Учёба / lab_mat-met
.pdf
^bn_j_gp•cg• j•\gyggy lZdh` klZxlv g_e•g•cgbfb >ey pbo \biZ^d•\ lj_[Z g_e•g•cgm oZjZdl_jbklbdm Zijhdkbfh\m\Zlb qb •gl_jihex\Zlb gZ dh`ghfm djhp• ^bn_j_gpx\Zggy Hibk d_jmxqbo kb]gZe•\ lZ j•\gyggy ZijhdkbfZp•€ •gl_jiheyp•€ lj_[Z jhalZrh\m\Zlb \ nmgdp•€ j•\gygv a\¶yadm
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lZ[ebqghx nmgdp•}x Φ T |
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L = |
dΦ |
= var |
(12.1) |
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dt |
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T1 , Φ T 2 , ..., Φ Tn ] . |
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dt |
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U = iR + |
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di dt |
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dΦ |
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iR – ^bn_j_gp•cg_ j•\gyggy m ghjfZevg•c nhjf• Dhrb |
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dt |
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i = |
f (Φ ) |
– g_e•g•cg_ j•\gyggy a\yadm |
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Φ (0) = 0 – ihqZldh\• mfh\b
>ey \•^hfh€ lZ[ebqgh€ aZe_`ghkl• Φ T = f (iT ) fh`gZ jhajZom\Zlb Φ (i) ^ey [m^v-ydh]h agZq_ggy • aZ ^hihfh]hx ZijhdkbfZp•€ qb •gl_jiheyp•€ Ijb ZijhdkbfZp•€ djb\bo gZfZ]g_qm\Zggy a\bqZcgh \bdhjbklh\mxlv klmi•g_\• ihe•ghfb -]h Z[h -]h ihjy^dm h[h\¶yadh\h g_iZjgh]h lhfm sh nmgdp•y Φ (i) p_gljZevgh kbf_ljbqgZ
50
Nmgdp•y ydZ f•klblv m kh[• hibk g_e•g•cgbo ^bn_j_gp•cgbo j•\gygv lZ j•\gyggy a\yadm fh`_ fZlb gZklmigbc \b]ey^ m \biZ^dm
ZijhdkbfZp•€ |
•gl_jiheyp•€ |
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function dy=frn_a(t,y) |
function dy=frn_i(t,y) |
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global R U A |
global R U it Ft |
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F=y(1); |
F=y(1); |
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i=polyval(A,F); |
i=interp1(Ft,it,F); |
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dy(1)=U-i*R; |
dy(1)=U-i*R; |
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=heh\gZ ijh]jZfZ fh`_ fZlb gZklmigbc \b]ey^ ^ey \biZ^d•\ |
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ZijhdkbfZp•€ |
•gl_jiheyp•€ |
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global R U A |
global R U it Ft |
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U=… |
R=… y0=… tk=… |
U=… |
R=… y0=… tk=… |
it=[…] |
Ft=[…] |
it=[…] |
Ft=[…] |
A=polyfit(it,Ft,5); |
[t,y]=ode23(‘frn_i’,[0 tk],y0); |
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[t,y]=ode23(‘frn_a’,[0 tk],y0); |
i=interp1(Ft,it,y); |
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i=polyval(A,y); |
plot(t,y,t,i) |
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plot(t,y,t,i) |
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M k_j_^h\bs• Simulink ML ^ey •gl_jiheyp•€ \bdhjbklh\mxlv [ehd³Look-Up- Table´ a [•[e•hl_p• ³Functions&Tables´ 0/ ydbc a^•ckgx} dmkdh\h-e•g•cgm ZijhdkbfZp•x aZ\^Zgh€ lZ[ebqgh€ nmgdp•€ IZjZf_ljZfb pvh]h [ehdZ } \_dlhj Zj]mf_gl•\ lZ \_dlhj agZq_gv M a\¶yadm a pbf 6LPXOLQN-fh^_ev fh`_ fZlb gZklmi gbc \b]ey^
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Integrator |
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Look-Up |
To |
W orkspace |
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Table1 |
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Look-Up |
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To W orkspace1 |
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Table |
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Clock |
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To W orkspace2 |
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51
AZ\^Zggy
JhajZom\Zlb i_j_o•^g• ijhp_kb m ko_fZo gZ^Zgbo gZ jbk IZjZf_ljb ko_f m lZ[ebp• oZjZdl_jbklbdb g_e•g•cgbo _e_f_gl•\ L i R gZ^Zg• m lZ[e m klZ[•e•ljhgZ oZjZdl_jbklbdZ •^_ZevgZ jbk Ih[m^m\Zlb ]jZn•db kljmf•\ m ]•edZo _e_dljbqgh€ ko_fb m nmgdp•€ qZkm
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V D 1 |
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8kl |
89' |
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V D 2 |
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5,6) U = 0.1Em sin125t |
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Jbkmghd |
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LZ[ebpy |
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U=Em,B |
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LZ[ebpy |
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N <[ |
0 |
0.181 |
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0.451 0.551 0.632 |
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EZ[hjZlhjgZ jh[hlZ ‹
J1R?GGY LJ:GKP?>?GLGBO L: :E=?;J:1QGBO J1<GYGV
P•ev jh[hlb gZ\qblbky jha\¶yam\Zlb ljZgkp_^_glg• lZ Ze]_[jZ•qg• j•\gyggy
L_hj_lbqg• \•^hfhkl• Qbk_evgbc jha\¶yahd j•\gyggy
F(x)=0 |
(13.1) |
ih^Ley}lvky gZ ^\Z _lZib: \•^^•e_ggy dhj_g•\ lZ mlhqg_ggy €o ihqZldh\bo gZ[eb`_gv •l_jZp•cgbfb f_lh^Zfb
GZc[•evr jhaih\kx^`_gbfb f_lh^Zfb mlhqg_ggy dhj_g•\ } f_lh^b [•k_dp•c ohj^ ^hlbqgbo lZ f_lh^ ijhklbo •l_jZp•c
M iZd_l• ML j•r_ggy g_e•g•cgbo j•\gygv \bdhgm} nmgdp•y
x = fzero ( Fun, x0, Options, p1, p2…)
Fun – kljhdh\Z af•ggZ •f¶y m-nZceZ m ydhfm f•klblvky hibk nmgdp•€ Z[h Matlab-\bjZa ^ey €€ jhajZomgdm
x0 – ijb[ebag_ agZq_ggy dhj_gy fh`_ [mlb kdZeyj Z[h \_dlhj jhaf•jhf M ^jm]hfm \biZ^dm j•r_ggy rmdZ}lvky gZ aZ\^Zghfm •gl_j\Ze•
Options – \_dlhj hip•c yd• d_jmxlv ijhp_khf h[qbke_ggy lZ \b\h^m j_amevlZl•\
p1, p2– \bdhjbklh\mxlv ydsh nmgdp•y fZ} [•evr h^gh]h Zj]mf_glZ F(x, p1, p2…);
Options, p1, p2 … – g_h[h\'yadh\• iZjZf_ljb
>ey j•r_ggy Ze]_[jZ•qgbo j•\gygv \ iZd_l• ML } nmgdp•y roots.
X = roots (P) – h[qbkex} \_dlhj dhj_g•\ X ihe•ghfZ a dh_n•p•}glZfb P.
F_lh^ [•k_dp•c
F_lh^ [•k_dp•c Z[h f_lh^ iheh\bggh]h ^LeHggy kdeZ^Z}lvky a ihke•^h\gh]h ih^•e_ggy \•^j•adZ ydbc f•klblv dhj_gv gZ\i•e
x=(a+b)/2,
53
^_ Z • b – e•\Z lZ ijZ\Z f_`• dhj_gy lh[lh |
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F(a)*F(b)<0. |
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>ey dh`gh]h gZklmigh]h ^•e_ggy h[bjZ}lvky lZ iheh\bgZ \•^j•adm gZ d•gpyo ydh€ nmgdp•y fZ} ijhlbe_`gbc agZd Ijb pvhfm •gl_j\Ze •kgm\Zggy dhj_gy a\m`m}lvky aZ jZomghd af•gb h^g•}€ a ch]h f_`: e•\h€ Z o) Z[h ijZ\h€ b o).
1l_jZp•cgbc ijhp_k aZd•gqm}lvky ydsh \bdhgm}lvky mfh\Z: |
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E − D ≤ ε, |
(13.4) |
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^_ ε - aZ\^ZgZ lhqg•klv h[qbke_ggy dhj_gy ε<<1 1gdheb |
\bfZ]Zxlv sh[ |
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h^ghqZkgh \bdhgm\ZeZky mfh\Z |
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F_lh^ [•k_dp•c – ijhklbc lZ gZ^•cgbc kihk•[ ihrmdm dhj_g•\ j•\gyggy F(x)=0 <•g a[•]Z}lvky ^ey [m^v-ydbo [_ai_j_j\gbo nmgdp•c F(x), m lhfm qbke• g_^bn_j_gpx}fbo R\•^dbklv a[•`ghkl• g_\_ebdZ AZjZ^b ^hky]g_ggy lhqghkl• ε
g_h[o•^gh \bljZlblb |
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•l_jZp•c P_ ihagZqZ} sh aZ^ey ihemq_ggy dh`gbo \•jgbo ^_kylbqgbo agZd•\ g_h[o•^gh ajh[blb [ebavdh •l_jZp•c
Ydsh gZ \•^j•adm [a,b] agZoh^blvky d•evdZ dhj_g•\ lh ijhp_k a[•]Z}lvky ^h h^gh]h a gbo F_lh^ g_ijb^Zlgbc ^ey ihrmdm djZlgbo dhj_g•\ iZjgh]h ihjy^dm
F_lh^ ohj^
F_lh^ ohj^ Z[h f_lh^ ijhihjp•cgbo qZklbg f•klblvky m ihke•^h\ghfm ih^•e_gg• \•^j•adZ >a,b@ ydbc fZ} dhj_gv gZ qZklbgb ijhihjp•cg• agZq_ggyf
nmgdp•€ gZ d•gpyo \•^j•adm |
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a\•^db
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=_hf_ljbqgh p_ _d\•\Ze_glgh aZf•g• ]jZn•dZ nmgdp•€ F(x ohj^hx ydZ ijhc^_ q_j_a lhqdb a,F(a lZ b,F(b)).
>ey aZd•gq_ggy •l_jZp•cgh]h ijhp_km aZf•klv mfh\b \bdhjbklh\mxlv
mfh\m |
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[L+ − [L ≤ ε, |
(13.9) |
^_ xi+1, xi – \•^ih\•^gh hklZgg•c h[qbke_gbc • ihi_j_^g•c ^h gvh]h gZ[eb`_ggy dhj_gy M j_rl• p_c f_lh^ ihoh^blv gZ f_lh^ [•k_dp•c Ze_ aZ[_ai_qm} [•evr r\b^dm a[•`g•klv
F_lh^ ^hlbqgbo
F_lh^ ^hlbqgbo Z[h f_lh^ GvxlhgZ ihey]Z} m ihke•^h\g•c ZijhdkbfZp•€ nmgdp•€ F(x ^hlbqgbfb ^h djb\h€ m lhqp• ihi_j_^gvh]h gZ[eb`_ggy ([L ) [L ) yd• i_j_lbgZxlv hkv Z[kpbk m lhqp• gZklmigh]h gZ[eb`_ggy o• 1 sh \bagZqZ}lvky aZ nhjfmehx
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Ihke•^h\g•klv a[•]Z}lvky ^h ^•ckgh]h agZq_ggy dhj_gy j•\gyggy F(x ydsh gZqZevg_ gZ[eb`_ggy dhj_gy e_`blv m •gl_j\Ze•>a,b] (F(a)*F(b gZ ydhfm iho•^g• ) ([) lZ ) ([) ljbfZxlv \eZkgbc agZd lZ \bdhgm}lvky mfh\Z
) [ ) [ > . |
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1l_jZp•€ ijbibgyxlv ijb \bdhgZgg• mfh\ lZ Z[h
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58
EZ[hjZlhjgZ jh[hlZ ‹
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F(X) = 0, X =[x1, x2, …xn].
jL\gygv Ll_jZpLc-
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>ey jLr_ggy lZdbo g_eLg•cgbo kbkl_f \bdhjbklh\mxlvLl_jZpLcgLf_lh^b M iZd_l• ML j•r_ggy kbkl_f g_e•g•cgbo j•\gygv \bdhgm} nmgdp•y
X = fsolve ( Fun, X0, Options, p1, p2…)
Fun – kljhdh\Z af•ggZ sh f•klblv •f'y m-nZceZ m ydhfm aZibkZgZ kbkl_fZ g_e•g•cgbo j•\gygv
X0 – \_dlhj gZqZevgbo gZ[eb`_gv dhj_g•\
Options – \_dlhj hip•c yd• d_jmxlv ijhp_khf h[qbke_ggy lZ \b\h^m j_amevlZl•\ p1, p2,.. - \bdhjbklh\mxlv ydsh Fun(X, p1,p2...) f•klylv [•evr h^gh]h Zj]mf_glZ Options, p1, p2 - g_h[h\'yadh\• iZjZf_ljb
[X, Fval] = fsolve (Fun, X0,...) - ih\_jlZ} dj•f dhj_g•\ agZq_ggy nmgdp•€ m lhqdZo O.
Jha]eyg_fh ^_yd• •l_jZp•cg• f_lh^b j•r_ggy kbkl_f e•g•cgbo j•\gygv
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59