Учёба / lab_mat-met
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>ey j•r_ggy ^bn_j_gp•cgbo j•\gygv m iZd_l• ML \bdhjbklh\mxlvky gZklmig• nmgdp•€ ode23, ode45, ode113, ode15s, ode23s, ode23t, ode23tb.
[t,Y]=ode23(‘Fun’, Tspan, Y0, Options, p1, p2, … ) – \bj•rm} kbkl_fm a\bqZcgbo ^bn_j_gp•cgbo j•\gygv a \bdhjbFlZggyf nhjfme Jmg]_-DmllZ ^jm]h]h lZ lj_lvh]h ihjy^dm
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Fun – •f'y m-nZceZ m ydhfm f•klblvky hibk kbkl_fb ^bn_j_gp•cgbo j•\gygv Fun(t,Y) (DY ih\bg_g [mlb \_dlhj-klh\i_pv
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Y0 – \_dlhj ihqZldh\bo mfh\
Options – \_dlhj hip•c yd• d_jmxlv ijhp_khf h[qbke_ggy lZ \b\h^m j_amevlZl•\ Ijh]eygmlb i_j_e•d \klZgh\e_gbo agZq_gv hip•c fh`gZ aZ ^hihfh]hx nmgdp•€ odeset Ydsh lj_[Z af•gblb agZq_ggy hip•€ gZijbdeZ^ Z[khexlgm lhqg•klv g_h[o•^gh \bdhgZlb gZklmig• ^•€
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Opt=odeset(‘AbsTol’, ‘1e-8’);
[t,Y]=(‘Fun’, [T0 Tfinal], Y0, Opt);
p1, p2, … - \bdhjbklh\mxlv ydsh nmgdp•y Fun(t, Y, flag, p1, p « f•klblv ^h^Zldh\• iZjZf_ljb
Options, p1, p2, … – g_h[h\¶yadh\• iZjZf_ljb
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kbghkh•^Zevgh]h |
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>`_j_eh i_j•h^bqgh]h |
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kb]gZem ^h\•evgh€ nhjfb |
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Jbkmghd
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< ML5 ^h kdeZ^m Simulink \oh^blv [•[e•hl_dZ Power System ijbagZq_gZ ^ey fh^_ex\Zggy i_j_o•^gbo ijhp_k•\ \ _e_dljbqgbo ko_fZo a \bdhjbklZggyf _e_f_gl•\
ijbgpbih\bo ko_f I_j_e•d ^_ydbo ihlj•[gbo [ehd•\ |
Power System gZ^Zgbc gZ |
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Breaker |
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arallel RLC Branch |
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Ihke•^h\gbc RLC IZjZe_evgbc RLC |
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eZgpx] |
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DC Voltage Source |
AC Voltage Source |
AC Current Source |
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Controlled |
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urrent Source |
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>`_j_eh ihkl•c- |
>`_j_eh kbgmkh•- |
>`_j_eh kbgmkh•- |
D_jm}f_ ^`_j_eh |
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gh€ gZijm]b |
^Zevgh€ gZijm]b |
^Zevgh]h kljmfZ |
kljmfm |
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(electrical sources) |
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Measurement |
easurement |
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oltage Source |
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D_jm}f_ ^`_j_eh |
:fi_jf_lj |
<hevlf_lj |
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gZijm]b |
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Jbkmghd |
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;ehd “To Workspace´ |
ajmqgh |
\bdhjbklh\m\Zlb |
^ey |
n•dkZp•€ j_amevlZl•\ |
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“Mux” – ^ey h[¶}^gZggy d•evdho \bo•^gbo \_ebqbg m fZljbpx Ijb \bdhjbklZgg• [ehd•\ ³Parallel RLC Branch´ ^ey 5/-eZgpx]Z ijbcfZ}fh K ^ey 5&-eZgpx]Z – / LQI ^ey /&-eZgpx]Z – 5 LQI ijb \bdhjbklZgg• [ehd•\ ³Series RLC Branch´ ^ey RL-eZgpx]Z ijbcfZ}fh K LQI^ey5&-eZgpx]Z –/ ^ey/&-eZgpx]Z –5 ;ehdb ³%UHDNHU´ • ³,GHDO 6ZLWFK´ \bdhjbklh\mxlv ^ey aZfdg_ggy lZ jha•fdg_ggy _e_dljbqgh]h dheZ <o•^ ³ ´ lZ \bo•^ ³ ´ ijb}^gmxlvky ^h _e_dljbqgh€ ko_fb
46
IhqZldh\• mfh\b ³Lnitial state´ aZ\^Zxlv klZg dexqZ ³ ´ – jha•fdg_gbc ³ ´ – aZfdg_gbc >ey af•gb klZgm dexqZ gZ \o•^ ³k´³%UHDNHU´Z[h ³g” (“Ideal Switch”) lj_[Z ih^Zlb d_jmxqbc kb]gZe Simulink Hkh[eb\hkl• [ehdZ³%UHDNHU´ajh[e_gbc m \b]ey^• ^`_j_eZ kljmfm – g_ j_dhf_g^h\Zgh \bdhjbklh\m\Zlb m ihke•^h\ghfm a\’yadm a ^`_j_ehf kljmfZ lZ •g^mdlb\g•klx \ pbo \biZ^dZo lj_[Z aZrmglm\Zlb \o•^-\bo•^ j_abklhjhf a ^m`_ \_ebdbf hi•jhf Hkh[eb\hkl• [ehdZ ³,GHDO 6ZLWFK´ajh[e_gbc m \b]ey^• aZrmglh\Zgh]h ihke•^h\gh]h RC-eZgpx]Z – \bo•^ ³P´ \bdhjbklh\mxlv ^ey \b\_^_ggy kljmfm • gZijm]b dexqZ i•^ qZk fh^_ex\Zggy Ydsh p_ g_ihlj•[gh ^h \bo•^m³P´i•^¶}^gmxlv l_jf•gZlhj
Jha]eyg_fh ijbdeZ^ |
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< _e_dljbqg•c ko_f• lj_[Z jhajZom- |
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\Zlb i_j_o•^g• ijhp_kb ijb aZfbdZgg• |
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dexqZ lh[lh agZclb i1(t), i2(t), i3(t), UC(t)). |
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AZ aZdhgZfb D•jo]hnZ fZl_fZlbq- |
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gbc hibk ko_fb ijb aZfdg_ghfm klZg• dexqZ fZ} \b]ey^ |
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E = i1r1 − U c ,
E = i1r1 + i2 r2 + i3r3 +
i + |
C |
dU c |
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2 |
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i2 + |
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L |
di3 |
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dt
(11.3)
(11.4)
A ydbo – ^bn_j_gp•cg• j•\gyggy – j•\gyggy a\¶yadm
JhajZom}fh ihqZldh\• mfh\b ko_fZ ijb jha•fdg_ghfm klZg• dexqZ
r2 r3
i2 |
i3 |
U |
C |
+ C dU C r + |
i r + |
L di3 = 0 , |
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dt |
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< klZehfm j_`bf• d = 0 a\•^kb dt
47
i3 (0) = |
J k , |
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U C (0) = − i3r3 = |
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LZdbf qbghf fZl_fZlbqgbc hibk ko_fb fZ} \b]ey^ ^bn_j_gp•cg• j•\gyggy m |
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ghjfZevg•c nhjf• Dhrb ihqZldh\• mfh\b |
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dU C |
= (i2 − i1) / C, |
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− |
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(E − i r |
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− i r ) / L, |
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J•\gyggy a\¶yadm |
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i1 = (E + U C ) / r1 , |
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>bn_j_gp•cg• j•\gyggy \ hi_jZlhjg•c nhjf• |
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pU C |
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pi3 = |
(E − i1r1 − i2 r2 − i3r3 ) / L. |
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KljmdlmjgZ ko_fZ kdeZ^_gZ aZ j•\gyggyfb - fZ} \b]ey^ |
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Lp |
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Cp |
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<•^ih\•^gZ ko_fZ \ [ehdZo Simulink: |
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To Workspace1
r1
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time |
Clock |
Uc |
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To Workspace2 |
48
Co_fZ \ [ehdZo Power System Simulink:
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i |
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c |
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To Workspace |
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R2 |
R3 |
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R1 |
1 |
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C |
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Constant |
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L |
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Voltage |
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E |
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Measurement |
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-1 |
Uc |
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t |
Gain |
To Workspace2 |
Clock |
To Workspace1 |
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J_dhf_g^h\Zgbc f_lh^ j•r_ggy ^bn_j_gp•cgbo j•\gygv ode15s.
AZ\^Zggy
JhajZom\Zlb i_j_o•^gbc ijhp_k m ko_fZo gZ jbkmgdm iZjZf_ljb ko_f gZ^Zg• m lZ[ebp• ^ey ljvho \biZ^d•\
•U=Um– ^`_j_eh ihkl•cgh€ gZijm]b
•U=UmVLQ&t – ^`_j_eh kbgmkh•^Zevgh€ gZijm]b;
•i_j•h^bqgZ gZijm]Z \b]ey^ kb]gZem gZ jbk T=0.1 c, T1=0.07 c.
Ih[m^m\Zlb ]jZn•db gZijm]b gZ dhg^_gkZlhj• lZ kljmf•\ m ]•edZo _e_dljbqgh€ ko_fb m nmgdp•€ qZkm
EZ[hjZlhjgZ jh[hlZ
J1R?GGY G?E1G1CGBO >BN?J?GP1CGBO J1<GYGV
P•ev jh[hlb gZ\qblbky \bj•rm\Zlb qbk_evgbfb f_lh^Zfb g_e•g•cg• ^bn_j_gp•cg• j•\gyggy a ihqZldh\bfb mfh\Zfb lZ €o kbkl_fb
L_hj_lbqg• \•^hfhkl•
< _e_dljhl_ogbp• lZ iho•^gbo \•^ g_€ ^bkpbie•gZo j•r_ggy ^bn_j_gp•cgbo j•\gygv \bdhjbklh\mxlv ijb jhajZomgdZo i_j_o•^gbo ijhp_k•\ \ _e_dljbqgbo ko_fZo Ydsh \ pbo ko_fZo ijbkmlg• _e_f_glb a g_e•g•cgbfb oZjZdl_jbklbdZfb lh
49