B CNG THNG
TRNG I HC THNH OKHOA IN T-VIN THNGBI GINGTIN HC CHUYN NGNH
T-VTTS. Cng Hngi tng: HSSV trnh i hc, Cao ngNgnh o to: in t- Vin
thngH Ni 2013MC LC
5LI GII THIU
1CHNG 1: C S MATLAB
11.1.Khi nim v Matlab
11.1.1.nh ngha
21.1.2. Ci t chng trnh
41.1.3 Khi ng v thot khi Matlab
61.2.Bt u lm quen vi Matlab
61.2.1. Ca s lnh
61.2.2.Hiu chnh, sa i dng lnh
61.2.3.Xo ca s lnh
71.2.4.Dng mt chng trnh ang chy
71.2.5. Ngn khng cho hin th kt qu tnh ton ra mn hnh
71.2.6.Dng lnh di
71.2.7. Cc Menu ca Matlab
91.2.8. Mt s phm chuyn dng v lnh thng dng
101.2.9.Bin trong Matlab
111.2.10. Cc php ton trong Matlab
131.3.S dng cc lnh trc tip t Matlab
131.4. S dng cc lnh t file lnh
141.5. Dng nhc gn gi tr cc bin
151.6. Cc to mt hm
161.7. S dng hm c sn
161.8. V cc hm
171.9. Lu v ly d liu
171.10. Cc ton t Logic v cc lnh iu kin
171.10.1.Cc ton t logic
181.10.2. Cu trc cu lnh iu kin:
211.11.Vng lp
211.11.1.Vng lp for
211.11.2.Vng lp for lng nhau
221.11.3.Vng lp While
221.11.4 Cc lnh break, return, error:
231.12. Bin ton cc (global variables)
231.13.Mt s hm ton hc
241.14. nh dng s
26CHNG 2: SYMBOLIC TOOLBOX
262.1. Gii thiu v symbolic
262.2. Lnh v hm trong Symbolic Matlab
262.2.1. Cu trc :
262.2.2 Bin symbolic mc nh
272.2.3. Php o hm
282.2.4. Php tch phn
292.2.5. Tm gii hn
292.2.6. Tnh tng ca dy s symbolic
302.2.7. Tch t s v mu s ca mt biu thc symbolic
312.2.8 Thay th
312.2.9 Biu din biu thc symbolic di dng ton hc
322.2.10. Gii phng trnh i s
322.2.11. Phng trnh vi phn
332.2.12 Bin i laplace v laplace ngc
34CHNG 3:MA TRN V MNG TRONG MATLAB
343.1 Nhp ma trn trong Matlab
343.1.1 Cc Cch nhp matrn trong Matlab
363.2 Ma trn s phc
373.3 To vec t
373.4 Truy nhp cc phn t ca ma trn
383.5 Php tnh ma trn v mng
393.6 Gii h phng trnh tuyn tnh
393.6.1 H phng trnh tuyn tnh :
393.6.2 H Phng trnh tuyn tnh khng ng nht
403.6.3 H phng trnh tuyn tnh ng nht
413.6.4 Gii h phng trnh tuyn tnh bng Matlab(Dng ton t \)
413.7 iu kin c nghim
423.8 H iu kin yu
433 .9 Lnh cond Tnh iu kin ca ma trn
45Cu hi n tp
46CHNG 4: HO TRONG MATLAB
464.1 Mn hnh th
464.2.Cc lnh trn menu ha:
474.2.1 File:
504.2.2 Edit: .
514.2.3 Tools ( Ctrl + t) :
564.3.Thc hnh v th 2- D
564.3.1. th tuyn tnh:
564.3.2. th dng nh du:
574.3.3.V nhiu ng biu din trn cng mt th:
574.3.4 Ch thch v kim sot th:
584.3.5. th hnh thanh:
594.3.6. th to cc:
594.3.7. th hnh Pie:
604.3.9.Lnh staris:
604.4 Thc hnh v th 3- D
62CHNG 5: C S PHNG PHP TNH
62MC TIU CA CHNG
625.1. Ni suy v thut ton ni suy
625.1.1 Ni suy lagrange cho bi ton mt chiu
655.1.2 Ni suy cho bi ton hai chiu
665.2 Gii phng trnh phi tuyn
705.3 Dng Laplace gii bi ton trong L thuyt Mch
725.4 Gii h phng trnh i s tuyn tnh
725.5 Phng trnh vi phn thng
76CHNG 6:M HNH HA,M PHNG H THNG
76MC TIU CA CHNG
766.1 Khi nim v simulink
766.2 Th vin simulink v mi trng lm vic
786.3. Phng php xy dng m hnh
84TI LIU THAM KHO
LI GII THIU
Hc phn Tin ng dng thuc khi kin thc c s chung ca cc ngnh i hc k
thut chuyn ngnh in. Trang b cho sinh vin nhng kin thc c bn v: Phn
mm Matlab v ng dng ca n m phng cc bi ton iu khin cc qu trnh cng ngh
thng dng
Sau khi ci t xong, chng ta hy xem MATLAB c th lm c nhng g. Trong
phn ny chng ta s trnh by mt s nhng ng dng ca n; v trnh by tt c nhng
ng dng ca MATLAB s rt di v tn thi gian. Nu bn c quyn hng dn ny, bn
s thy MATLAB l ngn ng rt mnh gii quyt nhng vn quan trng v kh khn ca
bn. N s rt hu ch khi bn c phn hng dn c bn v n s cung cp cho bn nhng
kin thc c bn bn hiu r MATLAB v pht trin c nhng kh nng ca mnh sau
ny.
C l cch d nht hng dung v MATLAB l n c y cc c im ca my tnh c nhn:
ging nh cc my tnh c bn, n lm tt c cc php tnh ton hc c bn nh cng,
tr, nhn, chia; ging nh my tnh k thut, n bao gm: s phc, cn thc, s m,
logarithm, cc php ton lng gic nh sine, cosine, tang; n cng ging nh
my tnh c kh nng lp trnh, c th lu tr, tm kim li d liu, cng c th to,
bo v v ghi trnh t cc lnh t ng php ton khi gii quyt cc vn , bn c th
so snh logic, iu khin thc hin lnh m bo tnh ng n ca php ton. Ging nh
cc my tnh hin i nht, n cho php bn biu din d liu di nhiu dng nh: biu
din thng thng, ma trn i s, cc hm t hp v c th thao tc vi d liu thng
cng nh i vi ma trn.
Trong thc t MATLAB cn ng dng rt rng ri trong nhiu lnh vc v n cng
s dng rt nhiu cc php tnh ton hc. Vi nhng c im v kh nng thn thin vi
ngi s dng nn n d dng s dng hn cc ngn ng khc nh Basic, Pascal,
C.
N cung cp mt mi trng phong ph cho biu din d liu, v c kh nng mnh
m v ho, bn c th to cc giao din ring cho ngi s dng(GUIs) gi quyt
nhng vn ring cho mnh. Thm vo MATLAB a ra nhng cng c gii quyt nhng
vn c bit, gi l Toolbox (hp cng c). V d Student Edition ca MATLAB
bao gm c Toolbox iu khin h thng, Toolbox x l tn hiu, Toolbox biu
tng ton hc. Ngoi ra bn c th to Toolbox cho ring mnh.
Vi nhng kh nng mnh m, rng ln ca MATLAB nn n rt cn thit cho bn bt
u t phn c bn. Sau y chng ta s nghin cu tng phn, v cun sch ny s gip
bn hiu c chng. Trc tin, mt cch n gin nht l chng ta quan nim nh l mt
my tnh c bn, tip theo l nh my tnh k thut v nh my tnh c th lp trnh
c, cui cng l nh my tnh hin i nht. Bng cch quan nim ny bn s d dng
hiu c nhng cch m MATLAB gii quyt nhng vn thng thng v xem MATLAB gii
quyt nhng vn v s phc mm do nh th no.
Tu thuc vo kin thc ca bn, bn c th tm thy nhng phn trong cun sch
hng dn ny hng th hay bun t...
Nhm bin son
K tn
Nguyn Vn A
K tn
Nguyn Th ANhm sa cha
K tn
Nguyn Vn B
K tn
Nguyn Th B
CHNG 1: C S MATLAB
MC TIU CA CHNG
- Hiu r khi nim v cch ci t phn mm Matlab
- Nm c cc menu v cc lnh c bn trong Matlab
- V thi : Hc sinh, Sinh vin : Bit cch khai bao bin trong Matlab,
to v s dng function v script file.NI DUNG BI GING L THUYT
1.1.Khi nim v Matlab
1.1.1.nh ngha
MATLAB l 1 phn mm ng dng chy trong mi trng Windows do hng
MathWorks sn xut v cung cp. C th coi Matlab l ngn ng ca k thut. N
tch hp cc cng c rt mnh phc v tnh ton, lp trnh, thit k, m phng,...
trong mt mi trng rt d s dng trong cc bi ton v cc li gii c biu din
theo cc k hiu ton hc quen thuc.
Cc ng dng in hnh l: - Ton hc v tnh ton.
- Pht trin thut ton.
- To m hnh, m phng v to giao thc.
- Kho st, phn tch s liu.
- ho khoa hc k thut.
- Pht trin ng dng, gm c xy dng giao din ngi dng ho GUI.
Matlab l mt h thng tng tc m phn t d liu c bn l mt mng (array)
khng cn khai bo kch thc. iu ny cho php bn gii nhiu bi ton tnh ton k
thut c bit l cc bi ton lin quan n ma trn v vc t.
Matlab l vit tt ca hai t ting Anh Matrix Laboratory (Phng th
nghim ma trn). Ban u Matlab c vit ch phc v cho vic tnh ton ma trn.
Tri qua thi gian di, n c pht trin thnh mt cng c hu ch, mt ngn ng ca
k thut. Trong mi trng i hc, n l mt cng c chun cho cc kho hc m u v
cao cp v ton hc, khoa hc v k thut. Trong cng nghip, n l cng c c la
chn cho vic phn tch, pht trin v nghin cu hiu sut cao.
Matlab cung cp mt h cc gii php theo hng chuyn dng ho c gi l cc
Toolbox (hp cng c). Cc toolbox cho php ngi s dng hc v p dng cc k
thut chuyn dng cho mt lnh vc no . Toolbox l mt tp hp ton din cc hm
ca Matlab (M-file) cho php m rng mi trng Matlab gii cc lp bi ton c
th. Cc lnh vc trong c sn cc toolbox bao gm: X l tn hiu, h thng iu
khin, logic m, m phng,...
H thng Matlab gm c 5 phn chnh:
- Ngn ng Matlab: l mt ngn ng ma trn/ mng cp cao vi cc cu lnh,
hm, cu trc d liu, vo/ ra, cc tnh nng lp trnh hng i tng. N cho php
lp trnh cc ng dng t nh n cc ng dng ln v phc tp.
- Mi trng lm vic Matlab: y l mt b cc cng c v phng tin m bn s dng
vi t cch l ngi dng hoc ngi lp trnh Matlab. N bao gm cc phng tin cho
vic qun l cc bin trong khng gian lm vic Workspace cng nh xut nhp
khu d liu. N cng bao gm cc cng c pht trin, qun l, g ri v nh hnh
M-file, ng dng ca Matlab.
- X l ho: y l h thng ho ca Matlab. N bao gm cc lnh cao cp cho
trc quan ho d liu hai chiu v ba chiu, x l nh, nh ng,... N cng cung
cp cc lnh cp thp cho php bn tu bin giao din ho cng nh xy dng mt
giao din ho hon chnh cho ng dng Matlab ca mnh.
- Th vin ton hc Matlab: y l tp hp khng l cc thut ton tnh ton t
cc hm c bn nh cng, sin, cos, s hc phc,... ti cc hm phc tp hn nh
nghch o ma trn, tm tr ring ca ma trn, php bin i Fourier nhanh.
- Giao din chng trnh ng dng Matlab API (Application Program
Interface): y l mt th vin cho php bn vit cc chng trnh C v Fortran
tng thch vi Matlab.
Simulink, mt chng trnh i km vi Matlab, l mt h thng tng tc vi vic
m phng cc h thng ng hc phi tuyn. N l mt chng trnh ho s dng chut
thao tc cho php m hnh ho mt h thng bng cch v mt s khi trn mn hnh. N
c th lm vic vi cc h thng tuyn tnh, phi tuyn, h thng lin tc theo thi
gian, h gin on theo thi gian, h a bin,...
1.1.2. Ci t chng trnh
a. Khi ng windows.
Matlab l mt phn mm chy trong mi trng Windows nn qui trnh ci t
Matlab cng tng t nh vic ci t cc chng trnh phn mm khc trong Windows,
ch cn lm theo cc hng dn ca chng trnh ci t.
b.Tin hnh ci t
- a a CD vo a (nu ci t a CD-ROM)
Do chng trnh c cu hnh theo ch Autorun (t chy) nn khi a a CD vo a
th trnh Setup t ng c kch hot. Trng hp ch Autorun khng c kch hot (do
tp tin Autorun b li), dng. Hoc ta c th kch chut vo nt Start trn
thanh tc v (Task bar) ca windows, chn lnh run, g vo ng dn ca file,
nhn Enter hoc kch vo nt lnh Run. Sau lm theo cc hng dn ca trnh ci t
ca Windows.
- Trng hp ci t Matlab t a cng:
Trng hp ny yu cu phi c sn b ci t trong a cng. Khi , ta s dng
Windows Explorer hy My Computer duyt cng, tm n th mc (folder) ci t
ri kch p chut vo file (tp tin) Setup.exe. Sau lm theo cc hng dn ca
trnh ci t ca Windows.
Sau khi file setup.exe c kch hot, ca s Welcom to MATLAB Setup
hin ln trong giy lt. Kch vo nt lnh Next chuyn sang ca s ci t k
tip.
c.Nhp thng tin ca ngi dng v Personal License Password
Ca s th hai th hin cc thng tin v bn quyn ca chng trnh. Kch Yes
sang ca s ci t k tip. Trong ca s thng tin v khch hng Customer
Information (hnh 1.2), nhp h tn vo khung Name, a ch hoc tn cng ty
vo khung Company. Nhp m kho (Serial Key) ca chng trnh vo khung
Personal License Password. Kch chut vo Next tip tc qu trnh ci
t.
d) La chn cc thnh phn s ci t
Trong ca s Select Matlab Components (hnh 1.3), b nh du nhng thnh
phn khng cn thit trong chng trnh tit kim dung lng a cng. Mun kim
tra dung lng ca chng trnh, kch vo Disk Space quan st.
Mun thay i th mc ci t Matlab, kch chut vo nt Browse v to ng dn
ti a ch cn t th mc Matlab. Th mc mc nh l C:\MATLABR11.
tip tc kch Next, mn hnh hin khung thng tin Setup v trnh setup bt
u copy cc tp tin vo th mc ci t.
e.Hon thnh ci t
Sau khi hon thnh qu trnh Copy cc file ca chng trnh vo th mc ci
t, mn hnh hin khung thoi Setup Complete. B nh du Yes, launch the
Help Desk to view the Release Note nu khng mun trnh setup khi ng
Help Desk (phn tr gip). B nh du Yes, launch Matlab nu cha mun khi
ng Matlab ngay. Kch Finish kt thc qa trnh ci t.
Sau khi kt thc ci t ca s k tip l Internet Explorer (nu khng b nh
du Yes, launch the Help Desk to view the Release Note). Kch Close
tr v ca s nn Desktop ca windows, biu tng ca Matlab s c t ng a ra
Desktop ca windows..
1.1.3 Khi ng v thot khi Matlab
a) Khi ng MATLAB
Cng nh cc chng trnh ng dng khc chy trn nn Windows, c rt nhiu cch
khi ng Matlab.Kch p chut vo biu tng Matlab5.3 trn mn hnh Desktop ca
Windows:
hoc kch chut theo trnh t nh sau:
Start/ Programs/ Matlab/ Matlab 5.3Sau khi khi ng xong ca s
Matlab Command Window hin ra nh hnh 1.4.
Cng nh cc chng trnh chy trong mi trng Windows khc Matlab cng c
nhng thnh phn giao din ca chng trnh.
Dng trn cng l thanh tiu gm:
+ Tn tri l biu tng chng trnh. Khi kch vo biu tng ny Matlab hin
menu x cha cc lnh lin quan ti vic x l khung ca s chng trnh cng nh
thot khi chng trnh.
+ K tip biu tng l tn chng trnh cng vi ca s chng trnh. Tn cng l
ba biu tng c chc nng phong to, thu nh v thot khi chng trnh.
Dng th hai l thanh menu (Menu bar thanh thc n) ca chng trnh gm
cc menu chnh cha cc lnh lin quan n vic to, x l, gn thuc tnh,... cho
cc i tng, thit lp cu hnh phn mm,...
Dng th ba l thanh cng c (Tool bar thanh cng c) cha biu tng ng tt
(Shortcut) ca cc lnh thng s dng, gip ngi s dng truy cp nhanh vo cc
lnh ca Matlab.
Phn chim gn chn mn hnh l ca s lnh, l ni nhp cc lnh v hin th kt
qu cng nh cc thng tin khc.
Cui cng l thanh tc v hay thanh trng thi (status bar) hin thng
tin v tnh trng ang x l, thc hin i vi i tng.
b) Thot khi MATLAB
Trong Windows, c rt nhiu cch thot khi mt chng trnh ng dng, thot
khi Matlab ta c th s dng mt trong nhng cch sau:
T ca s lnh Matlab Command Window nh lnh quit hoc kch biu tng
close nm ngay gc phi trn thanh tiu Matlab. Hoc kch chut theo ng dn
sau:
File / Exit MATLAB
Hoc nhn t hp phm : Ctrl + Q.
1.2.Bt u lm quen vi Matlab
1.2.1. Ca s lnh
Ca s lnh l ca s chnh trong ngi s dng giao tip vi Matlab. Trnh
dch ca Matlab hin th mt du nhc >> biu th rng n sn sng nhn v
thc hin lnh ca bn. V d, khi mun nhp dng lnh gn bin x=5, ta g nh
sau:
>>x=5 (Sau khi nhn phm enter ((), Matlab p ng nh sau:
>>x=5
x=
5
1.2.2.Hiu chnh, sa i dng lnh
Cc phm mi tn, cc phm iu khin trn bn phm cho php gi li, sa i v ti
s dng cc lnh g vo trc . V d, gi s ta g vo dng lnh:
>>a=(1+sqt(5))/2 %sqrt(x) l hm tnh gi tr cn bc hai ca
x
Do ta g thiu ch r trong c php ca hm sqrt nn Matlab bo li nh
sau:
Undefined function or variable sqt c ngha l hm hoc bin sqt khng
c nh ngha. Thay v g li c dng lnh, n gin l ta nhn phm (, cu lnh b
sai trn s c hin th li. S dng phm ( (hoc dng chut) di chuyn con tr n
v tr gia ch q v ch t ri chn vo ch r sau nhn enter, kt qu l:
>>a=(1+sqrt(5))/2 (
a=
1.6180
Ta c th s dng phm nhiu ln tm cc lnh g trc . Cng c th gi nhanh li
mt cu lnh thc hin trc bng cch g k t u ca dng lnh ri nhn (. V d, gi
li chnh xc lnh trn nh sau:
>>a (1.2.3.Xo ca s lnh
S dng lnh clc xo ca s lnh (xo mn hnh). Lnh ny khng xo ni dung
trong khng gian lm vic Workspace, m ch xo mn hnh. Sau khi s dng clc
ta c th s dng phm ( gi li lnh c.
1.2.4.Dng mt chng trnh ang chy
V nguyn tc c th dng mt chng trnh ang chy trong Matlab ti bt k
thi im no bng cch nhn t hp phm Ctrl + C. Tuy nhin, ta vn c th phi i
cho n khi mt hm ang thc thi bn trong hoc MEX-file kt thc hot ng ca
n.
1.2.5. Ngn khng cho hin th kt qu tnh ton ra mn hnh
Nu bn ch n gin l g vo mt cu lnh (php tnh) v nhn (, Matlab s t ng
hin th kt qu ca cu lnh (php tnh) ra mn hnh. Tuy nhin nu bn kt thc
dng lnh vi mt du (;) th Matlab s thc hin vic tnh ton nhng khng hin
th kt qu ra mn hnh. iu ny c bit c ch khi thc hin tnh ton vi cc vc t
hoc Matlab trn c s phn t rt ln.
1.2.6.Dng lnh di
Nu mt cu lnh qu di, khng va trn mt dng, ta s dng mt ton t ba chm
() sau nhn ( biu th rng cu lnh cn tip tc dng k tip. V d:
s = 1 1/2 + 1/3 1/4 + 1/5 1/6 + 1/7 ...
1/8 + 1/9 1/10 + 1/11 1/12;
S k t ti a cho php trn mt dng l 4096 k t. Cc khong trng (du cch)
xung quanh cc du =, +, -, *, /, l tu (khng nht thit phi c) nhng
chng gip ta d c hn.
1.2.7. Cc Menu ca Matlab
a.Menu File
Kch chut vo File hoc nhn t hp phm Alt-F, xut hin menu x cha cc
lnh lin quan n vic to mi, qun l, gn thuc tnh cho i tng (cc tp tin -
file) c sn, thit lp cu hnh phn mm....
- New (hnh 2.1): Hin menu cha ba lnh to i tng mi. i tng y c th l
mt script, mt ca s ho hay mt m hnh m phng h thng.
+ M-file: Hin ca s Editor/ Debugger. y l mi trng bn to mi cng nh
sa i, g ri cc tp tin chng trnh nh M-file hoc MEX-file hoc cc i tng
no thc hin mt nhin v no . c th to c cc tp tin ny, bn phi dng ngn ng
lp trnh C hoc FORTRAN.
+ Figure : y l mi trng ho bn t v cc i tng hoc Matlab v cc th
theo hm lnh bn nhp t khung ca s lnh ca MATLAB hoc m th c vi lnh
Open ca Matlab.
- Open (hnh 2.5): M tp tin th hoc hnh nh trong ca s Figure x
l.
+ Trong ca s Matlab Command windows kch: File/Open. Xut hin
khung thoi Open.+ T khung thoi, g a ch ca file vo file name, nhn
open hoc kch chn tn tp tin cng kiu tp tin (file type) mun m v kch
Open. - Run Script :
Chy mt chng trnh lu thnh mt tp tin.
Trong ca s Matlab Command window kch: File/Run Script. Trn mn
hnh xut hin khung thoi Run Script (hnh 2.9).
G a ch v tn tp tin vo trong khung nhp lnh Run ri kch OK. tm kim
cc tp tin lu trong my, kch vo nt duyt. T khung thoi Browse chn ngun
cha v tn tp tin cn m ri kch vo Open v khung thoi Run Script vi ton
b ng dn cng tn tp tin mun m. Kch OK.
- Print Setup :
Hin khung thoi Print cng cc chc nng ph lin quan n vic in n (hnh
2.18).
-Exit MATLAB ( Ctrl + Q ):
Thot khi chng trnh MATLAB v tr v Windows
B.MENU EDITSHin menu con cha cc lnh lin quan n vic x l cc i tng
(hnh 2.19).
- Undo: Hu lnh hoc thao tc thc hin trc . Sau khi chn lnh Undo hu
lnh, lnh s i thnh Redo ngi s dng khi phc nhng g hu trc vi lnh
Undo.
- Cut (Ctrl +X):
Xo tm thi i tng trong khung ca s lnh hin hnh v a vo b nh m ca
chng trnh, sau c th dn i tng tr li vo v tr c chn. i tng c ct c th l
mt cng thc, mt chui k t, hm lnh
+ Chn i tng mun ct trong khung ca s lnh MATLAB v n Ctrl + X hoc
chn Cut t menu Edit. i tng s tm bin mt ti v tr hin hnh.
+ Chn v tr cn dn ri nhn Ctrl + V hoc Paste. i tng s c dn vo v tr
chn.
- Copy (Ctrl + C):
Sao chp i tng trong khung ca s lnh MATLAB v sau dn vo v tr chn.
i tng c Copy c th l mt cng thc, mt chui k t, hm lnh
+ Chn i tng cn Copy ti ca s lnh MATLAB v sau n Ctrl + C hoc
Copy.
+Chn v tr cn copy n v n Ctrl + V hoc chn Paste t menu Edit.
- Paste (Ctrl + V):
Dn i tng c Cut hoc Copy vo v tr chn. Ngoi ra, bn cn c th dng lnh
Paste ca MATLAB dn cc i tng khc vo MATLAB.
- Clear: Xo i tng c chn trong khung ca s MATLAB.
- Select All: Chn ton b ni dung trong khung ca s lnh ca
MATLAB.
- Clear Session:
Xo ton b ni dung ca ca s lnh MATLAB sau khi chn vi lnh Select
All. Lnh ny cho php xo tt c cc thng tin trong b nh ca chng trnh,
tng t nh vic ta ng Matlab li sau khi ng li Matlab.
C.MENU VIEWnh du chn hin hay n thanh cng c trong khung ca s lnh
MATLAB COMMAND WINDOW.
D.MENU WINDOW
Hin thng tin v s tp tin ang m trong khung ca s lnh MATLAB.
1.2.8. Mt s phm chuyn dng v lnh thng dng
( Hoc Ctrl + p : Gi li cc lnh thc hin trc .
( Hoc Ctrl +n : Gi li lnh va thc hin trc .
( Hoc Ctrl + f : chuyn con tr sang bn phi 1 k t.
( hoc Ctrl + b: chuyn con tr sang tri mt k t.
Du ; dng trong [] kt thc mt hng ca ma trn hoc kt thc mt biu thc
hoc cu lnh m khng hin th kt qu ra m hnh.
nhy xung dng di
Ctrl + A hoc Home : chuyn con tr v u dng.
Ctrl + E hoc End: Chuyn con tr n cui dng.
BackSpace: Xo k t bn tri con tr.
Esc: xo dng lnh.
Ctrl + K : Xo t v tr con tr n cui dng.
Ctrl + C : Dng chng trnh ang thc hin.
Clc : lnh xo mn hnh.
Clf: Lnh xo mn hnh ho.
Input: lnh nhp d liu vo t bn phm.
Demo: lnh cho php xem cc chng trnh mu.
Help: lnh cho php xem phn tr gip.
Ctrl c: Dng chng trnh khi n b ri vo trng thi lp khng kt thc.
Dng lnh di: Nu dng lnh di qu th dng chuyn xung dng di.
1.2.9.Bin trong Matlab
a.c im ca bin trong Matlab:- Khng cn khai bo bin v kiu ca bin.
Tuy nhin trc khi gn mt bin thnh mt bin khc th cn m bo rng bin bn
phi ca php gn c mt gi tr xc nh.
- Bt k mt php ton no gn mt gi tr vo mt bin s to ra bin nu cn
(bin cha xc nh) hoc ghi ln gi tr hin ti nu n tn ti trong
Workspace.
- Tn bin bao gm mt ch ci sau mt s bt k cc ch ci, ch s v du gch
di. Matlab phn bit ch in hoa v ch in thng, v vy X v x l hai bin phn
bit.
- Tn bin l mt dy k t bao gm cc ch ci hay cc ch s hoc mt s k t c
bit dng ch tn ca bin hoc tn ca hm. Chng phi c bt u bng ch ci sau c
th l cc ch s hoc mt vi k t c bit. Chiu di ti a ca tn l 31 k t.
- Bnh thng Matlab c s phn bit cc bin to bi ch ci thng v ch ci in
hoa. Cc lnh ca Matlab ni chung thng s dng ch ci thng. Vic phn bit c
th c b qua nu chng ta thc hin lnh : >> casensen off
b. Mt s lnh vi bin
clear: lnh xo tt c cc bin c nh ngha trc trong chng trnh .
clear bin1, bin 2... : xo cc bin c lit k trong cu lnh.
Who: hin th cc bin c nh ngha trong chng trnh.
Whos: hin th cc bin c nh ngha trong chng trnh cng vi cc thng s v
bin.
Size (tn bin c nh ngha): cho bit kch c ca bin di dng ma trn vi
phn t th nht l s hng ca ma trn, phn t th 2 l s ct ca ma trn.
Save: Lu gi cc bin vo mt File c tn l Matlab. mat.
Load: Ti cc bin c lu gi trong mt File a vo vng lm vic.
c.Mt s bin c nh ngha trc
ans: Answer - t ng gn tn ny cho kt qu ca mt php tnh m ta khng t
tn. VD >> [ 1 2]
ans =
2
- pi ( = 3.1415926535897...
realmax: a ra gi tr ca s ln nht m my tnh c th tnh ton c.
realmin: a ra gi tr ca s nh nht m my tnh c th tnh ton c.
i, j: n v o ca s phc.
inf: infinity- v cng ln.
1.2.10. Cc php ton trong Matlab
a.Php ton s hc
Matlab c hai kiu php ton s hc, l php ton ma trn (matrix
arithmetic operation) v php ton mng (array arithmetic operation).
Php ton ma trn c nh ngha bi cc lut ca i s tuyn tnh. Php ton mng c
thc hin tng ng tng phn t, chng hn php nhn mng hai ma trn A c cc phn
t l a(i,j) v B c cc phn t l b(i,j) c thc hin bng cch nhn tng ng tng
phn t ca A v B:
c(i,j) = a(i,j)b(i,j)
phn bit gia php ton ma trn v php ton mng ngi ta a thm vo trc cc
ton t mt du chm ..
Php ton ma trnPhp ton mng
Php tonTon tPhp tonTon t
Cng
Tr
Nhn
Chia phi
Chia tri
Lu tha
Php gn+
-
*
/
\
^
=Cng
Tr.
Nhn.
Chia phi
Chia tri
Lu tha.
Php gn.+
-
.*
./
.\
.^
=
b.Th t u tin trong php ton s hc
ngoc n.
lu tha
nhn, chia.
Cng, tr.
c.Cc php ton quan h v php ton logic
Cc php ton quan h bao gm:
Nh hn: =
Bng: ==
Khng bng (khc): ~=
Biu thc c cc ton t quan h nhn gia tr ng l (true) hoc sai
(false). Trong Matlab, biu thc ng s c gi tr l 1, biu thc sai c gia
tr l 0.
V d 1
>>12.2>12
ans =
1
>>1~=1
ans =
0>> A=[ 1:3;4:6;7:9]
A =
1 2 3
4 5 6
7 8 9
>> A=[ 1:3;4:6;7:9]
A =
1 2 3
4 5 6
7 8 9
>> B=[1:3;2:4;10:12]
B =
1 2 3
2 3 4
10 11 12>> A==B
ans =
1 1 1
0 0 0
0 0 0
1.3.S dng cc lnh trc tip t Matlab
V d 1: Gii phng trnh bc hai ax2 +bx +c = 0Ta bit cc nghim ca
phng trnh ny c dng:
x =
V Matlab l mt chng trnh tnh ton s nn chng ta phi xc nh cc gi tr
a, b, c.
Du = c s dng gn gi tr ca a, b, c nh sau ( g phm Enter cui mi
hng)
>>a = 2
a =
2
>>b = 5;
>>c = -3; %Du ; cui dng th Matlab s khng hin th li gi tr
va nhp.
>> x1= (-b + sqrt(b^2- 4*a*c))/(2*a)
x1 =
0.5000
>> x2= (-b - sqrt(b^2- 4*a*c))/(2*a)
x2 =
-3
V d 2: Tnh gi tr ca a thc.>> a = x^3 -2*x^2 - 6;
>>b = x^2 + 5*x -7;
>>x=3;
>> w = a/b
w =
0.1765
1.4. S dng cc lnh t file lnh
Nhng lnh ca Matlab c th c a vo mt file. Sau bn s hng dn Matlab
lm vic vi cc lnh . By gi, vi v d 1, chng ta s a ton b cc lnh trn vo
mt file ly tn l vidu.m. Tn ca file phi c bt u bng mt k t v phn m
rng l .m. Cc bc nh sau:
Bc 1: File / New/ M-file, Mi trng son tho Editor / Debugger s
xut hin
Bc 2: Trn mn hnh son tho, ta g cc lnh ca Matlab.
a = 2;
b = 5;
c=-3;
x1= (-b + sqrt(b^2- 4*a*c))/(2*a)
x2= (-b - sqrt(b^2- 4*a*c))/(2*a)
Bc 3: Ghi li ni dung tp tin vi tn vidu.m ri thot khi mi trng son
tho tr v ca s lnh (Matlab Command window).
Bc 4: Ti ca s lnh ta g tn tp tin.
>>vidu.m
1.5. Dng nhc gn gi tr cc bin
thay i cc gi tr a,b,c ta phi son tho li file vidu.m ri chy li.
Ta sa li chng trnh c dng nhc nhp a,.b,c vi cc ln chy chng trnh khc
nhau.
Bc 1: File / New/ M-file, Mi trng son tho Editor/Debugger s xut
hin (hnh 3.1)
Bc 2: Son tho nhng dng lnh sau trong ca s Matlab
Editor/Debugger:
a=input('nhap a= ');
b=input('nhap b= ');
c=input('nhap c= ');
x1=(-b+sqrt(b^2-4*a*c))/2*a)
x2=(-b-sqrt(b^2-4*a*c))/2*a)
Bc 3: Lu li ni dung tp tin vi tn vidu.m
Bc 4: Quay li ca s Matlab Command Windows. Ti ca s lnh ta g tn
tp tin.
>>vidu
nhap vao a= 3
nhap vao b= -4
nhap vao c= 1
x1 =
1
x2 =
0.3333
Hai nghim ng vi cc gia tr a,b,c va nhp vo v l nghim thc.
Hnh 3.3 l trng hp phng trnh c nghim o.
VD v Script file: Gii bi tp mch: cho mch in nh hnh v
Hy tnh dng trong mch v in p trn tng phn t .
Hy vo ca s son tho v trong ca s ny ta vit chng trnh nh sau:
R=input( 'nhap gia tri cho R = ')
C=input( 'nhap gia tri cho C = ')
L=input( 'nhap gia tri cho L = ')
U=input( 'nhap gia tri cho U = ')
ZL=2*50*pi*L*i
ZC=1/(2*50*pi*C*i)
Z=R+ZL+ZC
i= U/Z
UR=i*R
UL=i*ZL
UC=i*ZC
Sau khi vit xong chng trnh ta kch vo biu tng save trong ca s son
tho v tn l vd1.
Mun chy ta tr li ca s MATLAB command Window v t du nhc lnh:
>> vd1
nhap gia tri cho R = 1000
R = 1000
nhap gia tri cho C = 0.1
C = 0.1000
nhap gia tri cho L = 0.2
L = 0.2000
nhap gia tri cho U = 220
U = 220
ZL = 0 +62.8319i
ZC = 0 - 0.0318i
Z = 1.0000e+003 +6.2800e+001i
i = 0.2191 - 0.0138i
UR = 2.1914e+002 -1.3762e+001i
UL = 0.8647 +13.7687i
UC = -0.0004 - 0.0070i
1.6. Cc to mt hm
Mi mt file hm ca Matlab (M - file) u c khai bo nh sau:
Function [Tn kt qu] = tn hm (danh sch cc bin).
Phn thn ca chng trnh trong hm l cc lnh ca Matlab thc hin vic tnh
ton gi tr ca i lng c nu trong phn tn kt qu theo cc bin c nu tronhg
phn danh sch bin. Cc bin ch c tc dng ni trong hm va c khai bo. Tn
ca cc bin dc cch nhau bnh du phy (,).
V d ta thnh lp hm i t sang radian:
function rad = change(do)
rad = do*pi/180; % doi do sang radian
Trong Matlab cc dng ghi ch sau du % khng c tc dng thc thi, chng
n gin l nhng dng nhc ngi c chng trnh d hiu m thi. File.m thng ly tn
l tn ca hm, ta t tn file hm va lp l change.m. Nu mun i 450 sang
radian, ch cn g:
>>rad = change(45)
rad =
0.7854
V du: to hm gii phng trnh bc hai, tn tp tin c t l bachai.m.
function [x1,x2] = bachai(a,b,c)
delta = b^2-4*a*c;
x1 = (-b + sqrt(delta))/(2*a);
x2 = (-b - sqrt(delta))/(2*a);
>>[x1,x2]=bachai1(4,6,-7)
x1 =
0.77707
x2 =
-2.2707
1.7. S dng hm c sn
C rt nhiu hm c sn, l cc hm c lp trnh sn v c a vo th vin. xem mt
hm cng nh cu trc v cch s dng ta dng lnh
>>help tn_hm
V d Ta mun xem cu trc hm ode23
>>help ode23
1.8. V cc hm
Khi mun v mt hm no , phi xc nh hm trong mt file.m sau s dng lnh
:
Fplot(tn hm,[khong v])
V d v hm y = 4x2+6x-7 trong on [-6, 6], ta lp file
bachai1.m.
function y = bachai1(x)
a = 4;b = 6; c = -7;
y =a*x^2 + b*x + c;
>>fplot(bachai1, [-6,6])
1.9. Lu v ly d liu
Ta c th c th to lp mt file d liu, sau khi cn dng th ly ra. V d
to lp mt ma trn A:
Sau ta lu ma trn vo mt file c tn l dulieu1.
>>A = [1 1.1 1.2;2 2.1 2.2;3 3.2 3.2]
A =
1.0000 1.1000 1.2000
2.0000 2.1000 2.2000
3.0000 3.2000 3.2000
>>save dulieu1
Nh vy, ta c mt file d liu (file ny nm trong th mc work ca
Matlab). Khi cn s dng file d liu ny, ta ly nh sau:
>>load dlieu
Sau lnh load, ta c th ly d liu s dng:
>>A
A =
1.0000 1.1000 1.2000
2.0000 2.1000 2.2000
3.0000 3.2000 3.2000
1.10. Cc ton t Logic v cc lnh iu kin
1.10.1.Cc ton t logic
a.Php v( and): K hiu l &VD: php & 2 ma trn cng c A, B l
mt ma trn c cc phn t bng 1 nu cc phn t tng ng ca c 2 ma trn u u khc
0 v bng 0 nu 1 trong 2 phn t tng ng ca 2 ma trn bng 0.
>>A=[1 2 7; 0 4 9;1 3 5]; B=[0 2 4; 2 4 6; 3 0 7];
C=A&B
C =
0 1 1
0 1 1
1 0 1
b. Php hoc (or) : K hiu l |
VD : php or 2 ma trn cng c A,B l mt ma trn c cc phn t bng 0 nu
cc phn t tng ng ca c 2 ma trn u u bng 0 v bng 1 nu 1 trong 2 phn t
tng ng ca 2 ma trn khc 0.
>>A=[0 2 7; 0 4 9;1 3 0];
>> B=[0 2 4; 2 4 6; 3 0 0];
>> C=A | B
C =
0 1 1
1 1 1
1 1 0
c.Php o( not): K hiu l ~
V D : php o ca mt ma trn l mt ma trn c cng c vi cc phn t c gi tr
bng 1 nu cc phn t ca ma trn u c gi tr bng 0 v bng 0 nu cc phn t ca
ma trn u c gi tr khc 0.
>>A=[0 2 7; 0 4 9;1 3 0]
>> B=~A
B =
1 0 0
1 0 0
0 0 1
1.10.2. Cu trc cu lnh iu kin:
a.Lnh if n:
C php: if
Nhm lnh;
end
Nu biu thc logic ng nhm lnh s c thc hin. Nu biu thc logic sai th
chng trnh chuyn n lnh sau end.
VD:
function y=f(a,b,c)
if a> ht(2,4,2) hinh thang nguocans = 6b. Cu trc lnh if
lng nhau:C php: if Nhm lnh 1;if Nhm lnh 2;endNhm lnh 3;endNhm lnh
4;Nu biu thc logic 1 ng th Thc hin nhm lnh 1. Kim tra biu thc logic
2. Nu ng thc hin nhm lnh 2 Nu sai b qua nhm lnh 2 Thc hin nhm lnh
3.Nu biu thc logic 1 sai th Thc hin nhm lnh 4.c.Lnh else:C php: if
Nhm lnh A;elseNhm lnh B;endNhm lnh A s c thc hin nu biu thc logic
ng. Nu khng nhm lnh B s c thc hin.d. Lnh elseifC php: if Nhm lnh
A;elseif < BT logic 2>Nhm lnh B;elseif < BT logic 3>Nhm
lnh C;......endNu BT logic 1 ng nhm lnh A s c thc hin. Nu sai kim
tra Btlogic 2, nu ng thc hin nhm lnh B. Nu sai kim tra BT logic3,nu
ng thc hin nhm lnh CNu khng c biu thc logic no ng th khng c lnh no
trong cu trc trn c thc hin.e.Kt hp cu trc elseif v elseC php: if
Nhm lnh A;elseif < BT logic 2>Nhm lnh B;elseif < BT logic
3>Nhm lnh C;......else < BT logic n>Nhm lnh n;endNu BT
logic 1 ng nhm lnh A s c thc hin. Nu sai kim tra Btlogic 2, nu ng
thc hin nhm lnh B. Nu sai kim tra BT logic3, nu ng thc hin nhm lnh
CNu khng c biu thc logic no ng th nhm lnh n c thc hin.a=input(' vao
a=')b=input(' vao b=')c=input(' vao c=')d=b^2-4*a*cif d < 0
disp(' pt vo nghiem')elseif d==0 disp (' pt co nghiem kep')
x12=-b/2*aelse disp (' pt co 2 nghiem phan biet')
x1=(-b+sqrt(d))/2*a x2=(-b-sqrt(d))/2*aendf.Cu iu kin v lnh BreakC
php: if< biu thc logic> break endthot khi vng lp nu iu kin
logic ng. Ngc li s thc hin lnh tip theo trong vng lp.1.11.Vng
lp1.11.1.Vng lp forc php: for ch s = biu thcnhm lnh ;endV d 1: Tnh
tng ca n s t nhin lin tip, n vo t bn phm (vit trong Script
file):n=input('vao so tu nhien n=');s=0;for i=1:n;
s=s+i;enddisp(s)V d 2: bc tnh ca bin c th khc 1:n=input('vao so tu
nhien n=');s=0;for i=1:5:n; s=s+i;enddisp(s)1.11.2.Vng lp for lng
nhauc php: for ch s 1 = biu thc 1for ch s 2 = biu thc 2nhm lnh 2end
nhm lnh 1;endV d: n=input(' vao n=');m=input(' vao m=');for i=1:n;
for j=1:m; a(i,j)=i+j; disp([a(i,j)]) end disp(i)endVD3:n=4a =
zeros(n,n) % To ma trn khngfor i = 1:nfor j = 1:na(i,j) = 1/(i+j
1);endenddisp(Ket qua =)disp(a)1.11.3.Vng lp WhileC php: while <
biu thc>Nhm lnh A;endNu biu thc ng th thc hin nhm lnh A. Khi thc
hin xong th kim tra la iu kin. Nu iu kin vn ng li thc hin nhm lnh
A. Nu sai vng lp kt thc.1.11.4 Cc lnh break, return, error:Lnh
break: kt thc s th thi vng lp for hoc whileLnh return: thng c s dng
trong cc hm ca Matlab. Lnh return s cho php quay tr v thc thi nhng
lnh nm trong tc dng ca lnh return.Lnh error (dng nhn): kt thc thc
thi lnh v hin th dng nhn trn mn hnh.V d: Chn mt s dng bt k. Nu s l
s chn th chia ht cho hai. Nu s l s l th nhn vi 3 ri cng 1. Lp li qu
trnh cho n khi kt qu l 1. Chng trnh: while 1 n=input ('Nhap vao mot
so : '); if n1 if rem(n,2)== 0% phan du cua n chia cho 2 n=n/2 else
n= 3*n+1 end endKhi chy chng trnh ta s thy tc dng ca lnh break (dng
chng trnh khi nhp s m hoc s 0) 1.12. Bin ton cc (global variables)
Matlab cho php s dng cng mt bin cho cc hm hoc gia cc hm v chng trnh
chnh ca Matlab, iu ny c thc hin thng qua vic khai bo bin ton cc:
Global tn1 tn2 tn3 .(Tn cc bin cch nhau bng du khong trng, khng s
dng du phy). Vic khai bo bin ton cc phi c thc hin chng trnh chnh
hoc file lnh (script) hoc file hm (function) c s dng cc bin. Bin
ton cc c tc dng cho n khi kt thc qu trnh tnh ton hoc khi ton b
Workspace c xo. Khng c a tn bin ton cc vo danh sch cc i s ca hm.
Khi s dng bin ton cc cc lnh sau t ra rt cn thit: Clear global : Lnh
ny cho php loi b cc bin ton cc. Isglobal(Tn bin) : Lnh ny cho php
kim tra xem mt bin no c phi l bin ton cc hay khng. Nu l bin ton cc
th gi tr tr v s l 1.1.13.Mt s hm ton hcMc ny ch gii thiu mt s hm n
gin v thng gp trong khi lp trnh:Tn hmC phpGii thchsinsin(x)hm
sincoscos(x)hm costantan(x)hm tangasinasin(x)hm arcsinacosacos(x)hm
arccosatanatan(x)hm arctangacosacos(x)hm arccossinhsinh(x)--hm sin
hyperboliccoshcosh(x)hm cos hyperbolictanhtanh(x)hm tang
hyperbolicasinhasinh(x)hm arcsin hyperbolicacoshacosh(x)hm arccos
hyperbolicatanhatanh(x)hm arctang hyperbolicabsabs (x)Ly gi tr tuyt
i hoc ln ca s phcroundround(x)lm trn n s nguyn gn nhtfixfix(x)lm
trn hng v khngfloorfloor(x)lm trn hng v -ceilceil(x)lm trn hng v
+remrem(x)phn d sau khi chiagcdgcd(x)c s trung ln nhtlcmlcm(x)bi s
trung nh nhtexpexp(x)lu tha eloglog(x)logarit c s
elog2log2(x)logarit c s 2log10log10(x)logarit c s 101.14. nh dng s
Cc php tnh trong Matlab c thc hin vi chnh xc rt cao. Ta c th nh dng
cho cc s xut ra mn hnh tu theo mun bng cch s dng lnh format. Lnh ny
ch nh hng n vic hin th ca cc s m khng nh hng n vic tnh ton v lu gi
ca Matlab ngha l khng nh hng n chnh xc ca php tnh. Ta ly v d vi s
4/3: ti ca s lnh g vo dng lnh >>4/3( format short ( y l ch mc
nh ): a = 1.3333 format short e a = 1.3333e + 000 format long a =
1.33333333333333 format long e a = 1.33333333333333e + 000 format
bank a = 1.33 format hex a = 3ff5555555555555 format rat a=4/3 thay
i ch nh dng mc nh ta c th Preferences t menu File, chn nh dng s
mong mun t th (tap) General.Ngoi cc nh dng s trn, cn c hai nh dng b
i hoc thm vo cc dng trng gia cc kt qu ca lnh hoc gia cc dng lnh:
format compactlnh ny xo b cc dng trng lm cho ta c th quan st c nhiu
thng tin hn trn mn hnh hoc ca s. format loose s thm vo cc dng
trng.NI DUNG THO LUN 1. Ni dung phn tho lun 1: ci t v khai bao bin
trong Matlab, 2. Ni dung phn tho lun 2: to v s dng function v
script file. TM TT NI DUNG CT LICch ci t phn mm Matlab v thc hin cc
lnh c bn trong MatlabBI TP NG DNG, LIN H THC T1. Bi tp ng dng, lin
h thc t 1. Lp trnh M_file thc hin v cc th sau y1=10sin(x)+cos(2x);
y2=4x2+6x-7 Vi x nm trong khong [-5,5] trn cng 1 trc to 2. Bi tp ng
dng, lin h thc t 2.Lp trnh dng M_File nhp vo mt s n nguyn dng sau
tnh v a ra kt qu tng : S=1+2+3+....+n;HNG DN T NH Xem trc phn
Symbolic Math Toolbox .CHNG 2: SYMBOLIC TOOLBOXMC TIU CA CHNG- Hiu
r khi nim v kiu d liu Symbolic Math Toolbox - Vn dng c cc lnh vo
vic gii cc bi ton- V thi : Hc sinh, Sinh : nm c cc cu lnh v vn dng
gii cc bi tonNI DUNG BI GING L THUYT2.1. Gii thiu v
symbolicSymbolic Math Toolbox nh ngha mt kiu d liu mi ca Matlab gi
l i tng Symbolic. Mt i tng Symbolic l mt cu trc d liu lu tr mt i
din kiu su k t ca mt biu tng (Symbol). Symbolic Math Toolbox s dng
cc i tng Symbolic biu din cc bin, biu thc v Matlab trn
Symbolic.2.2. Lnh v hm trong Symbolic Matlab2.2.1. Cu trc : - Lnh
sym cho php xy dng cc bin v biu thc symbolic. V d:>> x =
sym(x); y = sym(y) % lnh ny to ra x,y l cc bin symbolic.- To cc bin
thc:>> x = sym(x, real);y =sym(y,real) %x,y l bin kiu thc
symbolicshoc >> x = sym(x, real) % x l bin kiu thc >> y
= sym(y) %y l bin bt k kiu symbolic xo c tnh real ca cc bin x, y ta
dng lnh sau: syms x y unreal hay:>>x = sym(x, unreal)>>
syms t>> Q = sym(Q(t)); % t bin symbolic v Q l hm symbolic.
2.2.2 Bin symbolic mc nhKhi vn dng cc hm ton hc, vic chn bin c lp
thng l r rng t ng cnh. V d, ta xem xt biu thc ton hc f = sin(a.t +
b) c biu din trong Matlab nh sau: f =. Nu ta cn tnh o hm ca biu thc
ny m khng xc nh bin c lp th theo quy c ton hc ta nhn c f =
a.cos(a.t + b). Gi thit rng bin c lp trong biu thc ny l t th cc bin
cn li a, b c xem nh cc hng s hoc tham s. Theo quy c ton hc th bin c
lp thng l cc ch in thng nm cui bng ch ci (v d: x, y, z, t, u, v,).
>>syms a b t>>f = sin(a*t + b);>>diff(f)%Lnh ny
tnh o hm ca biu thc symbolic f.trong cu lnh diff(f), ta khng xc nh
l o hm biu thc f theo bin no (a, b hay x). Lm th no Matlab xc nh c
ta mun o hm theo bin t m khng phi l a hoc b. Trong symbolic math
toolbox s dng mt bin symbolic xc nh bin c lp mc nh trong trng hp
chng ta khng xc nh bin c lp, l mt hm tin ch findsym. Bin symbolic
mc nh c s dng trong cc php ton tnh ton, n gin ho biu thc, gii phng
trnh v cc php bin i.>>findsym(f,1) ans = t y, i s th hai
trong hm findsym biu th s bin symbolic m ta mun tm trong biu thc f.
Nu khng xc nh i s th hai th findsym s tr v mt danh sch lit k tt c
cc bin trong biu thc. V d:>> findsym(f)ans = a, b, tLut
findsym: Bin c lp trong mt biu thc symbolic l mt ch ci gn ch x nht
trong bng ch ci. Nu c hai ch gn ch x th ch sau x trong bng ch ci c
chn.v d: >>findsym(a+c-v*y,1)ans= y2.2.3. Php o hm tnh o hm
ca mt biu thc symbolic ta s dng hm diff()+ diff(S): o hm biu thc
symbolic S vi bin t do c xc nh bi hm findsym(S)+ diff(S,v) hay
diff(S,sym(v)): o hm biu thc symbolic S vi bin ly o hm l bin
symbolic v ngha l thc hin php ton dS/dv+ diff(S,n) : o hm cp n biu
thc S, n l s nguyn dngV d: >>syms x t>> y =
sin(x^2);>>z = diff(y);z = 2*cos(x^2)*x>>pretty(z) %hin
th dng quen thuc 2.cos2x.x>>y = diff(t^6,6) % o hm bc 6 ca hm
t6.y = 720>>syms u v>>y = u^2*v - u*v^3;>> y2u =
diff(y,u,2) %dao ham cap 2 theo u y2u = 2*v>> y3u =
diff(y,v,3) %dao ham cap 3 theo v y3u = -6*u2.2.4. Php tch phn tnh
tch phn ca mt biu thc symbolic ta s dng hm int()+ int(S) : tch phn
khng xc nh ca biu thc symbolic S vi bin mc nh xc nh bi findsym.+
int(S, v): Tch phn khng xc nh ca biu thc symbolic S vi bin tch phn
v.+ int(S,a,b): Tch phn khng xc nh ca biu thc symbolic S vi bin t
do v cn ly tch phn t [a,b].+ int(S,v,a,b): Tch phn khng xc nh ca
biu thc symbolic S vi bin tch phn v v cn ly tch phn t [a,b].Vid:
>>syms x t z alpha >>int(-2*x/(1+x^2)^2) ans =
1/(1+x^2) >>int(x/(1+z^2),z) ans = x*atan(z)
>>int(x*log(1+x),0,1) ans = 1/4>>int(-2*x/(1+x^2)^2)
ans = 1/(1+x^2) >> int([exp(t),exp(alpha*t)]) ans = [ exp(t),
1/alpha*exp(alpha*t)]Vd: Tnh tch phn I = >>Syms x s
real>>f = exp(-(s*x)^2);>>I = int(f,x,-inf,inf)% inf -
Infinity l v cng lnI = Signum(s)/s*pi^(1/2)Hm signum chnh l hm sign
(hm du), ngha l sign(s) cho ta:sign(s) = 1 khi s>0; sign(s) = 0
khi s =0; sign(s) = -1 khi s>syms x a t h>>limit(sin(x)/x)
ans = 1>>limit(1/x,x,0,right) ans =
inf>>limit(1/x,x,0,left) ans =
-inf>>limit((sin(x+h)-sin(x))/h,h,0) ans = cos(x)>>v =
[(1+a/x)^x,exp(-x)];>>limit(v,x,inf,left) ans =
[exp(a),0]2.2.6. Tnh tng ca dy s symbolic tnh tng ca mt biu thc
symbolic ta s dng hm symsum()+ symsum(S): Tng ca biu thc symbolic
theo bin symbolic k , k c xc nh bng lnh findsym t 0k -1.+
symsum(S,v): Tng ca biu thc symbolic S theo bin symbolic v,v c xc
nh t 0k - 1.+ symsum(S,a,b), symsum(S,v,a,b): Tng ca biu thc
symbolic S theo symbolic v, v c xc nh t v = s n v = b.V d:
>>syms k n x>>symsum(k^2)ans =
1/3*k^3-1/2*k^2+1/6*k>>symsum(k) ans =
1/2*k^2-1/2*k>>symsum(sin(k*pi)/k,0,n) ans =
-1/2*sin(k*(n+1))/k+1/2*sin(k)/k/(cos(k)-1)*cos(k*(n+1))-1/2*sin(k)/k/(cos(k)-1)>>symsum(k^2,0,10)
ans = 385>>symsum(x^k/sym(k!), k, 0,inf) ans = exp(x)Vi d:
Cho tng ca 2 dyS1 = 1 + .S2 = 1 + x + x2 +..>>syms x
k>>s1 = symsum(1/k^2,1,inf) %inf l v cng.s1 =
1/6*pi^2>>s2 = symsum(x^k,k,0,inf)s2 = -1/(x-1)2.2.7. Tch t s
v mu s ca mt biu thc symbolic[n,d] = numden(A): bin i mi phn t ca A
thnh dng hu t trong t s v mu s l cc a thc (tng i) nguyn t vi cc h s
nguynV d: >>syms x y a b>>A= (4-x)/5;>>[n,d] =
numden(A) n = 4-x d = 5>>[n,d] = numden(x/y + y/x) n =
x^2+y^2d = y*x>>A = [a, 1/b]>>[n,d] = numden(A) n = [a,
1] d = [1, b]2.2.8 Thay thTa c th thay th cc bin trong biu thc bng
cc bin hay cc s thuc kiu khc bi lnh subs hoc lnh subexpr.Lnh subs c
cc dng sau:+ subs(S): Thay th tt c cc bin symbolic trong biu thc
bng cc gi tr c c t vic gi hm hoc t Workspace ca Matlab.+ subs(S,
new): Thay th bin symbolic t do trong S bng new.+ subs(S, old,
new): Thay th old bng new trong biu thc S. Old l mt bin symbolic,
mt su i din cho mt tn bin, hoc mt biu thc su k t. New c th l mt
bin, mt biu thc symbolic, bin s hoc biu thc s.V
d:>>subs(a+b,a,4)ans = 4+bgi thit trong Workspace tn ti a =
980 v C = 3, cu lnh y=dsolve(Dy = -a*y) tr v y = exp(-a*t)*C, khi
cu lnh:>>subs(y)ans = 3*exp(-980*t)Ta c th thay th nhiu bin
mt lc bng cch s dng c php sau:+ subs(S, {old1, old2, ,oldn}, {new1,
new2,, newn})v d: >> subs(cos(a)+sin(b),{a,b},{sym('x'),2})
ans = cos(x)+sin(2)Hm (S) vit li biu thc S theo cc biu thc con
chung: [Y,SIGMA] = subexpr(X,SIGMA) hoc [Y,SIGMA] =
subexpr(X,'SIGMA') vit li biu thc X theo biu thc con chung ca
n.2.2.9 Biu din biu thc symbolic di dng ton hc S dng hm pretty(S)
hin th S di dng d c hn nh trong quy c ton hc thng thng. V
d:>>s=2*cos(x)^2-sin(x)^2s =
2*cos(x)^2-sin(x)^2>>pretty(s) 2 22 cos(x) -
sin(x)>>syms x
a>>s=solve(x^3+a*x+1);>>pretty(s)2.2.10. Gii phng trnh
i sS dng lnh solve gii h phng trnh i s. Gi s S l mt biu thc
symbolic. Lnh solve(S) s c gng tm cc gi tr ca bin symbolic trong S
(c xc nh bi findsym(S)) lm cho S bng khng. Lnh solve( ) c cc c php
nh sau:+ solve(PT1, PT2, , PTn)+ solve(PT1, PT2, , PTn, v1, v2,,
vn) + solve(PT1, PT2, , PTn, v1, v2,, vn) trong PT l phng trnh, v1,
v2,,vn l cc bin hay n. Cc bin symbolic khng c lit k trong danh sch
i s c coi l cc tham s.2.2.11. Phng trnh vi phnHm dsolve tnh ton li
gii symbolic cho cc phng trnh vi phn thng. Cc phng trnh c xc nh bi
biu thc symbolic cha ch D biu din k hiu vi phn d/dt. Cc k hiu D2,
D3,, Dn tng ng vi o hm bc 2, 3,, n. V vy, D2y tng ng vi d2y/dt2.
Trong li gii dsolve th bin c lp mc nh l t. Lu rng tn ca bin
symbolic khng c cha k t D.iu kin u c th c xc nh bng cch b xung thm
cc phng trnh. Nu iu kin u khng c xc nh th li gii s cha cc hng s tch
phn C1, C2,...C php ca lnh dsolve: dsolve(PT1, PT2,, PTn)V
d:>>y = dsolve('(D2y) =1','y(0) = 1')y =
1/2*t^2+C1*t+1>>[x,y] = dsolve('Dx = y', 'Dy = -x') x=
cos(t)*C1+sin(t)*C2 y = -sin(t)*C1+cos(t)*C22.2.12 Bin i laplace v
laplace ngcPhp bin i laplace ca hm f(t) c nh ngha nh sau: v php bin
i laplace ngc l:+ L = laplace(F): Bin i Laplace ca hm F vi bin c lp
mc nh l t. Kt qu tr v l mt hm ca s. Nu F = F(s) th Laplace tr v mt
hm ca t: L = L(t). Theo nh ngha, L(s) = int(F(t)*exp(-s*t),0,inf) v
php tch phn c thc hin vi t+ L = laplace(F,t): L l mt hm ca t thay
th bin mc nh sTM TT NI DUNG CT LI- p dng matlab trong tnh ton mch
in, gii mch in nhanh chng tin li- p dng gii phng trnhv h phng trnh
tuyn tnh.- Gii cc phng trnh phi tuyn v PT tham s.- Gii h PT vi
phn.BI TP NG DNG, LIN H THC T1. Bi tp ng dng, lin h thc t 1. Cho hm
s : a. Hy nhp hm y vo trong mt file Matlab t ca s son tho.b. Hin th
hm y sau khi nhp cc h s.2. Bi tp ng dng, lin h thc t 2.Dng Matlab
tnh cc php ton sau:a) b) khi x (0.c ) Gii h phng trnh sau :HNG DN T
NH Xem trc phn Ma trn CHNG 3:MA TRN V MNG TRONG MATLABMC TIU CA
CHNG- Hiu r khi nim v ma trn v mng trong Matlab- Vn dng c cc lnh vo
vic gii cc bi ton- V thi : Hc sinh, Sinh : nm c cc cu lnh v vn dng
gii cc bi tonNI DUNG BI GING L THUYT3.1 Nhp ma trn trong
Matlab3.1.1 Cc Cch nhp matrn trong Matlab Matlab cung cp mt vi phng
tin cho ngi s dng to ra mt matrn, mi phng tin c nhng u im ca n v c
s dng tu theo tng yu cu bi ton.Ni chung Matlab cung cp ba phng tin.
Nhp Matrn trc tip t ca s command Window. Nhp Matrn t mt file( s dng
M-file hoc load) Nhp matrn t nhng hm c sn trong Matlab.a. Nhp Matrn
trc tip t ca s command WindowTrong mn hc ton cao cp chng ta bit nhp
mt matrn nh sauA=y l mt ma trn c s hng m = 3 v s ct n= 3 nhp matrn
trn trong Matlab ta nhp trc tip nh sau T dng nhc lnh trong ca s
command Window >> ta nhp>> A=[ 1,2,3 ; 4 5 ,6;7 8 9];
hoc >>A=[ 1 2 3 4 5 6 7 8 9]; Cc hng c cch nhau bng mt du chm
phy (;) nh trn,cc phn t trong mt hng c cch nhau bng du cch(thanh
space) hoc du phy(,) . Kt thc dng lnh c hoc khng c du ; Nu khng c
du chm phy cui dng th Matlab s in ra kt qu matrn va nhpNh v d
trn:>> A=[ 1,2,3 ; 4 5 ,6;7 8 9] nhn Enter s cho kt qu lA= 1
2 3 4 5 6Trong trng hp s phn t trn mt hng qu di ta c th xung dng
bng du ba chm ...V d >> b=[1,2,3,4,... 5 6 7 8 9] % y matrn 9
hng v mt ctLu rng trong mt s trng hp matrn hoc mng d liu di th vic
khng thm du chm phy sau cu lnh nhp, Matlab s in ra s liu di trong
ca s command Window, gy kh nhn cho ngi dngb. Nhp Matrn t M-file Ta
c th nhp mt matrn bng ca s son tho M-file, m ca s ny bng cch vo
File- New- M-file. Mt ca s son tho s c hin ra cho php bn son tho di
dng text, do l ca s son tho dng text cho nn bn c th son tho t file
word sau copy vo ca s M-file. nhp matrn ta son tho tng t nh trong
ca s command window sau lu vo file nh sau:V d:A=[1 2 3 ; 4 5 6 ; 7,
8,9];% khng c du chm phy s in ra kt quCng tng t nh trn nu s phn t
trn mt hng qu nhiu th ta c th xung dng A=[1 2 3 4 ... 5 6 7 8 9
10];Sau khi kt thc son tho ta lu vo tn_file . thc thi cc lnh nhp
trong M-file ta dng lnh sau trong command window nh sau: >>
ten_file ;c. Nhp matrn t cc hm c sn Matlab c mt th vin cc hm cho
php to ma trn.Sau y l mt s hm ones(m,n) to ma trn m hng v n ct ,vi
cc phn t u bng 1, ones(m) to ma trn vung cp m, vi cc phn t u l 1.
zeros(m,n) to ma trn kch thc m x n, vi cc phn t u bng 0, zeros(m)
to ma trn vung cp m. eyes(m,n) to ma trn kch thc m xn vi cc phn t u
bng 1, eyes(m) to ma trn vung cp m .v d:ones(2,3)ans= 1 1 1 1 1 1
eyes(2,3)ans= 1 0 0 0 1 0zeros(2,3)ans= 0 0 0 0 0 03.2 Ma trn s
phcS phc trong matlab c vit nh sau:V d s phc 3+4*i dng i ch s o
>> a=3+ 4*ia= 3+ 4*iNu mun ii ch s oTa nh ngha ii= sqrt(-1)
Sau bn vit:>> a=3+ 4*iia= 3+ 4*i>>A=[ 1+2*i , 3+4*i ;
5+6*i, 4+5*i ]A=[ 1+2*i 3+ 4*i 5+6*i 4+5*i ]3.3 To vec tKhi ta cn
kho st c tnh ca th no trong mt khong xc nh, khong xc nh ny c biu
din di dng vectV d kho st c tnh th trong khong x=1 n 100>> x=
1:100; % x ly gi tr t 1 n100, bc tng ca x l 1>>t=0: 0.1 :
10;% bc nhy l ca t l 0.1 Cng thc chung to vec t l X=Xmin : bc_tng:
Xmax3.4 Truy nhp cc phn t ca ma trn truy nhp cc phn t ca ma trn ta
lm nh sau:Gi s ma trn A=Th >> A(i,j) ; s truy nhp n phn t hng
th i v ct th jV d truy nhp n phn t th nht ta :>> A(1,1) ans=
1c bit gi ton b s hng hoc ton b s ct dng ton t (:)>> A(:,1) %
gi ton b s hng tng ng vi ct 1ans= 1 4 7>>A(1,:) % gi ton b s
ct tng ng hng 1ans=2 3>> A(1:2,1) % gi hng 1 n hng 2 tng ng
vi ct th nhtans= 1 4>>A(1:2,:) % gi hng 1 n hng 2 tng ng vi
tt c cc ct ans= 1 2 3 4 5 63.5 Php tnh ma trn v mnga. Php tnh ma
trn Php tnh cng , php tnh tr :iu kin hai ma trn A v B phi c cng kch
thc hoc mt trong hai l s v hngv d:>>a=[1 2 3 ;4 5 6; 7 8
9];>>b=[2 3 4; 5 6 7; 8 9 10];>>a+b;ans= 5 79 11 1315
17 19 Nhn hai ma trnA*B lu rng s ct ca ma trn A phi bng s ct ca ma
trn B, ngoi tr mt trong hai l s v hng Chia tri ma trn (\)X=A\B tng
ng vi vic gii h phng trnh tuyn tnh A*X=B, gn tng ng vi X=inv(A)*B
Chia phi ma trn(/)X=B/A tng ng vi vic gii phng trnh tuyn tnh X*A=B
gn tng ng vi X= B*inv(A)b. Php tnh dyCho hai mng sau:>>x=[1 2
3];>>y=[2 3 4]; Php tnh cng , tr ging nh php tnh i vi ma
trn>>x+yans=5 7 Php tnh nhn(.*)>>x.*yans= 2 6 12 Php
tnh chia(./ hoc .\)>> x./yans=0.5 0.66 0.75>>x .\yans=
2 1.5 0.753.6 Gii h phng trnh tuyn tnh3.6.1 H phng trnh tuyn tnh
:Xt h phng trnh sau: a11*x1 + a12*x2+ . . . +a1n*xn=b1 a21*x2 +
a22*x2+ . . . +a2n*xn=b2 . . am1*x1 + am2*x2+ . . . +amn*xn=bmBi
ton t ra l tm vc tor x=[x1;x2;x3....;xn] sao cho tho mn bi ton trn
3.6.2 H Phng trnh tuyn tnh khng ng nhtPhng trnh nh sau gi l phng
trnh tuyn tnh KN a1*x1 + a2*x2 + . . . + an*xn = b b ng c lp (n
khng nhn vi bin no c)Xt h thng sau: a11*x1 + a12*x2+ . . .
+a1n*xn=b1 a21*x2 + a22*x2+ . . . +a2n*xn=b2 . . am1*x1 + am2*x2+ .
. . +amn*xn=bmVit theo ma trn A= [a11 a12...a1n; a21
a22...a2n,....am1 am2...amn] X=[x1 x2.... xn]; B=[b1 b2 ...
bn];Trong A c gi l ma trn h s, X l vector kt qu3.6.2.1 Gii h phng
trnh bng hm nghch o invNu m=n th A l ma trn vung, v nu det(A) l khc
0 th tn ti A-1 v vector kt qu X c cho bi : A-1*A*X=X=A-1*BV d Gii h
sau: 2*x1 - x2 = 2 x1 + x2 = 5Matlab command >> A=[ 2 -1 ; 1
1 ]; >> B=[ 2 ; 5]; >> X= inv(A)*B >> X= 2.3333
2.667 >> X= rats(X) X= 7/3 8/3Tuy nhin chng ta khng th p dng
phng php trn cho 2*x1 - x2 = 2 2*x1 - x2 = 0Ma trn h s A=[ 2 -1 ; 2
-1];V det(A)=0 => khng p dng c hm nghch o cho ma trn A3.6.3 H
phng trnh tuyn tnh ng nhtBiu din di dng ma trn nh sau A*x=0 Nu
det(A)#0 h c nghim duy nht l X=0V d xt h phng trnh tuyn tnh sau
2*x1 - x2=0 x1+ x2=0 y det(A)= 3 cho nghim x1=0 , x2=0 i vi h phng
trnh thun nht c det(A)=0 th h ny c v s nghim V d Xt h phng trnh
tuyn tnh sau -6* x1 + 3*x2 = 0 2* x1 - x2 = 0Ma trn h s A= [ -6 3 ;
2 -1] , det(A)= 0 biu din trn th thy rng hai ng ny trng nhau do vy
h trn c v s nghim Trng hp s bin n< s phng trnh mV d nh sau: 3*x1
+ 4*x2 - 2*x3= 0 -2*x1 + 3*x2 - 4*x3= 0 5*x1 + x2 + 2*x3= 0 -9*x1 +
5*x2 - 10*x3= 0Ma trn h s l ma trn 4 x 3 ,nh thc ln nht c th c xy
dng t ma trn A l nh thc ma trn 3 x 3, nhng nh thc ca ma trn kch thc
3 by 3 =0 ( A1=[ 3 4 - 2; -2 3 - 4 ; 5 1 2]=> det(A1)=0 )Do ta
xc nh tip ma trn 2 x 2V d nh sauA2=[ 3 4; -2 3] v det(A) # 0 ta ni
rng hng ca ma trn A(ma trn h s) l bng 2 ng ngha vi vic ta ch gii
hai phng trnh bt k trong s tt c cc phng trnh trn, v s bin chng ta
gn gi tr tu l = n- r ( trong n l s bin cn r l hng ca ma trn A) Gii
hai phng trnh : 3*x1 + 4*x2 - 2*x3= 0 -2*x1 + 3*x2 - 4*x3= 0Kt qu :
x1= (-10/17)*x3 v x2=(16/17)*x3 , vi x3 ly gi tr tu 3.6.4 Gii h
phng trnh tuyn tnh bng Matlab(Dng ton t \) 2*x1 - x2 = 2 x1 + x2 =
5>> A=[ 2 -1 ; 1 1];>> B=[2 ; 5];>>X=A\BPhng php
gii ny gi l phng php Gaussian eliminationTon t (\) thng thng cung
cp mt kt qu trong Matlab , trong mt s trng hp n l phng php gii ring
3.7 iu kin c nghim Theo Kronecker-Capelli th Mt h phng trnh c mt li
gii khi v ch khi ma trn h s A v ma trn [A B] c cng hng.Gi s hng ca
hai ma trn u l r th xy ra cc trng hp sau y r=n H phng trnh c nghim
duy nht, r< n H phng trnh c v s nghim, chng ta c th gii cho r
bin nh l hm ca n-r bin khc ,cc bin khc ny c th ly gi tr tu V d
trnrank(a)= rank([a b]) = n cho nn h nghim duy nht >>
rank(A), rank([A B]) ans= 2 ans= 2Chng ta xem xt v d sau: 2* x1 +
3* x2 + 4*x3 = 4 x1 + x2 + x3 = 5>> A=[ 2 3 4 ; 1 1
1];>>B=[ 4 ; 5];>>rank(A), rank([A B])ans= 2ans=
2>> X= A\BX= 8 0 3Hng ca hai ma trn A v [A B] bng nhau v bng
2 cho nn h c mt li gii , nhng do rank(A) < n cho nn ta ch gii
cho hai bin nh l hm ca bin cn li. Kt qu Matlab cho trn ch l mt trng
hp ring (n-r bin c gn =0)Xt h sau x1 + 2 *x2 + 3 *x3 = 12 3* x1 + 2
*x2 + x3 = 15 3*x1 + 4 *x2 + 7 *x3 = 13 10*x1 + 9 *x2 + 8 *x3 =
17Tnh ton bng Matlab nh sau>> A=[1 2 3 ; 3 2 1 ; 3 4 7; 10 9
8];>>B= [12 ; 15; 13 ; 17 ];>>rank(A), rank([A B])ans=
3ans=4>> X= A\Bans= 1.0887 -0.2527 1.5349Khi th li nh
sau>> A* ansans= 5.1882 4.2957 13.0000 20.8925Kt qu khng bng
BH phng trnh trn v nghim ,tuy nhin Matlab vn cho nghim ,nghim ny
khng phi nghim ng m l nghim xp x gii theo tiu chun bnh phng ti
thiu( ta khng cp ti)3.8 H iu kin yuChng ta ni rng mt vn c coi l iu
kin yu nu mt s thay i nh trong d liu s dn n thay i ln trong kt qu.
iu ny l rt nguy him i vi cc k s lm vic vi cc thit b , sai s cc thit
b , sai s do lm trn (iu ny chc chn xy ra) Nu d liu ny l u vo i vi
vn trn th kt qu thu c s khng khip Vn chng ta bn ti l iu kin yu ca h
phng trnh tuyn tnhMa trn yu in hnh l ma trn Hibert c dng nh sau:A=[
1 1/2 1/3.....1/n;1/2 1/3 ...1/(n+1) 1/3 1/4 1/5.... 1/(n+2) 1/n ..
1/(2n)]V d sau y: Gii h phng trnh tuyn tnh c ma trn h s sau A=[1 1;
1 1.01] B=[2 ; 2.01]; >> X= A\B X= 1.0000 1.0000Mt sai s nh c
th hin trong long format >> format long; X= A\B X=
1.000000000002 0.999999999998Nu ta thay i mt phn t ca A v d A(1,
2)=1.005 >> A(1,2)=1.005 ; X= A\B X= -0.0000000099991
1.9999999999991Thay i A(1,2) =1.005 so vi gi tr c l 1 tc l tng 0.5%
tng ng vi gi tr x(1) gim 101%, v tng x(2) tng 100%Cch gii h phng
trnh iu kin yu A*X=BNu A l ma trn Hillbert s dng hm tnh nghch o
invhilb(n) trong n l kch thc ca ma trn V d >>A= [ 1/1 1/2 ;
1/2 1/3]; >> B=[1 ;1/2] >>X= invhilb(2)* bNu A khng phi
l ma trn hilbert th s dng hm symbolic V d A= [ 1 1.01; 0.5 1.02];
A=sym( [1 1.01 ; 0.5 1.02] ); B=[ 1.1; 1.2]; X= A\b3 .9 Lnh cond
Tnh iu kin ca ma trnCu trc:>> cond(A) % A l ma trn kt qu tr
li dng nh sau: a* 10k ; 0 < a < 9k l s digits khng tin cy
trong kt qu gii h phng trnh tuyn tnh v trong vic nghch o ma trn. Nu
k xp x 1 th l ma trn c well -conditionV d >>A=[1/2 1/3 1/4 ;
1/3 1/4 1/5; 1/4 1/5 1/6]; >> cond(A) ans= 1.3533e+003Ta thy
rng k= 3 tc l c 3 s khng ng tin cyTng kt nh ngha :Hng ma trn Ar l
mt ma trn r hng r ct c xy dng t A , khng nht thit theo th t trong
ma trn A v det(Ar)#0 .Nu bt k ma trn Ar+1 no c xy dng t r+1 hng v
r+1 ct ca A, det(Ar+1)=0 th chng ta ni rng Matrn A c hng bng rMt h
thng m phng trnh tuyn tnh trong n bin (cha bit) a11*x1 + a12*x2+ .
. . +a1n*xn=b1 a21*x1 + a22*x2+ . . . +a2n*xn=b2 . . am1*x1 +
am2*x2+ . . . +amn*xn=bmC th vit di dng form ma trn AX=BTrong A l
ma trn h s v X l vector kt qu iu kin c nghim Matrn [A B] c gi l ma
trn m rng ca h. Theo Kronecker- Capelli th h phng trnh tuyn tnh c
nghim khi v ch khi hng ca ma trn A bng hng ca ma trn b xung Nu r= n
th nghim trn l duy nht Nu r Plot ( tn bin , tn hm)VD 1: v hm y =
sin (x) >> x = 0 : 0.1 : 10 ;% To vecter x t 0 ( 10 vi bc
0.1.>> y = sin(x);% Nhp hm. >> plot (x,y) % V hm y theo
bin x.>>grid on % To chia cho th.VD 2: v th y = ax+ bx vi a =
sin, b = cosx bin thin t 0 n 2*pi.>> x = 0: pi/100:
2*pi;>> y= sin(x)+cos(x);>> plot(x,y)>>grid onVD
3: To bin t hm linspace :Tn bin = linspace ( im u, im cui, s im cn
v )% v hm y = e-x.sin (x) vi x chy t 0 ( 50 vi s im cn v 50
im.>> x=linspace(0,10,50);>> y=exp(-x).*sin(x);>>
plot(x,y)4.3.2. th dng nh du: th dng nh du l loi th ch dng cc im nh
vng trn, hnh thoi . Thay v dng cc on thng ni li vi nhau.VD
4:>> a = [8 8.5 5 8 6.5 7 7.8 8.5 7 7.5 5 9 7.5
9.2];>>plot ( a,*);>>grid on4.3.3.V nhiu ng biu din trn
cng mt th:Cng mt bn th ta c th v nhiu th vi cc d liu khc nhau v loi
ng minh ho. Theo mc nh Matlab s t ng gn loi mu sc cho tng d liu phn
bit. Cng thc tng qut khi v nhiu th trn cng mt h to :Plot ( tn bin
1, tn hm1, tn bin 2, tn hm 2....)VD 5:>>x=0:0.1:10;>>
y1=sin(x);>> y2=sin(x).*3.^(-x);>> plot(x,y1,x,y2)4.3.4
Ch thch v kim sot th: title ( Tn tiu th ) xlabel ( Tn trc x) ylabel
( Tn trc y) text (x,y, chui k t) a mt chui k t vo im c to x,y trn
th. gtext(chui k t) a mt chui k t c xc nh bi du + hay con tr chut.
legend(chui 1,chui 2...) a ra mn hnh ho mt khung ch thch bao gm cc
chui. V tr ca khung c th c di chuyn bi chut. legend off: loi b chc
nng legend khi mn hnh ho. Grid on: bt ch li trong mn hnh ho. Grid
off: tt ch li trong mn hnh ho. Hold on: gi li cc th v ( dng v nhiu
th trn mt h trc to ) Hold off: ngc li vi hd onTrong Matlab ta c th
chn ng v v mu theo 1 trong cc kiu sau: K hiuMuK hiuKiuymcrgbwkvng
tixanhxanh l cyxanh thmtrngen.ox+*--.--Chm imVng trnDu xDu cngDu
saoNt linGch chmGch gchKhi ta dng lnh: plot(tn bin, tn hm,k hiu mu
k hiu kiu ng)VD 6: v hm Cos(x), cos (2x)>>
x=linspace(0,10,50);>> y=cos(x);y1 = cos(2*x);% v y bng du x
mu en, y1 bng du * mu xanh thm>> plot(x,y,xk,x,y1,*b);% Tn
th>> title(' Do thi ham cosx & ham cos2x')>>
xlabel(' Truc Hoanh')>> ylabel(' Truc Tung')>> grid
onGn gi tr thanh o: Ngoi gi tr thanh o theo mc nh ca chng trnh, c
th t chia thang o theo d liu ring.VD 7: >> x = -pi : .1 :
pi;>> y = sin(x);>> plot(x,y) >>
set(gca,Xtick,-pi : pi/2 : pi)>> set(gca,'Xticklabel',
'-pi','- pi/2','0',' pi/2','pi')4.3.5. th hnh thanh:Loi th ny thng
dng minh ho cc s liu theo dng thanh, c th theo trc x hoc trc y. VD8
: V biu khi lng nhp hng trong 12 thng.>> x = [230 255 270 210
170 240 265 280 240 300 320 345];>> bar (x)>>
xlabel(Thang)>> ylabel(Doanh
thu)>>set(gca,'Xticklabel','Th1','Th2','Th3','Th4','Th5','Th6','Th7','Th8','Th9','Th10','Th11','Th12')4.3.6.
th to cc: Thng c p dng trong lnh vc thin vn nh hng gi, hng di chuyn
ca cn boVD 9:>> th = [0:.1:10];>> r1 = th;>> r2 =
5*cos(th)+ 5;>> % mu en, ng chm.>> h1 =
polar(th,r1,'k.');>> set(h1,'Markersize',15)>> hold
on>> h2 = polar(th,r2,'k');% mu en, lin.4.3.7. th hnh Pie:L
loi th t l bch phn ca tng loi d liu minh ho. Theo mc nh Matlab s t
mu khc nhau cho tng thnh phn d liu.VD 10:>> x = [30 22 15 8
25];>> explot = [0 1 0 0 0];>> pie(x,explot)>>
colormap jet4.3.8.Hin nhiu th trong mt mn hnh: Trong mt mn hnh th,
c th cho hin nhiu th vi mi th l mt loi d liu khc nhau.VD
11:>> a = [3.2 4.1 5 6];>> b = [2.5 4 3.5 4.9];>>
subplot(2,1,1);plot(a)% to trc to >> subplot(2,1,2);plot(b)%
to trc to 4.3.9.Lnh staris: v th bc thang. VD 12:>>x = 0:
.25: 10;>>stairs (x,sin(x))4.4 Thc hnh v th 3- DLnh xc nh vng
v: >>a = linspace(1,5,50);>>b =
linspace(1,10,100);>>[ x,y] = meshgrid(a,b);>> z =
sin(x)+cos(y);Lnh v : plot3(x,y,z) : To cc i tng tuyn tnh trong mi
trng 3-D. VD 8:>> a =linspace(0,10,100);>>
b=linspace(0,6,100);>>[x,y]=meshgrid(a,b);>>z=sin(x)+cos(y);
>> plot3(x,y,z)Ngi ta dng lnhmesh(z): hnh v c
li.Vd>>a=linspace(0,10,100); >>
b=linspace(0,6,100);>> [x,y]=meshgrid(a,b);>>
z=sin(x).*cos(y);>> mesh(z) TM TT NI DUNG CT LI -Hiu c cch v
ha trong h 2D-3D -V th cho cc hm, Chn kiu ng v mu cho th, -V th li,
nhn, hp cha trc v li ch gii.BI TP NG DNG, LIN H THC TBi 1: V th cc
hm y=sin(x); y1=cos(x) vi x=0 : 2*pi;Bi 2: V th bar,bar3, barh v
stairs.V d v hm y=e^(-x2).Bi 3: Lnh plot3 v trong khng gian ba
chiu: C dng: plot3 ( x1, y1, z1, S1, x2, y2, z2, S2, .... ). Trong
x,y l cc vector hoc ma trn cn S l su k t dng cho khai bo mu, biu
tng hoc kiu ng.V d: v cc th hm s sau: x=sin(t), y=cos(t), z=t.HNG
DN T NH Xem trc phn c s phng php tnh CHNG 5: C S PHNG PHP TNHMC TIU
CA CHNG Cung cp cho sinh vin nhng kin thc c bn v ni dung, cu trc cu
lnh ca cc phng php tnhV thi : Hiu c ni dung cc thut ton p dng cho
cc bi ton ng dng, bi ton k thut v nm c cc cu trc cu lnh cc thut
tonNI DUNG BI GING L THUYT5.1. Ni suy v thut ton ni suy ngha: Trong
thc t khi o mt i lng vt l bt k ti nhng iu kin mi trng thay i (cn c
nhiu i lng khc thay i) ta nhn c cc gi tr ri rc v c tnh thng k, ng
vi mi thi im ta nhn c mt gi tr o nh vy khi ta mun xc nh gi tr o mt
thi im bt k th ta phi dng php ni suy.Trong chng ny ta ch tm hiu v
tnh ton cho 2 php ni suy l : + Ni suy lagrange cho bi ton mt chiu +
Ni suy lagrange cho bi ton hai chiu5.1.1 Ni suy lagrange cho bi ton
mt chiu Gi s c n im o ri rc tng ng vi kt qu o nh sau: x x0 x1 x2 .
. . . . . . . . . xn f f0 f1 f2 . . . . . . . . . . fnCng thc ni
suy lagrange bc N tnh gi tr o c ti mt im bt k l :Thut ton ni suy:%
thuat toan noi suy cho bai toan mot chieufunction T=NS1C(x,f,xa);
i=length(x); j=length(f); T=0;n=i; if(i~=j) error('Ban nhap sai');
end i=1; while(i x=[1 2 3 4]; >> f=[0.671 0.620 0.567 0.512];
>> interp1(x,f,1.5) ans = 0.64555.1.2 Ni suy cho bi ton hai
chiuMc ch ca bi ton: Xc nh gi tr f(x,y) ca mt v tr bt k trong mt mt
phng xc nh (bit cc to v gi tr cc im xung quanh x(i), x(i-1)...).
Mun xc nh gi tr ti mt im c v tr xi-1 y=[3 4];>> f=[5 6 7
8];>> xa=1.5,ya=3.5;>> g=C5(x,y,f,xa,ya)g = 6.5000C
nhiu cch ni suy tuy nhin chng ta ch xem xt hai phng php trn m
thi5.2 Gii phng trnh phi tuyn ngha: Dng phng php chia i xc nh nghim
ca cc phng trnh. Ni dung ton hc ca phng php:Xt phng trnh f(x)=0Trn
khong phn ly nghim [a b], chia i [a b] bi c=(a+b)/2Nu f(c)=0 th c l
nghim ca phng trnh, nu f(c)~=0 th so sanh du ca f(c) vi f(a) v
f(b), f(a)*f(c) < 0 khong phn ly nghim mi l [a c], f(c)*f(b)
< 0 th khong phn nghim l [c b]. Tip tc chia i cc khong phn ly
nghim cho n khi tm c gi tr cn no m f(cn)=0 th cn chnh l nghim.Tuy
nhin vic tm chnh xc cn l rt kh khn ngi ta ch tm nghim gn ng trong
mt sai s cho php, hnh 5.2.Nu sai s cho trc th s bc lp i hi l
(b-a)/2n=(ln(b-a)/tol)/0.6931;Trong b v a tng ng l cc khong phn ly
nghim miThut ton
gii:%------------------------------------------------------------------function
x= C5(a,b,t)% n la so lan lap % a la can duoi b la can treni=1;if(
f(a)*f(b)>0 ) disp('nhap lai a va b ');endwhile(abs(a-b)>t)
c=(a+b)/2; if( f(c)==0) disp('nghiem la x='); x=c; break; end
if(f(c)*f(a)> y=2*x.^2.*cos(x);>> trapz(x,y)ans =
0.5403>> t=[0:15:90]';>> x=t*pi/180;>> y=[sin(x)
cos(x)];>> trapz(x,y)ans =0.9943 s dng cng thc trn th x l
vctor ct c cng chiu di vi vector y, hoc y lmt mng m cc phn t c chiu
di ging x Tnh theo phng php thng thng chun:>> syms x>>
int(2*x^2*cos(x),0,1) ans = -2*sin(1)+4*cos(1) >>
eval(ans)ans = 0.4783Kt lun rng : phng php hnh thang gii theo trapz
th chnh xc km hn:5.3.2. Phng php Simpson
1/3I=)H=(b-a)/N;%----------------------- Chuong trinh viet theo
simpson--------function I= C5(a,b,n)% a va b la hai can% n la so
buoc tinhh=(b-a)/n;I=0;for i=0:n x=a+h*i; c=4; if((i==0)|(i==n))
c=1; end if(fix(i/2)*2==i) c=2; end
I=I+c*(2*x^2*cos(x));endI=I*h/3;Cch gii Dng matlab( for simpson)5.3
Dng Laplace gii bi ton trong L thuyt MchTrong L thuyt mch c rt nhiu
cc i lng o hm, cc i lng c th c bin i qua Laplace v thay th bi ton l
thuyt mch v bi ton gii bng Laplace.V dsyms t s;I1=
sym('I1(t)');k=laplace(I1,t,s); % Chuyen doi I1(t) sang Laplacesyms
t
s;I1=sym('I1(t)');laplace(i,t,s)dI1=sym('diff(I1(t),t)')l=laplace(dI1,t,s)
% chuyen dao ham I1(t) sang LaplaceCc lnh ph tr cn ch gii mt bi ton
k thuyt mch 1. Lnh collect( f , x) : l lnh nhm tha s chung theo bin
V d f= 2*x + 3*x; >>f= collect(f,x) f= 5*x2. Lnh thay th
subs( f,{ x,y,z},{ 1,2,3}) thay th x , y , z bng 1 2 3>> syms
x;>> syms R1 R2 R3;>> f= R1+R2 + R3*x;>>
subs(f,{R1,R2,R3},{1,2,3}) ans = 3+3*x3. Gii phng trnh :Chng ta
thay th phn t laplace(I1(t),t,s) bng LI1 nh sau>> syms t
s;>> sym(' diff( I1(t),t)');>> l=sym(' diff(
I1(t),t)');>> l=laplace(l,t,s) l =
s*laplace(I1(t),t,s)-I1(0)Ch : Sau khi gii ra nghim dng, p theo
laplace th ta chuyn i ngc li dng hm bin i ngc laplace (hm ngc l
illaplace)V d c thCho mch in c cc phng trnh nh sau:(dI1/dt)*R1 + R2
= I1*R3% gii h phong trnh trn bang cch bin i sang laplace%chng trnh
vit trong M-file v c ghi trong file C5.msyms R1 R2 R3
real;I1=sym('I1(t)');dI1=sym('diff(I1(t),t)');eq1= dI1*R1
+R2-I1*R3;syms t s ;q1=laplace(eq1,t,s)syms
I1p;q2=subs(q1,{R1,R2,R3,'I1(0)','laplace(I1(t),t,s)'},{1,2,3,2,I1p})q2=collect(q2,I1p);%
nhm li tha s chung l I1pI1p=solve(q2,I1p)% Gii phng trnh trn vi bin
I1pilaplace(I1p)% bin i ngc li sang I1(t)Kt qu khi thc hin chng
trnh trn l:>>C5q1 =
R1*(s*laplace(I1(t),t,s)-I1(0))+R2/s-R3*laplace(I1(t),t,s) q2 =
s*I1p-2+2/s-3*I1p I1p = 2*(s-1)/s/(s-3) % kt qu
I1(t)ans=2/3+4/3*exp(3*t) % kt qu I1(t) 5.4 Gii h phng trnh i s
tuyn tnh Phn ny trnh by chng II 'Th vin ton hc Symbolic'Mun gii trc
ht hm phi l hm symbolic ca mt hoc nhiu bin no >>syms x
y;>> [x,y]=solve('x+y=1','x-11*y=5',x,y)x = 4/3 y = -1/3>
syms x y;>> n=solve('x+y=1','x-11*y=5',x,y) % kt qu dng cu
trc n = x: [1x1 sym] y: [1x1 sym]>> n.x % truy nhp cu trc bin
x ans = 4/3 >> n.y % Truy nhp cu trc bin y ans = -1/35.5 Phng
trnh vi phn thngDSOLVE Symbolic tm nghim ca phng trnh vi phn
DSOLVE('eqn1','eqn2', ...) ch chp nhn cc biu thc vi phn dng
symbolic ('eq1'....) v iu kin u. Mt s phng trnh hoc cc iu kin u c
th c nhm li vi nhau v cch nhau bng du phy (comma), i vi mt thng s u
vo, mc nh l bin 't' bin c lp ny c th c thay i t 't' n cc bin
symbolic khc bng cch thm bin nh l thng s u vo cui cng V d: Gi s ta
cn gii phng trnh vi phn dy/dx= x*y bin ly tch phn(phi l) x cho nn
ta coi x l thng s u vo cui cng ta vit nh sau syms x
y=dsolve('Dy=x*y','Dy(0)=1','x');k hiu 'D' nh ngha phng trnh vi phn
tng ng vi bin c lp v d thng thng s dng dy/dt . ''D'' c theo sau bi
mt s ,th s nh ngha bc vi phn v d D2y ngha l d2y/dt2 v d sau:y =
dsolve('D2y+y=1','y(0) = 0')kt qu: y = 1+C1*sin(t)-cos(t)Cn D3y tc
l d3y/dt3 ch rng bin symbolic khng c cha trong D v d nh khng th ghi
nh sau: syms y; dsolve('Dy') (sai)iu kin u xc nh bi biu thc
'y(a)=b' hoc 'Dy(a)=b' y l mt trong nhng binph thuc v a v b l s
khng i nu s iu kin u nh hn s bin ph thuc th kt qu s c cho trong mng
C1,C2C ba kiu u ra. i vi mt phng trnh vi phn th c mt u ra, i vi h c
nhiu phng trnh vi phn th c s u ra tng ng (u ra c th l mt structer)
Examples: dsolve('Dx = -a*x') returns ans = exp(-a*t)*C1 x =
dsolve('Dx = -a*x','x(0) = 1','s') returns x = exp(-a*s) y =
dsolve('(Dy)^2 + y^2 = 1','y(0) = 0') returns y = [ sin(t)] [
-sin(t)] S = dsolve('Df = f + g','Dg = -f + g','f(0) = 1','g(0) =
2') returns a structure S with fields S.f =
exp(t)*cos(t)+2*exp(t)*sin(t) S.g = -exp(t)*sin(t)+2*exp(t)*cos(t)
Y = dsolve('Dy = y^2*(1-y)') Warning: Explicit solution could not
be found; implicit solution returned. Y =
t+1/y-log(y)+log(-1+y)+C1=0 dsolve('Df = f + sin(t)', 'f(pi/2) =
0') dsolve('D2y = -a^2*y', 'y(0) = 1, Dy(pi/a) = 0') S = dsolve('Dx
= y', 'Dy = -x', 'x(0)=0', 'y(0)=1') S = dsolve('Du=v, Dv=w,
Dw=-u','u(0)=0, v(0)=0, w(0)=1') w = dsolve('D3w = -w','w(0)=1,
Dw(0)=0, D2w(0)=0') y = dsolve('D2y = sin(y)'); pretty(y)S dng
ode23 v ode45 dng gii phng trnh vi phn thng Cu trc: [T,Y] =
ODE23(ODEFUN,TSPAN,Y0) TSPAN = [T0 TFINAL] t hp h phng trnh vi phn
y' = f(t,y) t thi gian T0 n TFINAL vi gi tr ban u Y0. Hm
ODEFUN(T,Y) chc chn tr v mt vc tor ct tng ng vi f(t,y). Mi hng
trong mng kt qu Y tng ng thi im(t) tr v trong column vector T ly kt
qu ti cc thi im T0,T1,...,TFINAL(tt c l tng u hoc gim u) s dng
TSPAN = [T0 T1 ... TFINAL]. V d: [t,y] = ode23(@vdp1,[0 20],[2 0]);
plot(t,y(:,1));% giai phuong trinh vi phan bac hai sau% L*d2q/dt2 +
R * dq/dt + q/c = Eo* cos(w*t)% nguyen tac giai global R L C Eo
omegaL=100;R=100;C=0.25;Eo=10;omega=1;%t0=0;%ta=3;%x0=[1
1]'tol=1e-3;[t,x]=ode23(@Mach1,[0 3],[1 1],tol);kq=[t x(:,1)
x(:,2)]plot(t,x(:,1));%-------------- Ham
Mach1--------------------------------function f= Mach1(t,x)global R
L C omega Eof=[(Eo/L)*cos(omega*t)-x(1)/(C*L)-R*x(2)/L
x(2)]';%-------------------ket qua thuc hien trong command
window------kq = 0 1.0000 1.0000 0.0800 0.9216 1.0833 0.3585 0.5926
1.4308 0.5589 0.2895 1.7484 0.7093 0.0171 2.0319 0.8596 -0.3011
2.3615 1.0069 -0.6642 2.7362 1.1900 -1.1987 3.2858 1.4006 -1.9498
4.0557 1.6323 -2.9833 5.1132 1.8804 -4.3902 6.5518 2.1408 -6.2933
8.4990 2.4104 -8.8576 11.1269 2.6868 -12.3044 14.6669 2.9682
-16.9303 19.4292 3.0000 -17.5398 20.0576Nguyn tc gii bi ton : a
phng trnh vi phn cp n v n phng trnh vi phn cp mt trong v d trn ta t
x1= q ,x2=diff(x1) nh vy ta c hai phng trnh vi phn (ging nh phng
php t bin trng thi trong l thuyt iu khin t ng) NI DUNG PHN THO
LUN1. Ni dung phn tho lun 1.Hy lp chng trnh cho bi ton ni suy
Lagrange 1 chiu trong khong [1:4]. Hy tm kt qu bt k trong khong .S
liu: x 1 2 3 4 f 0.67 0.620 0.567 0.5122. Ni dung phn tho lun 2.Tm
nghim phng trnh phi tuyn (bng phng php chia i khong) sau: y = 3x3
2x2 x +3 x ( [0,3]TM TT NI DUNG CT LI Sinh vin nm c nhng kin thc c
bn v ni dung, cu trc cu lnh ca cc phng php tnh p dng cho cc bi ton
ng dng, bi ton k thut BI TP NG DNG, LIN H THC T1. Bi tp ng dng, lin
h thc t 1.Tm nghim gn ng hm (phng php Newton)y = x3 5x2 +6x+12. Bi
tp ng dng, lin h thc t 2.Lp chng trnh tnh tch phn (phng php hnh
thang) sau: HNG DN T NHTnh tch phn hm y = (1+ x2 3x3+ + 4x5)dx vi
cn a=-1, b =1 theo phng php Simson.CHNG 6:M HNH HA,M PHNG H THNG MC
TIU CA CHNG Cung cp cho sinh vin nhng kin thc c bn v m hnh ha, m
phng h thng ng s dng Simulink - V thi : Hiu c kin thc c bn v m hnh
ha, m phng h thng ng s dng Simulink vn dng vo cc bi ton k thut.NI
DUNG BI GING L THUYT6.1 Khi nim v simulinkSimulink l mt phn mm gi
gn c s dng xy dng m hnh v m phng, tnh ton phn tch h thng ng.
Simulink cho php m t h thng tuyn tnh, h phi tuyn, cc m hnh trong
thi gian lin tc hoc gin on(ly mu ) hay kt hp c hai. i vi m hnh,
Simulink cung cp mt giao din ho (GUI) cho vic xy dng m hnh nh l cc
khi (block diagrams), ngi s dng ch cn kch chut v drag( chn khi ri
gi nguyn chut tri ri r chut n v tr t cc khi). Vi giao din giao tip
nh vy, bn c th v M hnh nh l m hnh bn v trn ''giy'' Th vin simulink
bao gm cc khi th vin sinks, sources(to tn hiu), linear. . . .V bn
cng c th t to ra mt khi block ring ca mnh (vit trong S-function)Xy
dng m hnh 't trn xung 'hoc 't di ln trn ' xem k cc khi trong th vin
cc khi source hoc sink linear . . . bn kch p chut vo cc khi . Sau
khi nh ngha m hnh bn c th m phng m hnh , s dng scope xem biu din m
hnh ,v d nh mt khi pht hnh sin , u ra ca khi c mc vi mt scope th
hin kt qu ca khi 6.2 Th vin simulink v mi trng lm vic Bt u vo vng
lm vic ca simulink trong ca s command window ta g lnh
>>simulink nh sau:Trn mn hnh s xut hin thm mt ca s mi , ca s
ny cha ton b d liu th vin ca Simulink, n c th di chuyn c bng chut
nh sau:Bn c th kch p chut vo tng khi xem cc khi con ca n(hoc bn nhp
n chut vo danh mc tng ng vi khi t simulink) v d bn chn khi sourceTo
mi trng lm vic T ca s Library Browser (xem hnh trn) ta kch chut vo
file danh sch cc mc New , Open , Preferences xut hin . to mi trng
lm vic (vng v m hnh) ta chn mc New ri chn Model Ctr+N mt ca s lm
vic xut hin Ca s lm vic nh saut li tn cho m hnh bng cch vo mc file
-> Save as 6.3. Phng php xy dng m hnh Tt c cc bc trn l chun b
cho vic xy dng m hnh m phng Gi s ta mun xy dng m hnh phn tch sng
sin trn ca s lm vic nh sau:(xem hnh v di y)Cc bc:Sau khi to mi trng
lm vic mi (cc bc gii thiu trn) tip n tm khi hm sin trong khi th vin
no ( bng cch chn tng khi bng chut t cc mc di Simulink) v d ny hm to
sin trong khi Source (xem hnh trn), dng chut chn vo khi SineWave gi
nguyn chut ri ko sang vng ca s lm vic , trn ca s lm vic xut hin khi
hm SineWave, tng t ta lm nh vy vi Scope trong khi Sink vic ni cc
khu vi nhau c cc mi tn , dng chut ni cc mi tn li.t li cc thng s ca
cc hm bng cch kch i ln cc khi(cc khi trong vng ca s lm vic). i vi
khi SinWave th c cc thng s c th thay i c l: + Chu k( tn s)
Frequency(rad/s) + Bin Amplitude + Sample time (thi gian ly mu)Khi
Scope:Sau khi hon tt t li cc thng s , n cng vic quan trong nht l kt
qu m phng :1. Trn thanh cng c nhp chut vo mc SimulationV chn Start2
. Hoc nhp vo nt tamgic nh trn(tc dng lnh ging nh vo lnh Start)3.
Mun Dng qu trnh ang m phng ta kch vo nt vung bn cnh nt tam gic(nt
ny ch xut hin khi ta ang m phng)4. xem kt qu ca khi SineWave ta kch
i chut vo ScopeNI DUNG PHN THO LUN1. Ni dung phn tho lun 1.Minh ho
chc n (trong khi ny c 1 lng kh ln cc hm ton c chun b sn to Function
ng ca cc khi Product (php nhn), Gain (khuch i tn hiu u vo), Math
Function). Hy m phng phng trnh sau: f(t) =
80exp(-1/80t)sin(0.25+pi/3)Tham s ca khi Sine WaveAmplitude:1,
Frequency (rad/sec): 0.25, Phase: pi/3, Sample time:02. Ni dung phn
tho lun 2. Lm VD s v th m phng ca h thng iu khin nh hnh v :Tm tt ni
dung ct li Sinh vin nm c nhng kin thc c bn v m hnh ha, m phng h
thng ng s dng Simulink vn dng vo cc bi ton k thut. BI TP NG DNG,
LIN H THC T1. Bi tp ng dng, lin h thc t 1.Hy xy dng m hnh m phng
sau:Khi trong ca SubSystem2. Bi tp ng dng, lin h thc t 2.Hy xy dng
m hnh m phng sau:Khi trong ca SubSystemHNG DN T NH S dng SIMULINK m
hnh ho h thng ng hc Kho st h thng ng hoc c khu b u vo. Lp chng m
phngYu cu bi:Cho cc tham s ca b PID: KP =5; Ki = 2; Kd = 0Cho u vo
l hm 1(t), kho st qu trnh qu trong hai trng hp sau:1. Khng b: K =
0Thi gian qu : Tqd =20sec qu iu chnh (max ca h thng: (max = 32.7(2.
Khng b: K = 1Thi gian qu : Tqd =20sec. qu iu chnh (max ca h thng:
(max = 24.9(TI LIU THAM KHODANH MC T KHAHnh 1.3. La chn cc thnh phn
ca Matlab s c ci tHnh 1.2. Ca s Software License Agreement v ca s
thng tin v khch hngHnh 1. Ci t Matlab trong Windows v mn hnh
Welcome1 2 34 5 67 8 9 EMBED Equation.3 Hnh 1.4. Qu trnh copy file
ca chng trnh vo th mc ci t EMBED PBrush EMBED PBrush EMBED PBrush
Hnh 1.4. Ca s Command Windows ca Matlab EMBED PBrush EMBED PBrush
Hnh 2.1. Menu File v menu con ca lnh New EMBED Word.Picture.8 Hnh
2.2. Ca s MATLAB Editor/Debuger EMBED Word.Picture.8 Hnh 2.3. Ca s
ho ca MATLAB Hnh 2.7. Ca s Open filesHnh 2.9. Khung thoi Run Script
v hp thoi BrowseHnh 2.18. Ca s Print setupHnh 2.19. Menu EditHnh
2.20. Menu View EMBED PBrush Hnh 3.2. Kt qu khi chy tp tin Vidu
EMBED PBrush Hnh 3.3. Minh ho trng hp nghim ouRLC EMBED PBrush Hnh
3.4. Kt qu ca lnh fplot(bachai1, [-6,6])1 2 34 5 67 8
9e2e1R3R2R1Nhp x , y, xai = length(x)j =length(y)n=i; f=0i~=j ? Gn
i=1 i
