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OSNOVE ELEKTROTEHNIKE ii

Priprav= e za laboratorijske vaje
=

Vaja 1: = magnetno polje

Uporaba programov Matlab / Octave za izračun in = izris grafov

 

Matlab/Octave/Scilab

Matlab (Mathworks, ZDA)je visoko zmogljiv = programski paket, ki se v inženirstvu zelo pogosto uporablja. V osnovi je b= il namenjen predvsem reševanju sistemov enačb, torej delu z matrikami, dand= anes pa je nepogrešljiv tudi pri analizi in obdelavi signalov, numerični si= mulaciji, itd. Program je plačljiv, zato se pogosto za osnovne potrebe upor= ablja prosto dostopne programe, ki uporabljajo praktično enako sintakso in = bodo v našem primeru v celoti zadostovali za naše potrebe. Najpogosteje se = kot alternativo Matlabu uporablja Octave.

Obstaja zelo veiiko spletnih strani, kjer = se lahko naučite uporabljati Matlab/Octave. Nekaj naslovov je navedenih na = koncu poglavja. Matlab/Octave se lahko uporablja z vpisovanjem ukazov direk= tno v ukazni vrstici, v kolikor pa se ukazi ponavljajo ali pa jih je potreb= no izvršiti več hkrati, pa se zažene ukaze, ki jih vpišemo v določeno dadot= eko. Ta je tekstovna, zato lahko uporabimo za njeno urejevanje poljuben tek= stovni editor. Velja opozoriti na to, da se ukazna vrstica nanaša na določe= no mapo (direktorij) in da se morajo dadoteke, ki jih zaganjamo iz ukazne v= rstice, nahajati v tej mapi. Drugi način je, da programu "povemo"= v kateri mapi naj išče dadoteke ali pa se z ukazno vrstico pomaknemo v ust= rezno mapo. V te namene se uporabi že nekoliko starejše DOS ukaze (npr. cd,= mkdir, dir, ...). Matlab omogoča tudi grafičen način spreminjanja t.i. del= ovne mape.

 

 

 

 
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Primer uporabe za izračun funkcije in izris

 

Spodnji pri= mer izriše funkcijo na določenem intervalu. Funkcijo zapišemo v Matlabu/Octave v= obliki  i=3DI0*exp(-t/Tau).*sin(omega*t). t = zapišemo kot vektor vrednosti časa od nekega začetnega = do končnega časa z določenim časovnim korakom. Spodnja slika prikazuje izri= sano krivuljo. (Ukazne vrstice v spodnjem primeru lahko kopirate v dadoteko= in jo v programu Matlab/Octave zaženete iz ukazne vrstice)

Lahko tudi = izrišemo več krivulj na istem grafu. Če izbrišemo ukaz break v spodnjem pri= meru kode, dobimo poleg prvega še en graf na katerem pa imamo izrisane tri = krivulje hkrati.

Zamik krivulj v t osi lahko dosežemo tako= , da določimo novo spremenljivko za čas, ki je od osnovnega zamaknjen za do= ločeno vrednost, npr: t2=3Dt-0.2. Če izbrišemo drugi ukaz break v spodnjem = primeru dobimo sledeč rezultat:

 

 

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charset="windows-1250" Page Title

Programska koda za izrise

%% PRIMER IZRISA ANALITIČNE = FUNKCIJE v MATLABU / OCTAVE

% Želimo izrisati krivuljo t= oka kot funkcijo časa v obliki enačbe i(t)=3DI0*exp(-t/Tau)*sin(omega*t)

% kjer so I0, Tau in omega k= onstante, t pa čas

 

% Določitev konstant in opis= enot

I0=3D 10 % tok v= [A]

Tau=3D0.2  % časov= na konstanta v [s]

omega=3D20 % kotna= frekvenca v [1/s]

 

% Določitev časovnih točk, k= jer bomo računali funkcijo

tzac=3D0 % začet= ni čas

tkon=3D1 % končn= i čas

Nkorakov=3D100 % korak=

t=3Dlinspace(tzac,tkon,Nkorakov); = % generiram vektor časa v [s]

% po potrebi glej help linsp= ace za nastavitve

 

% Določitev funkcije toka v = Matlab sintaksi.

% Bodi pozoren na dodajanje = pike "." pred simboli za množenje in deljenje vektorjev

i=3DI0*exp(-t/Tau).*sin(omega*t);<= /span>

 

 

% Izris funkcije

plot(t,i,'Linewidth'= ,1.= 5)

xlabel('Cas   /s'<= /span>)

ylabel('Tok   /A'<= /span>)

 

 

% Za izpis tabele i in t

[t;i]'  % kreir= amo matriko z dvema kolonama

 

%% Dodatne možnosti izrisa, = odkomentiraj in preiskusi

% plot(t,i,'-*') % s simbolo= m in polno črto

% plot(t,i,'g*') % z zelenim= i simboli

% grid   % doda mrežo=

% title('Tok v odvnisnosti o= d časa, prehodni pojav')

 

break % kome= ntiraj to vrstico, če želiš izvršiti program do konca

%% Dodatni izris dveh krivul= j za različne parametre

figure;  % kreir= am nov graf

 

i1=3D1*exp(-t/0.2).*sin(20*t);

i2=3D2*exp(-t/0.5).*sin(20*t);

i3=3D3*exp(-t/0.2).*sin(10*t);

plot(t,i1,t,i2,t,i3)

 

% Prikaz s črticami,  glej h= elp plot za druge moznosti

plot(t,i1,'--'= ,t,= i2,'= .',t,= i3,'= .-')

 

xlabel('Cas   /s'<= /span>)

ylabel('Tok   /A'<= /span>)

legend('i1'= ,'= i2','= i3')  = % izris legende

 

% premaknitev krivulj v t os= i (ab= scisi)

break

t2=3Dt-0.2;

t3=3Dt+0.3;

i2=3D1*exp(-t2/0.2).*sin(20*t2);

i3=3D1*exp(-t3/0.2).*sin(20*t3);

plot(t,i1,t,i2,t,i3)

legend('i1'= ,'= i2','= i3')  = % izris legende

 

 

 

Primeri programčkov v Mat= labu:

zgornji pri= mer za izris grafov: izris.m

programa za izris polja v ravnini tanke tuljave: oe2_labvaja1_polje_precno.m in polje.m

 

 

Nekaj spletnih virov:

Matlab i= n Octave, osnovna stran:

http://ww= w.mathworks.com/products/matlab/

http://ww= w.gnu.org/software/octave/

Primerjava Matlab/Octave/Scilab:

http://www.dedoimedo.c= om/computers/scientific.html

http://us= erpages.umbc.edu/~gobbert/papers/SharmaGobbertTR2010.pdf

Učenje Matlaba/Octave:

http://us= erpages.umbc.edu/~gobbert/papers/SharmaGobbertTR2010.pdf

http://vo= lga.eng.yale.edu/sohrab/matlab_tutorial.html

http://ww= w-mdp.eng.cam.ac.uk/web/CD/engapps/octave/octavetut.pdf

http://ww= w.math.tamu.edu/~comech/tools/octave-basics/

http://lb= m.fe.uni-lj.si/dejan/OE/MATLAB/Mlab_oe1.html

 

 
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