin ngay trn ca s lnh (command window) ca Matlab.

II. Tham kho[1]. Nguyn Ha Duy Khang, Bi ging mn CAD, B mn Vin thng & T ng ha, khoa Cng ngh thng tin, i hc Cn th, 2001. [2]. The Mathworks Inc., Matlab Notebook Users Guide, 2003. [3]. Nguyn Hoi Sn - Thanh Vit - Bi Xun Lm, ng dng MATLAB trong tnh ton k thut, Tp 1, NXB HQG Tp. HCM, 2000 [4]. Nguyn Hu Tnh - L Tn Hng - Phm Th Ngc Yn - Nguyn Th Lan Hng, C s Matlab & ng dng, NXB KH v K thut, 1999. [5]. http://www.facstaff.bucknell.edu/maneval/help211/exercises.html [6]. http://www.glue.umd.edu/~nsw/ench250/matlab.htm

III. Thc hnhT ca s lnh ca Matlab, sinh vin ln lt thc hin cc thao tc sau:

III.1 Ma trn to ma trn trong Matlab ta ch cn lit cc phn t ca ma trn trong cp du ngoc vung ([]). Cc phn t trn cng hng c phn bit bi du phy (,) hoc khong trng (space). Cc hng ca ma trn, phn cch nhau bi du chm phy (;). V d, nhp ma trn A c 4 hng, 4 ct nh sau:>> A=[16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1] >> size(A)

truy xut n tng phn t ca ma trn ta dng ch s phn t tng ng. V d, phn t hng th 2, ct th 3 ca A l A(2,3).>> A(2,3)

Cho ma trn A=[2 4 1; 6 7 2; 3 5 9], sinh vin dng cc lnh cn thit :a. Ly dng u tin ca ma trn A. TcAD - 20035


b. To ma trn B bng 2 dng cui cng ca A. c. Tnh tng cc phn t trn cc ct ca A. (gi : tnh tng cc phn

t trn ct 1: sum(A(:,1))). d. Tnh tng cc phn t trn cc dng ca A. Cho ma trn A=[2 7 9 7; 3 1 5 6; 8 1 2 5], sinh vin gii thch kt qu ca cc lnh sau:a. A' b. A(:,[1 4]) c. A([2 3],[3 1]) d. reshape(A,2,6) e. A(:) f. [A A(end,:)] g. A(1:3,:) h. [A ; A(1:2,:)] i. sum(A) j. sum(A') k. [ [ A ; sum(A) ] [ sum(A,2) ; sum(A(:)) ] ]

1 0 1 1 v b= 1 . Gi : x=A\b. 2 5 3 Gii h phng Ax=b, vi: A= 3 1 0 2

III.2 VectVect thc cht cng l ma trn c kch thc (n x 1) hay (1 x n), nn ta c th to ra vect nh cch to ra ma trn. Ngoi ra, c th dng mt s cch sau:>>x=0:0.1:1 >>y=linspace(1, 10, 20) % vecto 20 phan tu cach deu nhau tu 1 den 10 >>z=rand(10,1)

Cho vect x = [3 1 5 7 9 2 6], gii thch kt qu ca cc lnh sau:a. x(3) b. x(1:7) c. x(1:end) d. x(1:end-1) e. x(6:-2:1) f. x([1 6 2 1 1]) g. sum(x)

Sinh vin hy to mt vect x c 100 phn t, sao cho: TcAD - 20036


xn =

(1) n +1 . (2n 1)

Gi : To vect n c 100 phn t t 1 n 100, dng ton t du chm (.) xc nh x.

III.3 Cc a thcCc a thc trong Matlab c m t bng cc vect hng vi cc phn t ca vect chnh l cc h s ca a thc, xp theo th t s m gim dn. V d, a thc m = s4-s3+4s2-5s-1 c biu din l:>>m=[1 -1 4 5 -1]

xc nh gi tr ca a thc, ta dng lnh polyval. V d, xc nh gi tr ca a thc ti im s=2:>>polyval(m,2)

xc nh nghim ca a thc, ta dng lnh roots. V d:>>roots(m)

Cho phng trnh x2-4x+5=0, gii phng trnh theo 2 cch, cch 1 tnh delta theo phng php c in, cch 2 dng hm roots, hy so snh kt qu.a. Cch1:>>a=1; >>b=-4; >>c=5 >>x1=(-b+sqrt(b^2-4*a*c))/(2*a) >>x2=(-b-sqrt(b^2-4*a*c))/(2*a)

b. Cch 2:>>m=[a b c]; >>x=roots(m)

Hy thay i cc gi tr khc nhau ca a, b v c tng ng trong 2 cch gii trn. So snh kt qu v nhn xt.

Gii phng trnh x3- 2x2+4x+5=0. Kim chng kt qu thu c bng hm polyval. Sinh vin c nhn xt g v kt qu kim chng. Lp li cu cho phng trnh x7-2=0. Sinh vin th dng hm poly to a thc t cc nghim cho trc.>>help poly

III.4 haMatlab h tr ch ha rt mnh, bao gm ha 2D v 3D, vi cc trc ta tuyn tnh v phi tuyn bt k.

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III.4.1. ha 2 D ha 2D ch yu da trn lnh plot. c gip , ta g:>>help plot

V th hm s y1=sinx.cos2x v hm s y2=sinx2 trong [0-2], trn cng h trc ta , ta ln lt thc hin nh sau:>>x=0:0.01:2*pi; >>y1=sin(x).*cos(2*x); >>plot(x,y1) >>grid on %hien thi luoi %nhan tuong tung tung phan tu

Sau khi thu c th hm y1, v y2 trn cng th, ta thc hin:>>hold on >>y2=sin(x.^2); >>plot(x,y2,k) >>axis([0 4*pi 1.25 1.25]) %giu hinh, mac nhien la hold off %luy thua tung phan tu %duong ve co mau den %dinh lai toa do hien thi

Ta c th t nhn cho cc trc cng nh tiu cho th:>>xlabel(Time) >>ylabel(Amplitude) >>title(y1=sinx.cos2x and y2=sin(x^2)) >>legend(sinx.cos2x,sinx^2)y1=sinx.cos2x and y2=sinx 2 1 0.5 Amplitude 0 -0.5 -1 0 1 2 3 Time 4 5 6 sinx.cos2x sinx 2

Hnh 1.1 Biu din th cc hm s trn cng h trc ta

Matlab h tr rt nhiu thuc tnh ha, c th kim sot cc thuc tnh ny ta cn dng n th ha. V d:>>close all >>x=[0 1 2 3]; >>y=[0 4 1 5]; >>h=plot(x,y)

h chnh l th ha ca hm plot, thy cc thuc tnh ho, ta dng lnh:

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>>set(h)

By gi ta th t mt s thuc tnh ha cho h.>>set(h,Color, r) >>set(h,'LineWidth',6) >>set(h,'Marker','v','MarkerSize',6)5 4 3 2 1 0 0 0.5 1 1.5 2 2.5 3

%dat lai mau do %dat do rong duong

Hnh 1.2 Thay i thuc tnh ng biu din

D liu dng v c t trong XData v YData.>> set(h,'XData',[0 1 1 3]) >>set(h,'YData',[0 3 5 1])

T kt qu ny, ta nhn thy nu d liu trong XData v YData bin thin theo thi gian, th trn ca s ha (figure) ta s thy hnh nh sinh ng kiu animation.5 4 3 2 1 0 0 0.5 1 1.5 2 2.5 3

Hnh 1.3 - Thay i d liu trong ca s ha

Tng t nh hm plot, sinh vin th dng cc hm semilogx, semilogy v loglog cho trng hp trc ta phi tuyn. Ngoi cc lnh biu din ng cong trong ta Descartes, Matlab cng h tr vic v th hm s trong h ta cc bng hm polar.>>theta=0:0.05:2*pi; >>r=sin(5*theta); >>polar(theta,r)

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Gio trnh th nghim CAD90 1

120 150 180 210 240

60 30 0 330

0.5

270

300

Hnh 1.4 Biu din th hm s trong h ta cc

III.4.2. ha 3 D Matlab cung cp nhiu hm v th 3D, chng hn: plot3 - dng v cc ng trong khng gian 3 chiu; mesh v surf - dng v vt th 3D (g help mesh v help surf bit thm cc hm 3D c lin quan). V th 3D bng hm plot3:>>t=0:pi/50:10*pi; >>x=sin(t); >>y=cos(t); >>z=t; >>subplot(121), plot3(x,y,z) >>grid on >>subplot(122), plot3(x,y,t.^2) >> grid on %ve tren o thu hai %ve tren o thu nhat

40 20 0 1 0 -1 -1 0

1000 500 0 1 0 -1 -1 0

1

1

Hnh 1.5 V th 3D bng hm plot3

V mt paraboloid z=x2+y2 trong khng gian 3 chiu:>>close all >>t=-5:0.1:5; >> [x,y]=meshgrid(t); >>z=x.^2+y.^2; >> subplot(2,2,1), mesh(z) TcAD - 2003

%dinh luoi ve

%ve mat luoi 3D10


>> title('mesh(z)') >> subplot(2,2,2), meshc(z) >> title('meshc(z)') >> subplot(2,2,3), meshz(z) >> title('meshz(z)') >> subplot(2,2,4), waterfall(z) %chi ve luoi theo 1 huong >> title('waterfall(z)') %co them luoi tren mat x,y %giong mesh nhung co them duong vien

Hnh 1.6 - V mt paraboloid

V mt z =

sin x 2 + y 2 x 2 + y2

(

) trong khng gian 3 chiu:

>>x=-8:0.5:8; >>y=x; >>[x,y]=meshgrid(x,y); >>r=sqrt(x.^2+y.^2); >>z=sin(r)./r; >>surf(x,y,z)1 0.5 0 -0.5 10 0 -10 -10 0

10

Hnh 1.7 Mt biu din th 3D khc TcAD - 200311


Sinh vin th v mt tr z = x 4 + y 2 bng hm mesh v hm surf.

IV. T chnGii h phng trnh sau:2x1 + 4x2 + 6x3 x1 + 2x2 + 2x4 = 0 = 1 = 2 = 10. x3 + 2x4

2x2 + 4x3 + 2x4 3x1 x2 + 10x4

Chng t rng (A+B)C=AC+BC, vi:10 2 3 1 20 4 , B= 10 2 v C= 3 4 . A= 6 1 3 0 6 5

Sinh vin th v hnh sau (Hnh 1.8):

(Hnh 1.8)

T ca s lnh ca Matlab, nhp: demos. Chn MATLAB Graphics 3D-plots. Chy chng trnh demo ny.

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Bi 2 HM V SCRIPT FILESI. Mc tiuBi th nghim ny gip sinh vin tip cn vi k thut lp trnh trong Matlab thng qua vic s dng cc hm c sn, xy dng cc hm mi da trn cc cu trc if - for - while v tm hiu cch xy dng script files, lm c s cho vic lp trnh m phng cc h thng Vin thng v T ng cc bi sau.

II. Tham kho[1]. Nguyn Ha Duy Khang, Bi ging mn CAD, B mn Vin thng & T ng ha, khoa Cng ngh thng tin, i hc Cn th, 2001. [2]. The Mathworks Inc., Matlab Notebook Users Guide, 2003. [3]. Nguyn Cng nh, Phn tch v tng hp cc h thng iu khin bng my tnh, NXB Khoa hc v K thut, 2002. [4]. Nguyn Hu Tnh - L Tn Hng - Phm Th Ngc Yn - Nguyn Th Lan Hng, C s Matlab & ng dng, NXB KH v K thut, 1999. [5]. http://www.mines.utah.edu/gg_computer_seminar/matlab/ [6]. http://www.glue.umd.edu/~nsw/ench250/matlab.htm

III. Thc hnhHm v Script files trong Matlab u c qun l di dng cc tp tin c phn m rng .m, thng c son tho bi Matlab Editor. Khi ng Matlab Editor bng mt trong cc cch sau:1. Nhp chut vo biu tng 2. File New M-file 3. Nhp vo biu tng Matlab Editor trn desktop (nu c). trn menu bar ca ca s lnh.

Chng ta ln lt kho st qui cch xy dng cc hm v script file. Sinh vin c v thc hnh ln lt theo cc phn sau.

III.1 Script filesTp hp cc dng lnh ca Matlab c sp xp theo mt cu trc no v lu thnh file c phn m rng *.m c gi l script file (file kch bn, file chng trnh). Ta c th chy file ny t ca s lnh ging ht nh cc lnh ca Matlab. Cu trc ca mt script file nh sau:

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% -----------------------------------------------------------------------------------------% Phn vit sau du % y dng cho lnh help % Thng thng phn ny m t chc nng, cch s dng, % v d minh ha hay nhng lu c bit m tc gi mong mun tr % gip cho ngi s dng. % ----------------------------------------------------------------------------------------[global tnbin1, tnbin2, ] % Khai bo bin ton cc % (nu c) % phn trnh by cu lnh

Hy khi ng Matlab Editor v to mt script file c tn bai21.m, vi ni dung nh sau:% Doan script file nay hien thi loi chao trong 2s. Sau do % hien thi logo cua matlab mot cach sinh dong roi thoat close all % ---------------------- Tao mot cua so do hoa -------------------------------figure('Color',[0 0 0],... 'Name','Welcome to Matlab Experiments',... 'NumberTitle','off',... 'MenuBar','none'); % ----------------------- Hien thi loi chao ---------------------------------------text( 'String','Welcome to MATLAB',... 'Color',[.25 .25 .25],... 'Position',[0.01 .501],... 'Fontsize',32,... 'FontAngle','italic'); text( 'String','Welcome to MATLAB',... 'Color','w',... 'Position',[0 .5],... 'Fontsize',32,... 'FontAngle','italic'); axis off; pause(2); logospin % ---- Thoat - xoa cac bien trong workspace va dong cua so lai ----clear close TcAD - 200314

% dung trong 2 giay

% ---------------------- Hien thi logo cua Matlab ------------------------------


% ket thuc script file

Sau khi lu file ny, t ca s lnh ca Matlab, sinh vin hy nhp:>>help bai21

thi hnh script file va son, hy nhp:>>bai21

Son tho script file c tn bai22.m lp biu tng s sinh vin in T - Tin hc tt nghip ti khoa Cng ngh Thng tin, i hc Cn th t nm 1996 n 2001 vi d liu nh sau:Nm 1996 1997 1998 1999 2000 2001 K s in t 38 33 36 31 60 70 K s Tin hc 48 54 120 92 110 131

Ni dung ca script file nh sau:% % Lap bieu do tong so sinh vien Dien tu Tin hoc tot nghiep ti % Khoa Cong nghe Thong tin, Dai hoc Can tho, tu 1996-2001 % svdt=[38 33 36 31 60 70]; svth=[48 54 120 92 110 131]; nam=1996:2001; subplot(211), bar(nam,svdt); title('Sinh vien Dien tu tot nghiep tu 1996-2001'); subplot(212), bar(nam,svth); title('Sinh vien Tin hoc tot nghiep tu 1996-2001'); Colormap(cool); % % sinh vien Dien tu %sinh vien Tin hoc

Thi hnh file ny t ca s lnh. Sinh vin c th dng lnh help bar bit cc thng s ca hm ny v hiu chnh (ty thch) mt s chc nng hin th ca hm bar trong file bai22.m. Sinh vin hy to mt script file c tn bai23.m v cc th trn hnh 2.1.

III.2 S dng cc hm xy dng snMatlab h tr mt th vin hm rt phong ph, xy dng trn cc gii thut nhanh v c chnh xc cao. Ngoi cc hm c bn ca Matlab, tp hp cc hm dng gii quyt mt ng dng chuyn bit no gi

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l Toolbox, v d: X l s tn hiu (Digital Signal Processing), iu khin t ng (Control), Mng Nron nhn to (Neural networks), Sinh vin xem li gio trnh bit thm v cc hm. Ngoi ra, c th dng lnh help bit chc nng ca toolbox v hm cng nh cch thc s dng chng.help >>help control help >>help plot % chuc nang toolbox % liet ke ham cua control toolbox % chuc nang ham % chuc nang ham plot

Ta c th tm kim cc hm lin quan bng cch cung cp cho hm lookfor ca Matlab mt t kha:lookfor >>lookfor filter % tm cc hm lin quan n mch lc

(Hnh 2.1 dng cho cu III.1.3)

Hm [Y I]=max(X) cho bit phn t ln nht ca vect (mng) X vi ch s tng tng I.>>help max >> x=[1 5 9 7 6 4]; >> [y,i]=max(x) y= 9 i= 3 Ngha l phn t th i=3 ca vect x c gi tr ln nht, y=9. TcAD - 2003

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Hm Y=exp(X), tnh eX, kt qu tr v cho Y.>>help exp >>x=0:0.05:1; >>y=exp(x); >>stem(x,y) % giong ham plot nhung ve cho tin hieu roi rac

Gi s ta mun iu ch bin sng mang c truyn hai bng cnh (Double sideband transmission carrier Amplitude Modulation) vi:- Tn hiu iu ch X=0.2*sin(2*pi*t) vi t:0:0.01:10 - Tn s sng mang fc=620KHz

Sinh vin hy tm hm thch hp v v tn hiu thu c sau khi iu ch, c dng nh hnh 2.2:0.4 0.2 0 -0.2 -0.4 0 1 2 3 4 5 6 7 8 9 10

Hnh 2.2 Tn hiu thu c sau khi iu ch bin

III.3 Xy dng hmVic xy dng hm cng c thc hin tng t nh script file. Tuy nhin, i vi hm ta cn quan tm n cc tham s truyn cho hm v cc kt qu tr v sau khi thc hin. C 3 im cn lu :- Tn hm phi c t trng vi tn file lu tr. - Phi c t kha function dng u tin. - Trong mt hm c th xy dng nhiu hm con (iu ny khng c trong script file). Kt thc hm con phi c t kha end (iu ny khng cn trong hm cha).

Qui cch xy dng hm c m t nh sau:function [out1,out2,]=tenham(in1,in2,) % --------------------------------------------------------------------------------------% Phn ny s hin th khi ngi s dng dng lnh help tenham % ---------------------------------------------------------------------------------------[global ] %khai bo bin ton cc (nu c) out1=kt qu1 out2=kt qu2 TcAD - 2003

%kt qu tr v ca hm

17


% Cc hm con (nu c) [ function [subout1,subout2,]=tenhamcon(subin1,subin2,) end ] %t kha end khong can doi voi Matlab Version 6.x

Xy dng hm gptb2 gii phng trnh bc hai ax2+bx+c=0. Ni dung hm nh sau:function [x1,x2]=gptb2(a,b,c) % Giai phuong trinh bac hai ax^2+bx+c=0 % [x1,x2]=gptb2(a,b,c) % Trong do: x1,x2 nghiem thuc hoac phuc % a,b,c la 3 he so cua phuong trinh % % Vi du: [x1,x2]=gptb2(1,-3,2) % % Copyright 2003 Nguyen Chi Ngon TcAD - CIT - Cantho University % Email: [email protected] if nargin>help gptb2 >>[x1,x2]=gptb2(1,6,-7) >>[x1,x2]=gptb2(2,7,14) >>[x1,x2]=gptb2(0,4,3) >>[x1,x2]=gptb2(1,6)

Cho bit ngha ca t kha nargin? Sinh vin hy vit li hm ny kt qu ch tr v nghim s thc. Xy dng hm vdcongdb(a,m,method) v mt s ng cong c bit trong h ta cc, vi a l bn knh v m l s ng cong v trn cng trc ta . Trng hp ny hm khng tr v gi tr nn ta khng cn bin ng ra. Tu theo gi tr ca tham s method m ta v th tng ng: TcAD - 200318


Nu method = Becnulli: V ng Lemniscat Becnulli: r = a 2 cos 2 Nu method = Astroit: V ng Astroit: r = a 1 sin 3 4

Nu method = Xoanoc: V ng xon c: r = cos + 1 Ni dung hm nh sau: function vdcongdb(a,m,method) % Ve duong cong trong toa do cuc: vdcongdb(a,m,method) % method = 'Becnulli' - Ve duong Lemniscat Becnulli: % r=a*sqrt(abs(2*cos(2*theta))) % 'Astroit' - Ve duong Astroit: % r=a*sqrt(abs(1-sin(3*theta)/4)) % 'Xoanoc' - Ve duong xoan oc: % r=a*cos(theta)+1 % Voi: a-ban kinh; m-so duong cong ve tren cung he truc % Vi du: vdcongdb(0.5, 4, 'Becnulli') % % Copyright 2003 Nguyen Chi Ngon, TcAD - CIT - CTU % Email: [email protected] if nargin>help vdcongdb >>vdcongdb(1,5,Becnulli) >>vdcongdb(1,5, Astroit) >>vdcongdb(1,5,Xoanoc) >> vdcongdb(1,5,saikieu) >> vdcongdb(5,becnulli) >> .

Xy dng hm dudoan() d on kt qu sau mi ln tung mt xc xc ng nht, 6 mt. Ni dung hm nh sau:function dudoan() % Du doan ket qua sau moi lan tung ngau nhien mot xuc xac 6 mat % Chuong trinh lap lai cho den khi nguoi su dung khong doan tiep % % Copyright 2003, Nguyen Chi Ngon TcAD - CIT, Cantho University % Email: [email protected] tiep = 'y'; sai=0; dung=0; disp('Chao mung ban den voi Casino nay!') while(lower(tiep)=='y') doan=input('Moi ban du doan ket qua (1-6):'); kqua=tungxx; if (doan ~= kqua) disp('Xin loi, ban da doan sai!') sai=sai+1; else disp('Xin chuc mung!') dung=dung+1; end tiep=input('Ban muon choi tiep(''y''/''n''):'); enddisp(['Dung ' num2str(dung) ' trong tong so ' num2str(sai+dung) ' lan doan'])

% subfunction -------------function mat = tungxx() mat=floor(6*rand(1,1))+1; % end

Sinh vin th s dng hm ny v cho bit s khc nhau gia script file v hm khng c tham s vo.

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IV. T chnVit chng trnh tm nghim thc ca phng trnh bc 2. Vit chng trnh in tam gic Pascal n dng trong mn hnh ha vi n c nhp t bn phm.

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Bi 3

SYMBOLIC V SIMULINKI. Mc tiuHiu mt cch c bn v hai cng c mnh v hu hiu ca Matlab, l Symbolic v Simulink, t sinh vin c th t mnh pht huy cc chc nng cao hn ca hai cng c ny trong tnh ton v m phng h thng.

II. Tham kho[1]. The Mathworks Inc., Matlab Notebook Users Guide, 2003. [2]. Nguyn Hoi Sn - Thanh Vit - Bi Xun Lm, ng dng MATLAB trong tnh ton k thut, Tp 1, NXB HQG Tp. HCM, 2000 [3]. Nguyn Ch Ngn, Bi th nghim K thut m phng trong iu khin t ng, B mn Vin Thng & T ng ha, khoa Cng ngh thng tin, i hc Cn th, 2002. [4]. Nguyn Cng nh, Phn tch v tng hp cc h thng iu khin bng my tnh, NXB Khoa hc v K thut, 2002. [5]. http://www-h.eng.cam.ac.uk/help/tpl/programs/Matlab/Symbolic.html

III. Thc hnhSymbolic v Simulink u cha th vin chc nng rt phong ph, bi th nghim ny ch c th cp n nhng g gi l c bn nht. T , sinh vin c th t mnh nghin cu v pht trin tip.

III.1 SymbolicPhin bn mi nht ca Symbolic toolbox c Mathworks gii thiu trong Matlab 6.5 vo thng 6-2003. l mt th vin ton hc kiu k t, c pht trin t Symbolic Maple ca trng i hc Waterloo, Canada. c ci nhn tng qut v cc chc nng ca Symbolic, sinh vin hy g:>>help symbolic

Mt s hm thng dng ca Symbolic:Tn hm diff int taylor det Chc nng o hm Tch phn Khai trin Taylor nh thc ca ma trn Tn hm fourier ifourier laplace laplace Chc nng Bin i Fourier Bin i Fourier ngc Bin i Laplace Bin i Laplace ngc 22

TcAD - 2003

Gio trnh th nghim CAD numden subs dsolve solve T v mu ca phn s Thay bin sym bng tr s Gii phng trnh vi phn Gii phng trnh i s ezplot ezpolar ezmesh ezsurf V hm, plot V hm, ta cc polar V mt li mesh V mt surf

bin i mt s, mt bin hay mt i tng no thnh kiu Symbolic ta c th s dng mt trong cc cch sau:>>s=sym(A) >>x=sym(x) >>syms x y z

% khai bo kt hp x, y v z l bin symbolic

Tnh o hm bng hm diff ca symbolic: Nu S l biu thc symbolic th:diff(S) diff(S,v) diff(S,v,n) o hm ca S theo bin t do o hm ca S theo bin v o hm cp n ca S theo v.

V d: Tnh o hm ca y = sinx3.>> syms x >> y=sin(x^3); >> z=diff(y) z= 3*cos(x^3)*x^2 >>pretty(z) 3 cos(x3) x2 >>ezplot(x,y) % ve y theo xx = x, y = sin(x 3 ) 1 0.5 0 -0.5 -1 0 1 2 3 x 4 5 6 y

% khai bao x la bien kieu symbolic % dao ham cua y % sinh vien kiem tra ket qua % hien thi dang quen thuoc

Hnh 3.1 V th hm symbolic

Tnh vi phn bng hm int - Nu S l biu thc Symbolic th:int(S) tch phn khng xc nh ca S theo bin mc nhin (mun bit bin mc nhin ny ta dng hm findsym). int(S,v) tch phn khng xc nh ca S theo v. int(S,a,b) tch phn xc nh ca S trn cn [a,b] int(S,v,a,b) tch phn xc nh ca S theo v trn cn [a,b]

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V d: Tnh

2x 2 19 + 12x 2 7 x 2 + 1 dx 0

1

( (

)

)

>>syms x >>S=2*x^2*(19+12*x^2)/(7*(x^2+1)) >>y=int(S,x,0,1) % tch phn S theo x trn cn [0,1] >>subs(y) % i sang kiu s

Gii h phng trnh bng hm solve:>>help solve >>syms x y >>[x,y]= solve('x^2*sin(x^2)-3*y=7','x+y=1')

Sau khi thu c nghim x v y, sinh vin hy thay vo 2 phng trnh trn v nhn xt kt qu. V mt 3D bng hm ezsurf: V d v mt S = f ( x , y) = min xc nh: -5S=y/(1+x^2+y^2) >>ezsurf(S, [-5 5 2*pi 2*pi])

y 1+ x + y22

trn

Hnh 3.2 V th 3D cho hm s symbolic

III.2 SimulinkSimulink 5.0 (Simulation and Link - R13) c MatWorks gii thiu vo thng 6 nm 2003. N cho php phn tch, m hnh ha v m phng cc h thng ng tuyn tnh v phi tuyn, lin tc v ri rc mt cch trc quan trong mi trng giao tip ha, bng cc thao tc chut n gin. C th ni, khng tn dng c Simulink l mt thit thi ln cho ngi lm cng tc m phng! Khi ng Simulink bng mt trong cc cch sau:nhp: >>simulink TcAD - 200324


hoc nhp chut vo

trn menubar ca Matlab

Th vin simulink hin ra nh hnh 3.3: Trc tin, sinh vin hy nhp chut vo cc thanh cun ca th vin c ci nhn thn thin v simulink. T y, c th to m hnh bng simulink, hy:nhp chut vo biu tng ca th vin simulink chn: File New Model trong Menu ca th vin Simulink chn: File New Model trong ca s lnh ca Matlab

Hnh 3.3 Ca s chnh ca th vin Simulink

Hnh 3.4 Mi trng son tho ca Simulink

Ca s ny (hnh 3.4) cho php ta nhp - ko - th vo tng khi chc nng trong th vin simulink. V d, t vo y khi Sine Wave trong ca (hnh 3.5): th vin

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Hnh 3.5 Ly mt khi t th vin

Sau khi t tt c cc khi cn thit ca m hnh, ta ni chng li bng cch nhp - gi v ko mt ng t ng ra ca khi ny n ng vo ca khi khc ri th phm tri chut, mt kt ni s c thit lp. Xy dng m hnh h thng xe ti:

Hnh 3.6 M hnh xe ti dv 1 dv cho bi phng trnh: m = u bv hay = (u bv) . dt dt m

Trong m l khi lng xe, u l lc tc ng ca ng c (ng vo ca m hnh), b l h s ma st v v l vn tc t c (ng ra ca m hnh). Xut pht im ca vic xy dng cc m hnh h thng t cc phng trnh vi phn tng ng l cc khi tch phn (Integrator). Nu trong phng trnh m t h thng c vi phn bc n th ta s t vo m hnh n khi tch phn, do quan h

dt

dv

= v.

M mt ca s m hnh mi. t vo m hnh khi Integrator t th vin Continuous v k cc ng thng ni n ng vo v ng ra ca khi ny. t nhn vdot (dv/dt) cho cho ng ni n ng vo v v cho ng ni n ng ra bng cch nhp p chut ngay pha trn cc ng ny.

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T phng trnh h thng ta thy dv/dt (vdot) bng tch ca thnh phn (1/m) v thnh phn tng (u-bv), nn ta thm khi 1/m ngay trc khi tch phn:t vo khi Gain trong th vin . Nhp p chut vo khi ny thay i li thnh 1/m. t nhn inertia cho khi ny tng trng cho qun tnh ca xe (nhp p vo nhn Gain bn di khi).

By gi ta t khi tng vi 2 ng vo +-, ng vo + s c ni vi u, ng vo - s c ni vi thnh phn bv c (u-bv)t vo khi Sum trong th vin Nhp p vo khi ny i ng vo t ++ sang +-

c thnh phn bv ta ch cn t thm khi Gain vi li b:t khi Gain c li b t nhn l damping tng trng cho thnh phn lc cn ca xe.

n y vic xy dng m hnh xe ti vi ng vo u v ng ra v coi nh hon thnh. Tuy nhin, m phng m hnh ny, ta cn t thm khi Step vo u v hin th v trn khi Scopet khi Step trong th vin t khi Scope trong th vin bin u ngay ng vo. ngay ng ra v.

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Nh rng m, b v u l cc bin cn c gn tr trc khi m phng.>>m=1000 >>b=50 >>u=500

Thi gian m phng h thng ty thuc vo thng s Stop time trong menu SimulationSimulation paramrters, gi s t 120 (Hnh 3.7). chy m phng, ta c th thc hin bng 1 trong cc cch:nhp chut vo biu tng chn: Simulation Start Ctrl-T trn menubar ca m hnh

Nhp p vo Scope xem kt qu m phng.

Hnh 3.7 Thay i thng s m phng

Xy dng m hnh h thng iu khin v tr motor DC cho bi phng trnh vi phn sau:d 2 1 d = K ti b 2 J dt dt di 1 d = Ri + V K e dt L dt

Trong :J = 0.01 Kgm2/s2 b = 0.1 Mms K = Ke = Kt = 0.01 Nm/A R = 10 ohm L = 0.5 H TcAD - 2003

l moment qun tn ca rotor l h s ma st ca cc b phn c kh l hng s sc in ng l in tr dy qun l h s t cm28


V i

l in p t ln cun dy ca motor l v tr trc quay (ng ra ca m hnh) l dng in chy trong cun dy ca motor.

Hnh 3.8 M hnh ton h iu khin v tr motor DC

Quan st tng phng trnh m t h thng ta thy cu trc ca chng cng tng t nh phng trnh ca cu . Sinh vin ln lt thc hin trn tng phng trnh c (hnh 3.9):

(Hnh 3.9)

Kt hp 2 phng trnh:

(Hnh 3.10)

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t vo m hnh khi Step lm tn hiu tham kho, khi Scope quan st p ng. Sinh vin hy gn tr cho tt c cc thng s ca m hnh, thc hin m phng v quan st p ng (Hnh 3.11). Hy thay i ng vo m hnh bng khi to xung vung. M phng, quan st kt qu v nhn xt.

IV. T chnSinh vin hy tnh o hm cp 2 ca hm y = xe (1 x ) bng tay v kim chng kt qu bng symbolic.2

Tnh tch phn sau v kim chng kt qu bng symbolic: e x0

2

Hnh 3.11 - M hnh Simulink hon chnh ca h iu khin v tr motor DC

Xy dng m hnh h thng xe la cho bi phng trnh:d 2 x1 dx = F k ( x 1 x 2 ) M 1g 1 2 dt dt 2 d x2 dx M2 = k ( x 1 x 2 ) M 2 g 2 2 dt dt M1

(Hnh 3.12 Photo courtesy: Dr. Howard Blackburn)

Trong cc thng s tng trng nh sau:M1=1 kg M2=0.5 kg TcAD - 2003

l khi lng toa ko; l khi lng toa khch;30


k=1 N/sec F=1 N =0.002 sec/m g = 9.8 m/s^2 x1, x2

l cng l xo kt ni gia 2 toa; l lc tc ng ca u my (ng vo m hnh); l h s ma st ln; l gia tc trng trng v tr 2 toa (ng ra).

Hnh 3.13 M hnh ton ca h thng xe la

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BI 4 M HNH H THNG VIN THNGI. Mc tiuBi th nghim ny tm hiu phng php m hnh ha mt h thng thng tin n gin nh hnh 4.1:

Hnh 4.1 - Mt m hnh truyn tin tiu biu

Chng ta s x l tn hiu ngun (m ha, kim sot li, iu ch) v truyn qua mt knh truyn c nhiu sau khi phc tn hiu nhn c (gii iu ch, gii m) v xc nh xc sut li tn hiu.

II. Tham kho[1]. The Mathworks Inc., Matlab Users Guide Communications Toolbox, 2003. [2]. Nguyn Hu Tnh - L Tn Hng - Phm Th Ngc Yn - Nguyn Th Lan Hng, C s Matlab & ng dng, NXB KH v K thut, 1999. [3]. http://murray.newcastle.edu.au/uers/staff/eemf/ELEC352/notes.htm

III. Thc hnh c th thc tp tt bi th nghim, sinh vin cn c kin thc v X l s tn hiu (Digital Signal Processing), Truyn d liu (Data transmittion) v C s Vin thng. Do , bi th nghim ny khng bt buc i vi sinh vin chuyn ngnh Tin hc (nu c) v sinh vin in t hng KT. Trong trng hp , sinh vin c th chn bi 5 hoc bi 7 thc tp.

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Xy dng m hnh h thng thng tin ni chung l mt vic rt ln, vi nhiu vn cn gii quyt. Do trong phm vi bi th nghim ny chng ta ch c th kho st mt s khu trong tng th ca mt h thng truyn thng.

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III.1 H thng thng tin lin tc (Analog Communications)Trong phn ny chng ta s tm hiu cc phng php iu ch v gii iu ch tn hiu lin tc (Analog Modulation and Demodulation). iu ch bin sng mang b nn hai bng cnh (Double-Sideband Suppressed Carrier Amplitude Modulation DSB-SC): Phng php iu ch ny da theo cng thc sau:y(t) = m(t)cos(2fct+c)

Trong : m(t) l tn hiu h tn (thng tin) dng iu ch sng mang tn s cao c(t) = cos(2fct+c) thu c tn hiu iu ch y(t).

Hnh 4.2 Nguyn tc iu ch bin

Ta c th thc hin phng php iu ch ny trong Matlab nh sau (sinh vin nn ghi trong file .m thun tin cho vic s dng li cc cu sau):>>Fc=10; >>Fs=60; >>Fm=1; >>t=[0:1/Fs:3]; >>c=cos(2*pi*Fc*t); >>m=sin(2*pi*Fm*t); >>subplot(311), plot(t,m) >>subplot(312), plot(t,c) >>y=m.*c; >>subplot(312), plot(t,y) >>z=abs(fft(y)); >>z=z(1:length(z)/2+1); >>frq=[0:length(z)-1]*Fs/length(z)/2; >>figure >>plot(frq,z); % tn s sng mang [Hz] % tn s ly mu m phng % tn s tn hiu h tn % time window % tn hiu sng mang % tin hiu h tn 1Hz % v tn hiu h tn % v sng mang % iu ch % v tn hiu iu ch % ph tn hiu iu ch % ly 1/2 % frequency window % new figure % v ph

Sinh vin hy quan st ph tn hiu iu ch, v hy so snh vi tn s sng mang. Th dng hm amod ca Communications toolbox thc hin cng vic trn.>>help amod TcAD - 200334


>>Y=amod(m, Fc, Fs, 'amdsb-sc'); >>subplot(313),plot(t,Y)1 m 0 -1 1 0 -1 1 0 -1 0 0.5 1 1.5 2 x 0 0.5 1 1.5 2 c 0 0.5 1 1.5 2

% iu ch

2.5

3

2.5

3

2.5

3

Hnh 4.3 Tn hiu iu ch bin

Tng t nh trn, sinh vin hy thc hin iu ch bin sng mang b nn n bng cnh (Single-Sideband Suppressed Carrier Amplitude Modu-lation SSB-SC). So snh vi phng php iu ch bin DSB-SC. Gii iu ch bin : C nhiu phng php gii iu ch bin . y ta xt phng php gii iu ch ng b (Synchronous Demodulation), p dng cho phng php iu ch bin vi sng mang b nn SC (Suppressed Carrier) v phng php iu ch bin vi sng mang c truyn TC (Transmission Carrier), theo m hnh sau:

Hnh 4.4 Nguyn tc gii iu ch bin

Thc hin gii iu ch nh sau (phi m bo rng tn hiu iu ch y cn trong WorkSpace ca Matlab):>>y_mix=y.*c; % trn tn hiu iu ch vi sng mang >>[num,den]=butter(3, (Fc/2)/(Fs/2)); % low-pass filter tn s ct Fc/2 >>m_r=filter(num,den,y_mix); >>close all >>plot(t,m) >>hold on >>plot(t,m_r,'r') % cho tn hiu trn qua b lc % % v tn hiu h tn ban u % % v tn hiu h tn va hi phc

Gii thch v sao ta dng b lc thng thp vi tn s ct Fc/2. TcAD - 200335


Sinh vin hy quan st v so snh s khc bit gia tn hiu gii iu ch v tn hiu h tn ban u. Gii thch. Th dng hm ademod ca Communications toolbox gii iu ch:>>help ademod >>M_R=ademod(y,Fc,Fs,'amdsb-sc'); % gii iu ch >>plot(t,M_R,'g')

III.2 H thng thng tin ri rc (Digital Communications)Trong phn ny, chng ta s thc hin m hnh mt h thng truyn thng ri rc nh s sau:

Hnh 4.5 M hnh mt h thng truyn tin ri rc

Sinh vin cn c phn help ca tng lnh hiu v bit cch s dng. To tn hiu ngun:>>clear >>close all >>K=11; >>msg=randint(K*2,1); >>subplot(411),stem(msg,.) >>ylabel(digital message) % chiu di t tin (message length) % to tn hiu ngun (digital message) % v tn hiu ngun

M ha BCH:>>N=15; >>subplot(412), stem(code,.) >>ylabel(BCH) %chiu di t m (codeword length) %m ha BCH >>code = encode(msg,N,K,'bch');

iu ch QASK: S dng b iu ch s M-QASK vi M=16 (sinh vin cn xem li l thuyt v b iu ch ny)>>M=16; >>Fd=1; >>Fc=10; >>Fs=30; >>modu = dmod(code,Fc,Fd,Fs,'qask',M); >>subplot(413),plot(modu) >>ylabel(QASK) % multiple number % tc ngun tin % tn s sng mang % tn s ly mu % iu ch M-QASK % v tn hiu iu ch

Knh truyn c nhiu: Tn hiu sau khi iu ch c truyn trn knh truyn c nhiu trng Gaussian cng sut 0.1W. TcAD - 200336


>>std_value=0.1; % cong suat nhieu >>modu_noise = modu+randn(length(modu),1)std_value; % add noise

Gii iu ch QASK:>>demo = ddemod(modu_noise,Fc,Fd,Fs,'qask', M); % gii iu ch

Gii m BCH:>>msg_r = decode(demo,N,K,'bch'); >>subplot(414), stem(msg_r,.) >>ylabel(received message)Trans. msg 1 0.5 0 1 BCH 0.5 0 2 QASK 0 -2 1 Rec. msg 0.5 0 0 5 10 15 20 25 0 100 200 300 400 500 600 700 800 900 0 5 10 15 20 25 30 0 5 10 15 20 25

% tn hiu thu % v tn hiu s thu c

Hnh 4.6 So snh tn hiu truyn/nhn

Xc nh li:>>rate=biterr(msg,msg_r,M)

Sinh vin hy dng hm channel ca Communications toolbox m hnh ha knh truyn bc . Lp li cc qu trnh gii iu ch v gii m, so snh kt qu (lu : bng thng ca knh truyn phi ln).

IV. T chnThc hin iu ch v gii iu ch tn s FM vi Fm, Fc, Fs cu III.1. . Thc hin m hnh Digital Communications nh hnh sau:msgM ha Hamming iu ch FSK Knh truyn Gii iu ch FSK Gii m Hamming

msg_r

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Bi 5 M HNH H THNG IU KHIN T NGI. Mc tiuTrong bi th nghim ny chng ta s tm hiu phng php m hnh ha mt h iu khin t ng, bao gm:Hm truyn v phng trnh trng thi ca h thng p ng vng h v p ng vng kn ca h thng Xy dng b iu khin PID Chnh nh thng s ca b u khin v kho st p ng ca h thng.

Hnh 5.1 Mt m hnh h thng iu khin tiu biu

II. Tham kho[1]. The Mathworks Inc., Matlab Notebook Users Guide Control toolbox, 2003. [2]. Phm Vn Tn, Bi ging mn C s T ng hc, B mn Vin Thng v T ng ha, khoa Cng ngh Thng tin, i hc Cn Th, 2001. [3]. Nguyn Cng nh, Phn tch v Tng hp cc h thng iu khin bng my tnh, NXB Khoa hc v K thut, 2002. [4]. http://www.engin.umich.edu/group/ctm [5]. http://www.shu.ac.uk/schools/eng/teaching/rw/pidtutorial.htm

III. Thc hnh c th thc hin tt bi th nghim, sinh vin cn nm vng cc kin thc c bn v iu khin t ng (C s t ng hc). Do , bi ny khng bt buc i vi cc sinh vin Tin hc (nu c) v cc sinh vin in t theo hng Vin thng. Trong trng hp , c th sinh vin thc tp bi 4 hoc sinh vin c th chuyn sang bi 7. TcAD - 200338


III.1 Hm truyn v phng trnh trng thi ca h thngTrong iu khin t ng, ngi ta thng biu din mt h thng vt l bng hm truyn (transfer function) hay phng trnh trng thi (statespace equation) ca n (i vi cc h phi tuyn, t c iu ny, ngi ta phi dng phng php tuyn tnh ha tng on). Gi s c h thng iu khin tc motor DC nh hnh v 5.2 [4]. Trong :J = 0.01 kgm2/s2 b = 0.1 Nms K=Ke=Kt=0.01 Nm/Amp R = 1 ohm L = 0.5 H I: V: : l moment qun tnh ca rotor h s ma st cc hng s sc in ng in tr in cm dng in chy trong cun dy ca motor in p trn hai u cun dy motor ng vo v tr trc ng ra

Hnh 5.2 M hnh ton mt h iu khin tc motor DC

Phng trnh vi phn m t h thng nh sau:J d 2 d +b = Ki 2 dt dt di d L + Ri = V K dt dt

Hm truyn: Bin i Laplace 2 v ca phng trnh trn ta c:s( Js + b)(s) = KI(s) ( Ls + R )I(s) = V Ks(s)

K = Suy ra: (Ls + R )(Js + b) + K s = KV hay V (Ls + R )(Js + b) + K 22

[

]

Biu din hm truyn ny trong Matlab ta thc hin nh sau (sinh vin nn lu thnh file.m):>>J=0.01; >>b=0.1; >>K=0.01; >>R=1; >>L=0.5; >>num=K; TcAD - 2003

% t s ca hm truyn39


>>den=[(J*L) ((J*R)+(L*b)) ((b*R)+K^2)]; >>hamtruyen = tf(num,den)

% mu s hm truyn

p ng bc vng h:>>step(num,den) >>step(hamtruyen)Step Response0.1

% hoac

0.08

Amplitude

0.06

0.04

0.02

0 0 0.5 1 1.5 2 2.5 3

Time (sec)

p ng xung vng h:

>>impulse(hamtruyen)Impulse Response0.14 0.12 0.1

Amplitude

0.08 0.06 0.04 0.02 0 0 0.5 1 1.5 2 2.5 3

Time (sec)

Phng trnh trng thi: Dng tng qut:X = AX + BU Y = CX + DUvi X l vct trng thi, U l vct tn hiu vo v Y l vct tn hiu ra.

Bin trng thi v phng trnh trng thi: T phng trnh vi phn m t h thng, nu t x 1 = v x 2 = i , ta c:

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Gio trnh th nghim CAD b K x 1 = x 1 + x 2 + 0V J J K R 1 x 2 = x1 x 2 + V L L L Y = x1 + 0 x2 + 0 V

hay

K b 0 J J X + 1 V X= K R L L L Y = [1 0]X

Biu din phng trnh trng thi trong Matlab nh sau:>>J=0.01; >>b=0.1; >>K=0.01; >>R=1; >>L=0.5; >>A = [-b/J K/J; -K/L -R/L]; >>B = [0;1/L]; >>C=[1 0]; >>D=0;

p ng bc vng h:>>step(A,B,C,D)

p ng xung vng h:>>impulse(A,B,C,D)

Ta c th chuyn i qua li gia hm truyn v phng trnh trng thi bng lnh sau:>>[num,den]=ss2tf(A,B,C,D) >>[A,B,C,D]=tf2ss(num,den) % t PT trng thi sang hm truyn % t hm truyn sang PT trng thi

Kho st p ng vng h ca h thng i vi tn hiu bt k

(Hnh 5.3)

Phi m bo rng trong Workspace cn bin hamtruyen ca cu , sinh vin c th dng lnh lsim kho st p ng ca h i vi tn hiu bt k. Gi s l tn hiu sin:>>close all >>t=0:0.1:2*pi; >>u=sin(pi/4*t); >>lsim(hamtruyen,u,t) % mo phong dap ung voi tin hieu vao u TcAD - 200341


Linear Simulation Results0.1

0.05

Amplitude

0

-0.05

-0.1 0 1 2 3 4 5 6 7

Time (sec)

III.2 B iu khin PIDCu trc mt h thng iu khin PID nh hnh sau:

Hnh 5.4 S khi h iu khin PID K K s 2 + K Ps + K I Trong hm truyn ca khu PID l: K P + I + K D s = D s s

vi:

KP l li ca khu t l (Proportional gain) KI l li ca khu tch phn (Integral gain) KD l li khu vi phn (Derivative gain)

Vic hiu chnh ph hp 3 thng s KP, KI v KD s lm tng cht lng iu khin. nh hng ca 3 thng s ny ln h thng nh sau:. ng vng kn (C.L. response) KP KI KD T. gian tng (Rise time) Gim Gim t thay i Vt l (Overshoot) T ng Tng Gim T. gian qu Sai s xc lp (Settling time) (Steady-state err.) t thay I Tng Gim T ng Khng xc nh Thay i t

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Step Response1.5

Overshoot1.05 0.95 0.90

1

S-S error0.5

settling time rise time

0.1

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Time (sec)

B iu khin t l P:

Hnh 5.5 B iu khin t l P

Thc hin trong Matlab: Ta c hm truyn ca motor DC nh III.1. :>>J=0.01; >>b=0.1; >>K=0.01; >>R=1; >>L=0.5; >>num=K; >>den=[(J*L) ((J*R)+(L*b)) ((b*R)+K^2)];

Khi thm vo khu t l P, ta c hm truyn vng h:

>>Kp=100; >>numa=Kp*num; >>dena=den;

Xc nh hm truyn vng kn ca h thng ta dng lnh cloop:>>[numac,denac]=cloop(numa,dena) TcAD - 200343


p ng Step vng kn ca b iu khin t l nh sau:>>t=0:0.01:2; >>step(numac,denac)Step Response1.4 1.2 1

Amplitude

0.8 0.6 0.4 0.2 0 0 0.5 1 1.5 2

Time (sec)

Sinh vin hy so snh vi p ng ca h khi cha c b iu khin t l, cu III.1. (lu n cc thng s: thi gian ln, vt l, thi gian qu ). Tng t, sinh vin hy so snh vi p ng xung. B iu khin Vi tch phn t l PID:

Hnh 5.6 B iu khin PID

Khi thm b iu khin PID, hm truyn h ca h thng l:

>>Kp=100; >>Ki=1; >>Kd=1; >>numc=[Kd, Kp, Ki]; >>denc=[1 0]; >>numa=conv(num,numc); >>dena=conv(den,denc); % tch chp t s % tch chp mu s

Hm truyn vng kn hi tip m n v: TcAD - 200344


>>[numac,denac]=cloop(numa,dena);

p ng Step ca h iu khin PID:>>step(numac,denac)

Sinh vin so snh vi p ng ca b iu khin t l P cu xt.

, nhn

Da vo bng tng kt nh hng ca KP, KD v KI i vi h thng iu khin, sinh vin hy thay i 3 thng s ny v kim chng p ng ca h thng.Step Response1

0.8

Amplitude

0.6

0.4

0.2

0 0 50 100 150 200 250 300 350

Time (sec)

III.3 Hiu chnh thng s ca b iu khin PIDMt phng php c in nhng n gin v hiu qu chnh nh 3 thng s KP, KI v KD ca b iu khin PID l phng php ZieglerNichols (Ziegler Nichols Tuning Method). Th tc chnh nh nh sau:1. Ch iu khin h thng bng b iu khin t l KP (t KI=KD=0). 2. Tng KP n gi tr KC m h thng bt u bt n (bt u xut hin s giao ng - im cc ca hm truyn kn nm trn trc o j). Xc nh tn s c ca giao ng va t. T 2 gi tr KC v c va t, cc thng s s KP, KI v KD c xc nh nh bng sau:B iu khin P (t l) PI (tch phn t l) PID (vi tch phn t l) PID vi mt t vt l PID khng vt l KP 0.5 KC 0.45 KC 0.6 KC 0.33 KC 0.2 KC 0.191KPc 0.318KPc 0.785KP/c 0.318KPc 0.53KPc 2.07KP/c 3.14KP/c KI KD

3. Tinh chnh li 3 thng s ny t c p ng nh mong mun.

V d: Gi s cn thit k b iu khin PID cho h thng sau:

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Bc 1: iu khin h thng ch vi b iu khin t l:

Bc 2: Xc nh KC v c m h thng bt u giao ng dng hm rlocus ca Matlab (sinh vin nn lu thnh file .m hoc thao tc trong Matlab Editor sau copy v dn vo Workspace c on lnh d dng cho vic hiu chnh cc thng s phn sau):>>close all >>num=5; >>den=[1 10 100 0]; >>[numc,denc]=cloop(num,den); >>htkin=tf(numc,denc) % ham truyen vong kin >>rlocus(htkin); %ve qui dao nghiem >> axis([-10 10 -15 15])Root Locus 15 10 5 Imag Axis 0 -5 -10 -15 -10

-5

0 Real Axis

5

10

Xc nh Kc v c bng hm rlocfind:>>[Kc,Omegac] = rlocfind(htkin)

Nhp chut vo im giao nhau gia qu o nghim v trc o ca th, trong WorkSpace ta c:Kc = 199.5793 Omegac = -10.0145 0.0072 +10.0072i 0.0072 - 10.0072i

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Nh vy ta c KC=200 v c = 10. Suy ra thng s ca b iu khin PID: KP = 0.6KC = 120 KI = 0.318KPc = 381.6KD = 0.785KP/c = 9.4

Th p ng ca h:>>Kp=120; Ki=381.5; Kd=9.4; >>numc=[Kd, Kp, Ki]; >>denc=[1 0]; >>step(numac,denac) % ham truyen cua PID >>[numac,denac]=cloop(conv(num,numc),conv(den,denc))

Bc 3: Thc hin tng t nh III.2. , sinh vin hy iu chnh mt lng nh 3 thng s KP, KD v KI c p ng tt hn.Step Response1.5

Amplitude

1

0.5

0 0 0.5 1 T im e (sec) 1.5 2 2.5

Sinh vin hy thit k b iu khin PID cho h thng sau:

IV. T chnSinh vin hy thit k b iu khin Vi phn t l (ProportionalDerivative controller):

Sinh vin hy thit k b iu khin Tch phn t l (ProportionalIntegral controller):

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Bi 6 TO GIAO DIN TRONG MATLABI. Mc tiuBi th nghim ny trang b cho sinh vin mt s kin thc c bn xy dng giao din ngi dng trong mi trng Matlab, nhm hon thin mt chng trnh ng dng nht nh.

II. Tham kho[1]. The Mathworks Inc., Matlab Notebook Users Guide, 2003. [2]. Nguyn Hu Tnh - L Tn Hng - Phm Th Ngc Yn - Nguyn Th Lan Hng, C s Matlab & ng dng, NXB KH v K thut, 1999. [3]. Nguyn Hoi Sn - Thanh Vit - Bi Xun Lm, ng dng MATLAB trong tnh ton k thut, Tp 1, NXB HQG Tp. HCM, 2000 (trang 328-344).

III. Thc hnhCng nh cc ngn ng cp cao khc, Matlab h tr nhiu cng c chc nng cho php lp trnh to giao din s dng p v nhanh chng. V d, cc dng nt n, ca s son tho, cc dng menu, nh hnh 6.1.

Hnh 6.1 Cc cng c h tr giao din

Trong bi th nghim ny, sinh vin ln lt thc hin cc bc c nu ra c mt giao din n gin nh hnh v 6.2. Trong mi bc thc hnh, sinh vin hy quan st k p ng ca chng trnh, t t mnh rt ra kinh nghim v vic iu chnh cc thuc tnh ho ca Matlab. TcAD - 200349


To ca s chnh figure Welcome to User Interfaces Giude theo cch sau:M Matlab Editor Nhp ni dung sau: % User Interface's Guide % % Matlab Experiments 2003 % TcAD, CIT, Cantho University % ---------------------------------------------------------------------------------% Initialize whole figure... namefig = 'Welcome to User Interface''s Guide'; figpos = get(0,'DefaultFigurePosition'); % lay vi tri mac nhien figpos(1)= figpos(1)-10; figpos(3)= figpos(3)+10; % Tao figure fig=figure( ... 'Name', namefig, ... 'NumberTitle','off', ... 'Position',figpos); figpos(2)= figpos(2)-10; figpos(4)= figpos(4)+10;

Hnh 6.2 Mt giao din n gin TcAD - 200350


Lu thnh file giaodien.m >>giaodien < >

% thi hanh

Quan st kt qu trn hnh 6.3 (Lu cc thuc tnh: Name, Position)

(Hnh 6.3) >>set(fig) % xem thuc tnh ca figure trong ca s lnh

Thm vo figure mt axes cho php hin th ha:Nhp tip ni dung sau vo file giaodien.m % -------------------------------------------------------------------------------% main axes axs=axes('Position',[0.05 0.4 0.65 0.55]); Lu v thi hnh file ny.

(Hnh 6.4)

Hin th dng Matlab Experiments bn di axes:Nhp tip ni dung sau vo file giaodien.m % -------------------------------------------------------------------------------% text txtpos=[10 50 425 50]; txt=uicontrol(... 'Style','text',... 'BackgroundColor',[0.8 0.8 0.8],... 'ForegroundColor',[0.4 0.5 0.3],... 'String','Matlab Experiments',... TcAD - 200351


'Position',txtpos,... 'Fontname','Courier',... 'FontWeight','Bold',... 'FontSize',26); Lu v thi hnh file ny.

(Hnh 6.5)

To mt frame c shadow bn phi figure t cc nt chc nng:Nhp tip ni dung sau vo file giaodien.m % -------------------------------------------------------------------------------% Console frames p1=0.755; p2=0.05; p3=0.2; p4=0.90; frm1pos = [p1 p2 p3 p4]; frm2pos = [p1-0.005 p2+0.005 p3 p4]; % shadow frame frm1=uicontrol( ... 'Style','frame', ... 'Units','normalized', ... 'Position',frm1pos, ... 'ForegroundColor',[0.4 0.4 0.4],... 'BackgroundColor',[0.4 0.4 0.4]); % main frame frm2=uicontrol( ... 'Style','frame', ... 'Units','normalized', ... 'Position',frm2pos, ... 'ForegroundColor',[0.7 0.7 0.7],... TcAD - 200352


'BackgroundColor',[0.65 0.65 0.65]);

Lu v thi hnh file ny.

(Hnh 6.6)

To nt Close c chc nng ng ca s figure hin hnh:Nhp tip ni dung sau vo file giaodien.m % ---------------------------------------------------------------------------------% Close button closeHndl=uicontrol(... 'Style','pushbutton', ... 'Units','normalized', ... 'Position',[p1+0.01 p2+0.05 p3-0.025 0.05], ... 'String','Close', ... 'Foregroundcolor','b',... 'Fontsize',9,... 'Callback','close');


Vn quan trng nht i vi mt nt chc nng l thi hnh cng vic tng ng khi ngi s dng thao tc. Thuc tnh CallBack cho php: thi hnh mt lnh ca Matlab di dng chui (bao gm lnh gi hm, script file, biu thc ton, ). Sinh vin th thay lnh close bng mt lnh khc, chng hn demos v quan st p ng. TcAD - 200353


To nt Sphere v mt hnh cu 3D:Nhp tip ni dung sau vo file giaodien.m % ---------------------------------------------------------------------------------% Sphere button sph=uicontrol( ... 'Style','pushbutton', ... 'Units','normalized', ... 'Position',[p1+0.01 p4-0.05 p3-0.025 0.05], ... 'String','Sphere', ... 'Foregroundcolor','b',... 'Fontsize',9,... 'Callback',['[x,y,z]=sphere(35);', 'surfl(x,y,z);', 'axis equal']); Lu v thi hnh file ny.

(Hnh 6.7)

To nt Picture hin th nh mu:Nhp tip ni dung sau vo file giaodien.m % ---------------------------------------------------------------------------------% Picture button pic=uicontrol( ... 'Style','pushbutton', ... 'Units','normalized', ... 'Position',[p1+0.01 p4-0.125 p3-0.025 0.05], ... 'String','Picture', ... 'Foregroundcolor','b',... 'Fontsize',9,... 'Callback',['imshow(imread(''flowers.tif''))']); TcAD - 200354



(Hnh 6.8)

Sinh vin lu cch biu din nhiu lnh dng chui cho CallBack. Trong trng hp c qu nhiu lnh phc v chc nng ny, ta nn a chng vo mt script file hoc mt hm khc. Ngoi ra, nu ta to giao din di dng mt hm (function) th thuc tnh CallBack cho php gi mt hm con c vit ngay trong file ny. Sinh vin hy to thm nt About sao cho khi ngi s dng n nt s m ca s mi nm ngay gia mn hnh 6.9.

(Hnh 6.9)

IV. T chnSinh vin hy xem mt s file to giao din demo ca cc toolbox trong Matlab chng hn: graf3d.m trong \toolbox\matlab\demos, tham kho cch xy dng giao din theo dng hm. Vi cch ny, thuc tnh CallBack trong uicontrol cho php gi trc tip mt hm m hm c xy dng ngay trong file giao din (ngha l khng cn to mt file *.m khc phc v cho CallBack). TcAD - 200355


Th sa li giao din ca bi th nghim ny theo dng trn.

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BI 7 THIT K M PHNG MCH V V MCH INI. Mc tiuGip sinh vin bc u lm quen vi cc phn mm sau: Multisim V6.20 (Electronics WorkBench) dng m phng cc mch tng t v mch s; OrCAD Release 9 dng v Schematic, m phng v v mch in (PCB).

II. Tham kho[1]. OrCAD Inc., Users Guide - Capture, 1998. [2]. OrCAD Inc., Users Guide - Layout, 1998. [3]. http://www.electronicsworkbench.com/tutorial/ [4]. http://www.rit.edu/~labeee/

III. Thc hnhMc d Multisim v OrCAD/Pspice l cc phn mm rt ln vi nhiu tnh nng p dng mnh v phc tp, nhng sinh vin chuyn ngnh in t hon ton c th t nghin cu c. Do , bi th nghim ny l khng bt buc i vi tt c sinh vin (c bit l sinh vin Tin hc, nu c). Trong trng hp sinh vin khng chn bi th nghim ny th c th chn Control System Toolbox (i vi sinh vin KT) hoc Communications Toolbox (i vi sinh vin Vin Thng) hoc Image Processing Toolbox (i vi sinh vin Tin hc) ca MATLAB kho st. Bi th nghim ny tng i di, sinh vin cn sp xp thi gian hp l thc hin cc cng vic sau:

III.1 MultisimTrong phn ny, chng ta s lm quen vi Multisim 6.20 (hin c Multisim 2001 hon thin hn), y l Version mi ca Electronics WorkBench 5.x, n cho php s dng kt hp th vin linh kin Analog v Digital vi nhiu cng c thn thin, h tr tuyt vi cho vic m phng cc mch in t. Khi ng Multisim: TcAD - 200357


Chy file Multisim.exe t Start menu ca Windows Nhp vo biu tng trn Desktop.

Sinh vin hy nhp chut vo cc th vin linh kin ca Multisim trn Menu bn tri ca ca s chnh c ci nhn tng qut v cc linh kin chc nng.Khi mun t linh kin no vo khng gian thit k, ch cn nhp chut vo linh kin , ri chn thng s ph hp v t vo v tr mong mun. to mt kt ni gia 2 im, ch cn nhp chut vo im th nht ri ko n im th hai v nhp chut ln na.

Hnh 7.1 Giao din chnh ca MultiSIM

Sinh vin hy v v m phng mch in sau:

Hnh 7.2 Mt mch in in hnh TcAD - 200358


Dng Osilsoscope quan st dng tn hiu chn 2-6 v chn 3 ca LM555. Hy c lng tn s giao ng v chu k thao tc ca mch.

Kinh nghim: i lc Multisim a ra bng thng bo li trong qu trnh m phng hay hiu chnh thng s ca cc linh kin. Trng hp , ta g b khi Osilloscope, hiu chnh v m phng vi ln ri gn Osilloscope tr li quan st dng tn hiu. Ngoi ra, nu trong mch c s dng cc IC s (74xxx, 40xxx, ) ta phi c ngun Vcc=5V nh hnh v trn.

III.2 OrCADCc chc nng chnh ca OrCad gm: V s mch (OrCAD Capture), m phng mch (OrCAD Pspice) v v mch in (OrCAD Layout). Tuy nhin, trong phn th nghim ny chng ta khng cp n OrCAD Pspice (y l mt trong nhng chc nng rt mnh ca OrCAD phin bn 9.0 tr ln, ngh sinh vin t nghin cu).

III.2.1 V s mch (Schematic)Khi ng OrCAD Capture bng mt trong cc cch sau:Chn Capture CIS t Start Menu ca Window Nhp vo biu tng trn desktop

to mt Project mi cho vic v s mch ta thc hin:Chn File New Project hoc nhp vo icon trn Menu bar Khi hp thoi New Project xut hin: Chn Schematic v t tn project trong menu Name (gi s l BaiTN7). C th chn th mc lu project ny trong menu Location.

Mi trng v mch xut hin khi ta nhp p vo PAGE1 (hnh 7.3). T y ta ln lt t cc linh kin vo v kt ni c s mong mun.

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Hnh 7.3 Mi trng v mch in ca OrCAD

S dng Menu tt sau:

(Hnh 7.4)

Sinh vin hy v s mch nh hnh sau. Trong cc th vin linh kin c s dng nh sau:Discrete: Opamp: Amplifier: R, Capacitor Pol, Capacitor Non-Pol, Resistor Var, Photo PNP v Speaker. TL082 LM386

Lu Schematic va v vi tn BaiTN7.+9V -9V R3 10K R1 220 C1 + 3 Q1 1 VR 10K 2 LS1 8 4 8 .1 R2 2 1K 3 U1A TL082 1 1 3 7 2 U2 LM386 5 + 4 6 1 C3 .1 C2 C4 .1 C5 .1 +9V +9V

TcAD

+9V SPEAKER 3

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+

+ -

0

220 uF

0

(Hnh 7.5)60


III.2.2 To NetlistSau khi lu s va v, to Netlist phc v cho vic v mch in ta thc hin nh sau:ng ca s Schematic1:Page1, quay v Project Management BaiTN7

(Hnh 7.6) Chn Tools Annotate nh s th t cho linh kin. Chn Tool Create Netlist. to Netlist. Khi ca s Create Netlist xut hin, ta chn layout Tab (file d liu netlist l BaiTN7.MNL), OK.

Nu m bo rng c file BaiTN7.MNL trong th mc hin hnh th thot khi OrCAD Capture chun b cho vic v mch in. Lu : Trong phn trn chng ta khng cp n chc nng Kim tra mch ca OrCAD v mt s chc nng h tr khc.

III.2.3 V mch in (Printed Circuit Board-PCB)Khi ng OrCAD Layout bng mt trong cc cch sau:Chn Layout Plus trong Start Menu ca Window Nhp vo biu tng trn desktop.

Chn File New to mt PCB layout mi

Sau thao tc ny, ca s Load Template File xut hin, ta cn t ng dn ch n file DEFAULT.tch trong OrCAD/Layout_plus/DATA. Sau thc hin np file Netlist va to bc III.3.2 (v d: BaiTN7.MNL). t footprint cho cc linh kin: Nu trong qu trnh v Schematic ta khng chn footprint cho cc linh kin mi khi t vo th bc ny OrCAD s yu cu chn kiu chn cho cc linh kin theo menu sau:

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(Hnh 7.7)

Nhp vo menu Link existing footprint to component , chn la kiu chn ph hp cho tng loi linh kin. bc ny, kiu chn linh kin cn chn ng kch thc (c th phi to cc footprint mi). i vi bi th nghim ny, sinh vin c th tham kho bng sau:Linh kin Footprint Th vin

R C Photo NPN TL082, LM386 VR Speaker

Jumper600 CPCYL1/D.200/LS.100/.031 TO92 DIP.100/8/W.300/LS.100/.425 VRES1 CYL/D.150/LS.100/.31

JUMPER TM_CAP_P TO DIP100T VRES TM_CYLND

Sp xp linh kin: Quan st menu bar, chn chc nng thch hp v sp xp cc linh kin trn board mch. bc ny, nu cn thit ta c th a vo thm cc linh kin mi, chng hn cc l (hold) bt c cho board mch.

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(Hnh 7.8)

t kch thc cc ng mch v khai bo s lp:Chn Options Global Spacing t khong cch gia Track, Via v Pad:

(Hnh 7.9) Chn Options Jumper Settings , OK hoc View SpreadSheet Layer bo s lp v. Trong bi th nghim ny, ta v board mch 2 lp, nn ch c TOP v BOTTOM l Routing.

(Hnh 7.10) Chn View SpreadSheet Nets t kch thc cc ng mch:

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(Hnh 7.11)

V mch: OrCAD h tr nhiu nhiu chin lc v mch. khai thc tt cc chin lc ny i hi phi c mt s kinh nghim nht nh. Thng thng, ngi ta hay v cc ng Ngun Mass vi cc t lc ngun thch hp trc, sau thc hin v t ng tng phn v cui cng kt ni cc phn va v. Nn nh rng, ch v t ng ch gip gim thi gian, khng c phn mm no v mch t ng tt hn t duy ca con ngi.

(Hnh 7.12)

Mt s thng s cn lu (p dng cho cc sinh vin v v thu gia cng mch Lun vn tt nghip ti mt s c s Tp. HCM):ng knh ti thiu ca cc l chn cm v cc via xuyn mch: 55 mils (1000 mils=1 inches). Cc l chn linh kin nn t thnh hnh oval. rng ti thiu ca cc ng mch (track width): 15 mils (hin nay ti Tp. HCM mt s cng ty c th thc hin mch vi rng ng 6 mils). Khong cch Track to Track nn >15 mils c th v xuyn qua gia 2 chn IC, phi t khong cch Track to Pad thch hp, nn 12 15 mils.

IV. T chnT thit k v m phng mt mch in t bng Multsim V mch in cho mch va thit k bng OrCAD.

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Nguyn Ch Ngn, ThS., Ging vin B mn Vin Thng - T ng ha Khoa Cng ngh Thng tin, i hc Cn th Email: [email protected] Mobile Tel: 0913199766

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cach su dung matlab

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