Дослідження перехідних процесів вузла живлення виконавчих асинхронних моторів як елемента системи керування: Автореф. дис… канд. техн. наук / Аль Ра

Aea?aeaaiee oi?aa?neoao «Euea?anueea iie?oaoi?ea»

Aeue ?aaaaaa

Iaioi Noeaeiai

OAeE 658.012.011.56:658.512;681.58’8

AeINE?AeAEAIIss IA?AO?AeIEO I?IOeAN?A AOCEA AEEAEAIIss

AEEIIAA*EO ANEIO?IIIEO IIOI??A ssE AEAIAIOA

NENOAIE EA?OAAIIss

Niaoe?aeuei?noue

05.13.05 — aeaiaioe oa i?eno?i? ia/enethaaeueii? oaoi?ee

oa nenoai ea?oaaiiy

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Euea?a — 1998

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia o Aea?aeaaiiio oi?aa?neoao? «Euea?anueea iie?oao-

i?ea».

Iaoeiaee ea??aiee: aeieoi? oaoi?/ieo iaoe, i?ioani?

*aaai Aaneeue Eineiiae/, Aea?aeaaiee oi?aa?neoao «Euea?anueea
iie?oaoi?ea», i?io. eao. oai?aoe/ii? oa caaaeueii? aeaeo?ioaoi?ee

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

i?ioani? Iiiia Aiaaeai Ieaenaiae?iae/, aea?aeaaiiai iaoeiai-aeine?aeiiai
?inoeoooo ?ioi?iaoe?eii? ?io?ano?oeoo?e, i. Euea?a

aeieoi? oaoi?/ieo iaoe, aeioeaio

Naiioee Aieiaeeie? Aaneeueiae/, Aea?aeaaiee oi?aa?neoao «Euea?anueea
iie?oaoi?ea», aeioe. eao. “Aaoiiaoeea oa oaeaiaoai?ea”

I?ia?aeia onoaiiaa — Iaoeiai-ae?iaie/a ei?ii?aoe?y «Ee?anueeee ?inoeooo
aaoiiaoeee», IAeI 46, i. Ee?a.

Caoeno a?aeaoaeaoueny « 26» ethoiai 1999 ?. i 14 aiae 00 oa. ia

can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae35.052.08 o Aea?aeaaiiio
oi?aa?neoao? «Euea?anueea iie?oaoi?ea» (290646, i. Euea?a, aoe.
N.Aaiaea?e, 12).

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? Aea?aeaaiiai
oi?aa?neoaoo «Euea?anueea iie?oaoi?ea» (290646, i. Euea?a, aoe.
I?ioani?nueea, 1).

Aaoi?aoa?ao ?ic?neaiee «___»___________1998 ?.

A/aiee nae?aoa? niaoe?ae?ciaaii? a/aii? ?aaee,

aeieoi? oaoi. iaoe
ss.O. Eooeee

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue i?iaeaie. No/ani? caeiaooee iaoaiaoe/iiai iiaeaethaaiiy
iathoue aaeee? iiaeeeaino? aeine?aeaeaiiy ?aaeueieo o?ce/ieo i?ioean?a o
nenoaiao ea?oaaiiy oa ?o aeaiaioao o an?e ?o neeaaeiino?. Oea noaei
iiaeeeaei caaaeyee aaeaeiio ii?aeiaiith inoaii?o aeinyaiaiue
iaoaiaoe/iiai iiaeaethaaiiy, oai??? ae?i?eoi?a, ia/enethaaeueii?
iaoaiaoeee oa oaeaeeiae?th/eo aeaeo?iiiii-ia/enethaaeueieo iaoei.

Aeina?ae iieaco?, ui iaeiiai?oa ? iaei?ino?oa iienaoe aeaeo?iia?iaoi?
i?ioeane, ui a?aeaoaathoueny a nenoai? ea?oaaiiy aoe?eiio oa a ??
aeaiaioao cie?aia, o caaaeueiiio aeiaaeeo ia iniia? ii?aeiaiiy ??aiyiue
eaac?noaoe?iia?iiai aeaeo?iia?iaoiiai iiey ? ??aiyiue aeaeo?iia?iaoieo
e?e.

Aei /enea iaea?aeiia?aeaeuei?oeo aeaiaio?a nenoaie ea?oaaiiy ne?ae
a?aeianoe anaiiaeeea? aeeiiaa/? aeaeo?iiaoai?/i? i?eno?i?, na?aae yeeo
iniaeeaa ?ieue iaeaaeeoue aeeiiaa/ei aneio?iiiei iioi?ai, a?ae ni?aaii?
? iaae?eii? ?iaioe yeeo caeaaeeoue oni?oia ?iaioa nenoaie ea?oaaiiy
aoe?eiio.

Ia nueiaiaei?oi?e aeaiue ?niothoue i?eeiyoi? iaoaiaoe/i? iiaeae? ye
naieo iioi??a, oae ? o?ainoi?iaoi??a. Iaeiae, iayai?noue ??ciioeiieo
iioi??a ? o?ainoi?iaoi??a o nenoai? ea?oaaiiy, ia a?aei?io a?ae ?o
?iaeea?aeoaeueii? ?iaioe, — oea ye?nii ??ci? iiiyooy. O nenoai? aiie
ooai?ththoue ni?eueio eieeaio nenoaio, aeey yei? oa?aeoa?ia yaeua —
iai?i aeaeo?iia?iaoiith aia????th. Oaeo eieeaio nenoaio ooai?ththoue ye
i?aaeei aocee aeeaeaiiy aeeiiaa/eo iioi??a a?ae ni?eueiiai
o?ainoi?iaoi?a. C iiceoe?? iaoaiaoe/iiai iiaeaethaaiiy oa eiii’thoa?iiai
neioethaaiiy oae? aocee aeeaeaiiy aeioe?eueii ?icaeyaeaoe ye
aiaaoiooieoe?iiaeuei? aeaiaioe nenoaie.

Ie aeine?aeaeo?ii eiiooaoe?ei? oa ia?ao?aei? i?ioeane aocea aeeaeaiiy
aeeiiaa/eo aneio?iiieo iioi??a ye aeaiaioa nenoaie ea?oaaiiy.

A?aeii? o?e iniiai? eiino?oeoe?? aeeiiaa/eo aneio?iiieo iioi??a — c
ei?ioeicaieiooei ?ioi?ii o aeaeyae? a?ey/i? ee?oee, c nooe?eueiei
oa?iia?iaoiei ?ioi?ii ? c nooe?eueiei iaia?iaoiei ?ioi?ii. Iaoaiaoe/i?
iiaeae? iioi?a c ei?ioeicaieiooei ?ioi?ii aoaeothoueny ia iniia? oai???
iae?i?eieo aeaeo?iia?iaoieo e?e, a c nooe?eueiei oa?i- oa iaia?iaoiei
?ioi?aie — ia aca?iiiio ii?aeiaii? iaoiae?a oai??? aeaeo?iia?iaoieo e?e
oa oai??? aeaeo?iia?iaoiiai iiey.

Oeiiaee a?oiiaee aocie aeeaeaiiy aeeiiaa/eo iioi??a /a?ac ?ainoi?iaoi?
a?ae aeaea?aea noi??ii? iiooaeiino? ?icaeyaea?oueny ye aeaiaio nenoaie
ea?oaaiiy. I?e?iaeii, ui ia iioi?e oaeiai aocea iiaeathoueny anaiiaeeea?
ea??ai? aieeae, cai?ioi? ca’ycee ? o. i. Aea ine?eueee o ?iaio? i?ioeane
?icaeyaeathoueny o /ania?e iaeano?, oi a?aooaaiiy an?o oeeo oaeo??a ia
aeeeeea? o?oaeiiu?a. Ooo aeinoaoiuei aaanoe o ??aiyiiy iaaii? iaiioee
iioi?a oo /e ?ioo ooieoe?iiaeueio caeaaei?noue. Ine?eueee oe? ieoaiiy
?ica’ycothoueny aeey oiai /e ?ioiai eiie?aoiiai aeiaaeeo, oi a ?iaio? ie
cina?aaeeeeny ia iiaoaeia? ca’ycaii? nenoaie ??aiyiue aeaeo?iiaoai?/iiai
noaio aocea aeeaeaiiy iioi??a.

Aiae?c ia?ao?aeieo i?ioean?a nenoaie ea?oaaiiy ca aeeoa?aioe?aeueieie
??aiyiyie aeaeo?iiaoai?/iiai noaio ia?aaeaa/a? caaeaiiy ii/aoeiaeo oiia
— cia/aiue iaa?aeiieo o iiiaio t =+0. Oe? oiiae caeaaeaoue ye a?ae
iiia?aaeiueiai noaio eiea, oae ? eiai noaio i?e t > 0.

Aocie aeeaeaiiy iaeaaeeoue aei D-ae?iaeaeaieo, oiio a eiiooaoe?eieo
?aaeeiao ooo iiaeeea? no?eaeiiiae?ai? ci?ie no?oi?a a aeaeo?e/ieo
iaiioeao. Aac a?aooaaiiy oeueiai yaeua, ye iieacaee iao? aeine?aeaeaiiy,
?ac?aooiie iine?aeoth/iai i?ioeano i?aeoe/ii iaiiaeeeaee. ?ica’ycaiith
oe??? neeaaeii? oai?eoe/ii? i?iaeaie o aeena?oaoe?? a?aeaaaeaii iaeia c
aaaeeeaeo i?noeue.

O ?iaio? ?ica’ycai? oae? aaaeeea? aeey oai??? oa i?aeoeee caaea/?:

— cai?iiiiiaaii iaoiae oi?ioaaiiy aeeoa?aioe?aeueieo ??aiyiue
aeaeo?iiaoai?/iiai noaio aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a
c ei?ioeicaieiooei oa nooe?eueieie oa?i- oa iaia?iaoiei ?ioi?aie ye
aeaiaioa nenoaie ea?oaaiiy;

— ?ic?iaeaii iaoiae o?aooaaiiy no?eaeiiiae?aieo ci?i no?oi?a a
?iaeoeoeaieo iaiioeao aeaiaio?a aocea, iaoiiaeaieo aeaeo?e/ieie
eiiooaoe?yie;

— ?ic?iaeaii ae?i?eoi noi?niiai ?ioa??oaaiiy ci?oaieo iae?i?eieo
aeeoa?aioe?aeueieo ??aiyiue c? cae/aeieie e /anoeiieie iio?aeieie
aeaeo?iiaoai?/iiai noaio aocea aeeiiaa/eo aneio?iiieo iioi??a, ui
ia?aaeaa/a? a?aooaaiiy anaiiaeeeaeo eiiooaoe?eieo ci?i;

— ?ic?iaeaii eiii’thoa?io i?i??aio ?ic?aooieo ia?ao?aeieo
aeaeo?iiaoai?/ieo i?ioean?a aocea aeeaeaiiy nenoaie ea?oaaiiy
aeeiiaa/eie aneio?iiieie iioi?aie c ei?ioeicaieiooei, oa?i- oa
iaia?iaoiei ?ioi?aie.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa
aeeiioaaeanue ca?aeii c ieaiii iaoeiai-aeine?aeieo ?ia?o I?i?noa?noaa
ina?oe Oe?a?ie o AeO”Euea?anueea iie?oaoi?ea” a ?aieao ieaiiai?
aea?aeathaeaeaoii? oaiaoeee AeA/EAAC “Iieueia? iaoaiaoe/i? iiaeae?
aeaeo?ioaoi?/ieo i?eno?i?a”.

Iaoa oa caaea/? aeine?aeaeaiiy. ?ac?iaea iaoiae?a aiae?co ia?ao?aeieo
aeaeo?iiaoai?/ieo i?ioean?a aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo
iioi??a c ei?ioeicaieiooei oa nooe?eueiei ii?iaeienoei oa?i- oa
iaia?iaoiei ?ioi?aie ye aeaiaioa nenoai ea?oaaiiy, c o?aooaaiiyi
ieoo?aeo eiiooaoe?eieo ia?a?iciiae?e?a no?oi?a o ia?iaoieo iaiioeao.

Aeey aeinyaiaiiy oe??? iaoe iaiao?aeii aoei ?ica’ycaoe oae? iniiai?
caaea/?:

— noi?ioaaoe aeeoa?aioe?aeuei? ??aiyiiy aeaeo?iiaoai?/iiai noaio
aeeiiaa/eo aeaiaio?a nenoaie ia iniia? a?aeiieo o e?oa?aoo?? iaoiae?a;

— noi?ioaaoe aeeoa?aioe?aeuei? ??aiyiiy aeaeo?iiaoai?/iiai noaio aocea
aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a o aoceiaiio eii?aeeiaoiiio
aacen?;

— aaeaiooaaoe ocaaaeueiai? caeiie eiiooaoe?? ia ??aiyiiy aocea aeeaeaiiy
aeeiiaa/eo aneio?iiieo iioi??a o aoceiaiio eii?aeeiaoiiio aacen?.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a:

— ?ic?iaeaii iaoiae oi?ioaaiiy ci?oaieo iae?i?eieo aeeoa?aioe?aeueieo
??aiyiue aeaeo?iiaoai?/iiai noaio aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo
iioi??a ye aeaiaioa nenoaie ea?oaaiiy;

— ?ic?iaeaii iaoiae o?aooaaiiy ieoo?aiai ia?a?iciiae?eo eiiooaoe?eieo
no?oi?a o ia?iaoieo iaiioeao aeaiaio?a aocea aeeaeaiiy aeeiiaa/eo
aneio?iiieo iioi??a;

— iiaoaeiaaii ae?i?eoi oa eiii’thoa?io i?i??aio ?ic?aooieo ia?ao?aeieo
aeaeo?iiaoai?/ieo i?ioean?a aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo
iioi??a c ei?ioeicaieiooei oa c nooe?eueieie oa?i- e iaia?iaoiei
?ioi?aie, ui ia?aaeaa/a? no?eaeiiiae?aio ci?io eiiooaoe?eieo no?oi?a o
aeaeo?e/ieo iaiioeao.

Iaoiaee aeine?aeaeaiiy. Oai?aoe/i? aeine?aeaeaiiy ??oioothoueny ia
iae?i?eieo aeeoa?aioe?aeueieo ??aiyiiyo aeaeo?e/ieo e?e o cae/aeieo
iio?aeieo, iaoiae? aoceiaeo iai?oa o /ania?e iaeano? aeey aeaeo?e/ieo
e?e, iae?i?eieo aeeoa?aioe?aeueieo ??aiyiiyo o /anoeiieo iio?aeieo
eaac?noaoe?iia?iiai aeaeo?iia?iaoiiai iiey, iae?i?eieo
aeeoa?aioe?aeueieo ??aiyiiyo iaoai?/iiai ?ooo o cae/aeieo iio?aeieo,
iaoiaeao /enaeueiiai ?ioa??oaaiiy iae?i?eieo aeeoa?aioe?aeueieo
??aiyiue, iaoiaeao ?ica’ycaiiy iae?i?eieo ae?aa?e/ieo ??aiyiue,
ae?i?eoi?/ieo iiaao IE.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?ic?iaeai? eiii’thoa?i?
i?i??aie ?ic?aooieo aeaeo?iiaoai?/ieo ia?ao?aeieo i?ioean?a aocea
aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a c ei?ioeicaieiooei oa c
nooe?eueieie oa?i- oa iaia?iaoieie ?ioi?aie a?ae aeaea?aea noi??ii?
iiooaeiino? iiaeooue aooe aeei?enoai? aeey aiae?co ?nioth/eo nenoai
ea?oaaiiy, a oaeiae ia aoai? i?iaeooaaiiy iiaeo nenoai.

Ai?iaaaeaeaiiy ?acoeueoao?a ?iaioe. ?acoeueoaoe ?iaioe aeei?enoai? i?e
?ic?iaoe? nenoai oi?aae?iiy i?eaiaeii ?aae?ieieaoe?eii? aioaie o
Euea?anueeiio iaoeiai-aeine?aeiiio ?aae?ioaoi?/iiio ?inoeooo?, i.
Euea?a.

Iniaenoee aianie i?aoaiaeaioa:

— iiaoaeiaaii iaoaiaoe/io iiaeaeue aocea aeeaeaiiy aeeiiaa/eo
aneio?iiieo iioi??a c ei?ioeicaieiooei, nooe?eueieie oa?i- e iaia?iaoiei
?ioi?aie ye aeaiaioa nenoaie ea?oaaiiy;

— ?ic?iaeaii iaoiae ?ic?aooieo ia?a?iciiae?e?a eiiooaoe?eieo no?oi?a o
iaiioeao aeaeo?iiaeaaeiaiiy aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo
iioi??a c ei?ioeicaieiooei, nooe?eueieie oa?i- e iaia?iaoiei ?ioi?aie;

— ?ic?iaeaii eiii’thoa?io i?i??aio ?ic?aooieo ia?ao?aeieo i?ioean?a
aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a c ei?ioeicaieiooei,
nooe?eueieie oa?i- e iaia?iaoiei ?ioi?aie, c aeio?eiaiiyi ocaaaeueiaieo
caeii?a eiiooaoe?? o nenoai?.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??:

— Oe?a?inueea eiioa?aioe?y «Iiaeaethaaiiy e aeine?aeaeaiiy no?eeino?
nenoai», Ee?a, 1996;

— I?aeia?iaeia eiioa?aioe?y «The 1-st International modelling school»,
Crimea, Autumn’96, Alushta, 1996;

— I?aeia?iaeia eiioa?aioe?y «The 2-nd International scientific and
technical conference on unconventional electromechanical and
electrotechnical systems», Szczecin, 1996;

— I?aeia?iaeiee neiiic?oi «IV Miendzynarodowy seminarium metrologow
«Metody i technika prztwarzania sygnalow w pomiarach fizycznych»,
Rzeszow, 1996;

— I?aeia?iaeiee neiiic?oi «V Miendzynarodowy seminarium metrologow
«Metody i technika prztwarzania sygnalow w pomiarach fizycznych»,
Rzeszow, 1997;

— I?aeia?iaeia eiioa?aioe?y «The 2-nd International modelling school»,
Crimea, Autumn’97, Alushta, 1997;

— I?aeia?iaeiee iaoeiai-i?aeoe/iee neiiic?oi “I?iaeaie noaeiiaoaeoaaiiy:
noai, ?aea?, ??oaiiy”, Ieeiea?a, 1997.

— I?aeia?iaeia eiioa?aioe?y «The 3-rd International modelling school»,
Crimea, Autumn’98, Alushta, 1998;

Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?? iioae?eiaaii 12 iaoeiaeo
i?aoeue, c ieo 8 noaoae.

No?oeoo?a oa ia’?i ?iaioe. Aeena?oaoe?y neeaaea?oueny c /ioe?ueio
?icae?e?a, aeniiae?a ? nieneo aeei?enoaieo e?oa?aoo?ieo aeaea?ae e
e?eueeino? 69 iaeiaioaaiue. Aiia ia? 146 noi?., 63 ?en. ? 2 aeiaeaoee, 6
noi?.

INIIAIEE CI?NO AeENA?OAOe??

O ia?oiio ?icae?e? ia??oioiaaii aeooaeuei?noue, iaoeiao iiaecio ?
i?aeoe/io oe?ii?noue ?iaioe, noi?ioeueiaaii iaoo aeine?aeaeaiue oa
iniiai? iieiaeaiiy, ui aeiinyoueny ia caoeno.

O ae?oaiio ?icae?e? iiaeaii iaea?aeai? a ?acoeueoao? ii?aoethaaiiy
e?oa?aoo?e iniiai? oai?aoe/i? iieiaeaiiy aeena?oaoe?eii? ?iaioe, ia
iniia? yeeo aoaeothoueny iaoaiaoe/i? iiaeae? aeaiaioa nenoaie ea?oaaiiy,
iaoiaee oi?ioaaiiy aeeoa?aioe?aeueieo ??aiyiue aeaeo?e/iiai oa
aeaeo?iia?iaoiiai e?e, iaoiaee ?ac?aooieo ii/aoeiaeo oiia i?e
no?eaeiiiae?aieo ci?iao eiiooaoe?eieo no?oiia.

Aeaeo?e/ia eiei. Noaeieiiee no?oi?a iiiaeeie a?oie aeaeo?e/iiai eiea
iiaea?ii oae

(1)

aea Up, Ux, I?, Io — a?aeiia?aeii noaeieiiee iai?oa oa no?oi?a ?aaa? ?
oi?ae ??aoa, i?e/iio noaiao?eoe? M oa noaeieiiee N aeeth/athoue o naaa
neiaie aeeoa?aioe?thaaiiy ca /anii.

??aiyiiy eiea caienaia ca iaoiaeii aoceiaeo iai?oa ia? aeaeyae:

(2)

aea

, (3)

i?e/iio F — oiiiei??/ia iao?eoey; Ft — o?ainiiiiaaia iao?eoey F.

Aeaeo?iia?iaoia eiei. Aeeoa?aioe?aeuei? ??aiyiiy a?oie, ui iaeaaeaoue
aei ?aaa? ? oi?ae ??aoa, ia?iaoiiai noaeiea caieno?ii aiaei??/ii aei
(1):

(4)

aea V?, Vo, Op, Ox — a?aeiia?aeii noaeieiiee ia?iaoieo iai?oa ? iioie?a
?aaa? ? oi?ae ??aoa; Sp, Sx — noaeieiiee ao?aeieo neaiae?a; Pp, Px —
ae?a?iiaeuei? iao?eoe? aeeoa?aioe?aeueieo ia?iaoieo iii??a.

No?oeoo?i? ??aiyiiy ia?iaoiiai noaeiea caieno?ii o aeaeyae?:

(5)

Ae?ace (4), (5) ooai?ththoue iiaio nenoaio iae?i?eieo
aeeoa?aioe?aeueieo ??aiyiue aeaeo?iia?iaoiiai eiea.

Caoei iiaeathoueny iaoiaee /aniai? aeene?aoecaoe?? cae/aeieo
aeeoa?aioe?aeueieo ??aiyiue ca yaieie ? iayaieie i?eioeeiaie.

O o?aoueiio ?icae?e? ?icaeyaeathoueny oai??? o?ainoi?iaoi?a oa
aeeiiaa/eo aneio?iiieo iioi??a c ei?ioeicaieiooei ? c nooe?eueieie oa?i-
e iaia?iaoiei ?ioi?aie ye c o?eoaciei, oae ? c aeaioaciei noaoi?ii.

Aeeoa?aioe?aeuei? ??aiyiiy o?eoaciiai o?ainoi?iaoi?a, noi?iiaai?
noiniaii no?oi?a iaiioie oa iioie?a oac, caieno?ii oae:

, (6)

Iao?eoe? eiao?oe??io?a iathoue aeaeyae:

S1= A1; S2=A4; T1=A2; T2=A3;

E1=-A1R1I1-A2R2I2; E2=-A3R1I1-A4R2I2,

; (7)

,

+ (1+ (2,

— aeeoa?aioe?aeuei? ia?iaoi? iii?e noa?aei?a oac o?ainoi?iaoi?a; Ri —
?acenoeai? iii?e. Iao?eoeth W(t) iaea?aeo?ii ia i?aenoaa? ??aiyiue
ia?iaoii?iaiaeo (4), (5).

??aiyiiy iaeiioaciiai o?ainoi?iaoi?a ? ie?aiei aeiaaeeii ?icaeyiooeo.

Aeeiiaa/ee aneio?iiiee iioi? oaeiae iiaea i?aoethaaoe ye o o?eoaciiio
?aaeei?, oae ? a ?aaeei? aeeaeaiiy a?ae aeaio iacaeaaeieo aeaea?ae —
caoaeaeaiiy oa ea?oaaiiy.

Aeeoa?aioe?aeuei? ??aiyiiy o?eoaciiai iioi?a c ei?ioeicaieiooei ?ioi?ii
iathoue aeaeyae:

(8)

aea ?iaeaen S ? R oeacothoue a?aeiia?aeii ia i?e/aoi?noue aei noaoi?a e
?ioi?a, i?e/iio

Sj = Aj ; Tj = Ajk ; (9)

Aeaiaioe noaiao?eoeue ? noaeieiiie (8), (9) aeey aeiaaeeo o?eoaciiai
noaoi?a ciaoiaeeii oae:

Ej = -AjRjij + Ajk ((k(k -Rkik); j, k = S, R,

AS = (S (1 — (SG ), AR = (R (1 — (RG ), ASR = ARS = -(R(SG,

,

,

(10)

— iaa?iai? ?iaeoeoeaiino? ?icn?yiiy iaiioie noaoi?a ? ?ioi?a; ( = ((im)
— cai?ioia aeeoa?aioe?aeueia ?iaeoeoeai?noue iaoeie; ( = ((im) —
cai?ioia noaoe/ia ?iaeoeoeai?noue iaoeie.

Eooiao oaeaee?noue iaa?oaiiy aecia/a?ii c ??aiyiiy ?ooo

, (11)

— iiiaio iii?o; J — noia?iee iiiaio ?ia?oe??.

O ?iaio? i?eaiaeyoueny a?aeiia?aei? ??aiyiiy iioi?a c aeaioaciei
noaoi?ii.

O ianea? o?ea ?ioi?a aeeiiaa/iai aneio?iiiiai iioi?a c nooe?eueiei
?ioi?ii ?iaeoeothoueny ?ioaineai? aeo?ia? no?oie, aeey ?o a?aooaaiiy
aeiaiaeeoueny aeei?enoiaoaaoe ii?aeiaiiy iaoiae?a oai???
aeaeo?iia?iaoieo e?e ? oai??? aeaeo?iia?iaoiiai iiey.

Oaia?, ia a?aei?io a?ae iiia?aaeiueiai aeiaaeeo, ?icaeyiaii ??aiyiiy
iioi?a c oa?aiia?iaoiei ?ioi?ii c aeaioaciei noaoi?ii. ??aiyiiy eiea
noaoi?a ia? aeaeyae:

(12)

aea

,

, (13)

?en. 1 ?ic?aooieia? e?ea? eooiai? oaeaeeino? aneio?iiiiai aeeiiaa/iai
iioi?a c oa?iia?iaoiei ?ioi?ii (1) ? c iaia?iaoiei ?ioi?ii (2) a ?aaeei?
iiaoi?iiai caioneo

cia/aiiy iai?oaeaiino? aeaeo?e/iiai iiey ia iiaa?oi? ?ioi?a, ye
ooieoe?? eooiai? eii?aeeiaoe (; na, ny — noae? eiao?oe??ioe.

), iia’ycaia c ?ioa??oaaiiyi ??aiyiue eaac?noaoe?iia?iiai
aeaeo?iia?iaoiiai iiey a o?e? ?ioi?a.

??aiyiiy aeaeo?iia?iaoiiai iiey a ianea? ?ioi?a oi?io?ii noiniaii
aaeoi?iiai iioaioe?aeo aeaeo?iia?iaoiiai iiey a oeee?iae?e/i?e nenoai?
eii?aeeiao

, (14)

— i?inoi?ia? eii?aeeiaoe.

, aea R1, R — aioo??oi?e ? ciai?oi?e ?aae?one o?ea ?ioi?a.

Iiaeoeue oa ?aae?aeueiee ? eooiaee eiiiiiaioe aaeoi?a ia?iaoii?
?iaeoeoe?? ? aen?aeueiee eiiiiiaio aaeoi?a iai?oaeaiino? aeaeo?e/iiai
iiey o iiia?a/iiio ia?a??c? ?ioi?a ia/eneth?ii oae

, (15)

— ?aae?aeueiee oa eooiaee eiiiiiaioe aaeoi?a ia?iaoii? ?iaeoeoe??.

) iiaa?oiyo ?ioi?a oa acaeiaae ?aae?on?a iaae ?ioa??oaaiiy iathoue
aeaeyae

, A(r, () = — A(r, 0), (16)

i?e/iio

, .(17)

aea (m — noaoe/iee ia?iaoiee ii?? noaoi?a ? iia?o?yiiai i?ii?aeeo.

?en. 2 ?iciiae?e aaeoi?iiai iioaioe?aeo a iiia?a/iiio ia?a??c?
nooe?eueiiai ?ioi?a aeeiiaa/iai aneio?iiiiai iioi?a a iaeiiio c
ia?ao?aeieo i?ioean?a o o?eniaaiee /an

Aeeoa?aioe?aeuei? ??aiyiiy aeaeo?iia?iaoiiai noaio (12), (14)
aeiiiaiththoueny aeeoa?aioe?aeueiei ??aiyiiyi iaoai?/iiai ?ooo.

O ?iaio? iaea?aeaii a?aeiia?aei? ??aiyiiy aeaeo?iiaoai?/iiai noaio
iioi?a c aethi?i??aei ?ioi?ii, a oaeiae ??aiyiiy iaio iioi??a c
o?eoaciei noaoi?ii.

Iaoaiaoe/i? iiaeae? o?ainoi?iaoi??a ? aeeiiaa/eo aneio?iiieo iioi??a o
ianooiiiio ?icae?e? aeei?enoiaothoueny ye noaaeaiaioe aocea aeeaeaiiy
?o a?ae aeaea?ae aia????

Ia ?en. 1 i?eaaaeaii ?ic?aooieia? e?ea? eooiai? oaeaeeino? aneio?iiiiai
aeeiiaa/iai iioi?a c oa?iia?iaoiei ?ioi?ii (1) ? c iaia?iaoiei ?ioi?ii
(2) a ?aaeei? iiaoi?iiai caioneo.

Ia ?en. 2 i?eaaaeaii ?iciiae?e aaeoi?iiai iioaioe?aeo o iiia?a/iiio
ia?a??c? nooe?eueiiai ?ioi?a aeeiiaa/iai aneio?iiiiai iioi?a a iaeiiio c
ia?ao?aeieo i?ioean?a o o?eniaaiee /an.

O /aoaa?oiio ?icae?e? aoaeothoueny iaoaiaoe/i? iiaeae? aoce?a aeeaeaiiy
aeeiiaa/eo aneio?iiieo iioi??a. Ia ?en. 3 iieacaii noaio nenoaie
ea?oaaiiy, ui i?noeoue aeaa aocee aeeaeaiiy (aeaa o?ainoi?iaoi?e 1 ? 4,
o?e aeeiiaa/? aneio?iii? iioi?e 3, 5, 6, o?eueo? 2 ? ?acenoeaiee
niiaeeaa/ 7). ??aiyiiy (2) oaei? neeaaeii? aeaeo?iiaoai?/ii? nenoaie,
yeui o?ainoi?iaoi? 4 a?aeianoe aei aea?aaa ??aoa, iaaoaathoue aeaeyaeo

(18)

?en. 3 ?ic?aooieiaa noaia aeaeo?e/iiai noaeiea, ui i?noeoue 7
aaaaoiiiethniee?a oa 2 a?oiiaeo aocea.

?ica’ycaaoe ia eiaeiiio /aniaiio e?ioe? ?ioa??oaaiiy (18) noiniaii
iai?oa aoce?a (aiie ae iaeii/anii iai?oae o?ainoi?iaoi?a 4), iiaia
nenoaia ??aiyiue aeaeo?iiaoai?/iiai noaio ?iciaaea?oueny ia ??aiyiiy
ie?aieo aeaiaio?a (6), (8), (11), (12), (14).

Eiiooaoe?ei? ?aaeeie a aeaeo?e/ieo eieao aoce?a aeeaeaiiy aeeiiaa/eo
aneio?iiieo iioi??a /anoi noi?iaiaeaeothoueny no?eaeiiiae?aieie ci?iaie
no?oio a iaiioeao aeaeo?e/ieo iaoei oa o?ainoi?iaoi??a, ui
coiiaeth?oueny iio?aaith aeio?eiaiiy o iiiaio /ano t = +0 caeiio no?oi?a
E??oaioa. A?aooaaiiy oeueiai yaeua cae?enith?ii ia i?aenoaa? iiaoaeiae
canooiieo noai ?iaeoeoeaiinoae. ?o iaea?aeo?ii c aeo?aeii? neiiooiaaii?
noaie caei?i/oaaiiyi on?o aeaiaio?a, ie??i eioooie ?iaeoeoeaiinoae, oaeo
noaio, ui a?aeiia?aea? noai? ?en. 3, iieacaii ia ?en. 4.

No?oeoo?i? ??aiyiiy ?ic?aooieiai? i?aenoaie, neeaaeaia ca ia?oei caeiiii
E??oaioa ? i?eioeeiii caa?aaeaiiy iioieic/aieaiue caieiooeo aeaeo?e/ieo
eiioo??a, o iiiaio /ano t = +0 aoaea

, (19)

aea (?, (o — eieiiee iiaieo iioieic/aieaiue aeaiaio?a, ui iaeaaeaoue aei
?aaa? oa oi?ae ??aoa; ((-0) — eieiiea, ui aecia/a?oueny
iioieic/aieaiiyie, ui ia?aaeoaaee eiiooaoe??.

No?oeoo?i? ??aiyiiy (19) aeiiiaith?ii ??aiyiiyie no?oi?a ?aaa? ? oi?ae

. (20)

Ae?ace (19)-(20) iiaea?ii o aoceiaeo eii?aeeiaoao

A(?(+0) = X(-0); ((x= Ft((?, (21)

aea iao?eoe? A oa O ciaoiaeeii c ??aiyiue

A = G? + FGoFt; X(-0) = I?(-0) — FIo(-0). (22)

?en. 4 ?ic?aooieiaa i?aenoaia, ui a?aeiia?aea? neiiooiaai?e nenoai?
?en. 2 i?e ?aioiaiio ia?ea? o aoi?eiiiio

eie? o?ainoi?iaoi?a (1).

I?aaa /anoeia ae?oaiai ??aiyiiy (22) ? ??aiyiiyi, caienaiei ca ia?oei
caeiiii E??oaioa a iiiaio t = — 0. Ioaea, yeui o ?ic?aooieia?e noai? i?e
t=-0 aeeiio?oueny caeii no?oi?a E??oaioa, oi no?eaeiiiae?aii? ci?ie
iioieic/aieaiue oa no?oi?a ia a?aeaoaeaoueny.

O aeena?oaoe?? i?eaaaeaii iio??ai? ae?ace, ca yeeie cae?enith?oueny
ia?a?aooiie a?ae i?e?ino?a iiaieo iioieic/aieaiue iaiioie aei i?e?ino?a
a?aeiia?aeieo ?i no?oi?a.

O iaaaaeai?e ieae/a oaaeeoe? i?eaaaeaii ?acoeueoaoe ?ic?aooieo
eiiooaoe?eieo no?oi?a o aoce? aeeaeaiiy /ioe?ueio aeeiiaa/eo aneio?iiieo
iioi??a a?ae ni?eueiiai o?ainoi?iaoi?a. Eiiooaoe?y iieyaaea o aeieeaii?
iaeiiai c aeeiiaa/eo aneio?iiieo iioi??a o iaaiee iiiaio /ano
ia?ao?aeiiai i?ioeano. Oea i?ecaaei aei ii?ooaiiy caeiio no?oi?a
E??oaioa o aoce? aeeaeaiiy. Iaaeiionoei?noue aiae?co aac a?aooaaiiy
oeueiai yaeua ?ethno?othoue e?ea? ?en. 5 ? ?en. 6.

Ia ia?oiio c ieo niinoa??aa?ii i?enooi?noue aeaea?aea iino?eiiai
no?oio, coiiaeaiiai ianeiiiainiaaieie no?oiaie o aoce? a iiiaio t=+0.
Oea aeaea?aei noai?th? o?eoeaiee aoaeo aeeiai?/-

Oaae. 1

No?oie iaiioie noaoi?a 4-o iioi??a aei eiiooaoe??th No?oie iaiioie
o?ainoi?iaoi?a aei eiiooaoe??

Oace A Oace A ia?a. iai. aoi?. iai.

isA1 isA2 isA3 isA4 isB1 isB2 isB3 isB4 i1A i1B i2A i2B

-3.61

-1.71

-3.54

-4.70

-4.76

-2.17

-4.61

-5.97

-13.7

-17.7

13.7

17.01

I?ney eiiooaoe??

I?ney eiiooaoe??

Oace A Oace A ia?a. iai. aoi?. iai.

isA1 isA2 isA3 isA4 isB1 isB2 isB3 isB4 i1A i1B i2A i2B

-4.06

-1.97

-4.10

0.0

-5.28

-2.42

-5.27

0.0

-10.2

-12.9

10.13

?en. 6. Oa naia, ui ia ?en. 5, aea c ia?a?aooieii ii/aoeiaeo oiia

o iiiaio eiiooaoe??.

?en. 5. No?oi oace A aoi?eiii? iaiioee o?ainoi?iaoi?a a ?aaeei? ioneo
/ioe?ueio iioi??a c iiaeaeueoei aeieeaiiyi iaeiiai c ieo aac
ia?a?aooieo ii/aoeiaeo oiia o ii

iaio eiiooaoe??.

iiai aaeueioaaiiy iioi??a, ui ia a?aeiia?aea? aenia?eiaioaeueiei aeaiei.
O aeena?oaoe?? aeine?aeaeaii aaaaoi ?aaeei?a, ye? noi?iaiaeaeothoueny
iiae?aieie aoaeoaie.

AENIIAEE

1. A ?acoeueoao? aiae?co aeinooiii? iai e?oa?aoo?e anoaiiaeaii, ui ia
aeaiee /an a?aenooi? no?ia? iaoaiaoe/i? iaoiaee ?ic?aooieo eiiooaoe?eieo
? ia?ao?aeieo i?ioean?a aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a c
ei?ioeicaieiooeie ? nooe?eueieie ?ioi?aie ye aeaiaioa nenoaie ea?oaaiiy.
Cai?iiiiiaai? iaie iaoiaee

ia iathoue aiaei??a.

2. Cai?iiiiiaai? aeeoa?aioe?aeuei? ??aiyiiy o?ainoi?iaoi??a oa
aeeiiaa/eo aneio?iiieo iioi??a c ei?ioeicaieiooei oa nooe?eueiei
?ioi?aie iaeneiaeueii oi?o?eiaai? aeey ?o aeei?enoaiiy a yeino? ??aiyiue
aeaiaioii? aace nenoai ea?oaaiiy. Ui noino?oueny iioi??a c nooe?eueieie
?ioi?aie, oi oea c?iaeaii aia?oa.

3. A?aoiaoth/e no?oeoo?i? iniaeeaino? aeaeo?e/ieo e?e nenoai ea?oaaiiy
aeeiiaa/eie aneio?iiieie iioi?aie c ei?ioeicaieiooei ? nooe?eueiei
?ioi?aie, ui iieyaathoue o iayaiino? aaeeei? e?eueeino? aeaeo?e/ieo
eiioo??a e iaiaaeaii? e?eueeino? aoce?a, ??aiyiiy noaio nenoaie
iaiao?aeii oi?ioaaoe ca iaoiaeii aoceiaeo iai?oa o /ania?e iaeano?.

4. Oiane?aeie oiai, ui aeaeo?e/i? eiea nenoai ea?oaaiiy aeeiiaa/eie
aneio?iiieie iioi?aie c ei?ioeicaieiooei oa nooe?eueiei ?ioi?aie ?
D-ae?iaeaeaieie, eiiooaoe?ei? ?aaeeie noi?iaiaeaeothoueny
no?eaeiiiae?aieie ci?iaie no?oi?a a aeaeo?e/ieo iaiioeao aeaiaio?a
nenoaie ea?oaaiiy, anoaiiaeaii, ui aac a?aooaaiiy oeueiai yaeua
?ic?aooiie ia?ao?aeiiai i?ioeano noa? iaiiaeeeaei.

5. A?aoiaoth/e no?oeoo?i? iniaeeaino? aoce?a aeeaeaiiy nenoaie ea?oaaiiy
aeeiiaa/eie aneio?iiieie iioi?aie c ei?ioeicaieiooei e nooe?eueiei
?ioi?aie, a?aooaaiiy no?eaeiiiae?aii? ci?ie no?oi?a a iaiioeao aeaiaio?a
iaiao?aeii oi?ioaaoe o aoceiaeo eii?aeeiaoao ia iniia? ?ic?aooieiaeo
noai ?iaeoeoeaiinoae.

6. Aeeoa?aioe?aeuei? ??aiyiiy o?ainoi?iaoi?a oa aeeiiaa/eo aneio?iiieo
iioi??a c iaoith ni?iuaiiy aiae?co i?aaenoaaeai? o aeaeyae?, c?o/iiio
aeey ?o aeei?enoaiiy o iaoiae? aoceiaeo iai?oa, oiaoi ?ica’ycaieie
a?aeiinii ia?oeo iio?aeieo ca /anii ooeaieo iaa?aeiieo o ii?iaeuei?e
oi?i? Eio?.

7. Anoaiiaeaii, ui aeeoa?aioe?aeuei? ??aiyiiy aeaeo?iiaoai?/iiai noaio
aocea aeeaeaiiy nenoai ea?oaaiiy aeeiiaa/eo aneio?iiieo iioi??a c
ei?ioeicaieiooei e nooe?eueiei ?ioi?aie ? ia aei?noeeie, oiio ae?i?eoie
?o ?ioa??oaaiiy aeioe?eueii ?aae?ciaoaaoe ca yaiei i?eioeeiii.

8. ?ic?iaeai? ae?i?eoi oa eiii’thoa?ia i?i??aia ?ic?aooieo

ia?ao?aeieo aeaeo?iiaoai?/ieo i?ioean?a aocea aeeaeaiiy nenoai ea?oaaiiy
aeeiiaa/eo aneio?iiieo iioi??a c ei?ioeicaieiooei oa nooe?eueiei
?ioi?aie. O i?i??ai? ia?aaeaa/a?oueny a?aooaaiiy no?eaeiiiae?aieo
eiiooaoe?eieo i?ioean?a.

9. ?acoeueoaoe eiii’thoa?iiai neioethaaiiy ia?ao?aeieo i?ioean?a aocea
aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a c ei?ioeicaieiooei oa
nooe?eueiei ?ioi?aie ?ethno?othoue i?io?eaiiy aeaeo?iiaoai?/ieo
i?ioean?a a /an? oa no?eaeiiiae?aio ci?io no?oi?a o iaiioeao
iaia?ia/oaaiiy. Iieacaii oaeiae, ui iaoooaaiiy ocaaaeueiaieie caeiiaie
eiiooaoe?? i?eaiaeeoue aei iaa??ieo iaea?aeaieo ?acoeueoao?a.

10. Ine?eueee cai?iiiiiaaia iaoaiaoe/ia oai??y ??oioo?oueny ia
iae?i?eieo aeeoa?aioe?aeueieo ??aiyiiyo o cae/aeieo oa /anoeiieo
iio?aeieo o /ania?e iaeano?, a?aeia?aaeaiiy anaiiaeeeaeo ea?oth/eo
aieea?a oa cai?ioieo ca’yce?a ia noai?th? aoaeue yeeo i?iaeai. Aiie
iiaeooue aooe i?e iio?aa? aaaaeai? a caaaeueio nenoaio ??aiyiue o
?iaeea?aeoaeueiiio ii?yaeeo.

11. Cai?iiiiiaaiee iaoiae ?ic?aooieo ia?ao?aeieo ? eiiooaoe?eieo
i?ioean?a aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a c
ei?ioeicaieiooei oa nooe?eueiei ?ioi?aie ye aeaiaioa nenoaie ea?oaaiiy
aia?oa aea? iiaeeea?noue cae?enithaaoe aiae?c ? neioac ia no?ia?e
iaoaiaoe/i?e iniia? c aeei?enoaiiyi ia/enethaaeueieo iaoiae?a ?
eiii’thoa?iiai neioethaaiiy, ia caa?oath/enue aei aei?iaeo ? ia caaaeaee
?aae?ciaaieo ia i?aeoeoe? iaoo?ieo aenia?eiaioao.

NIENIE IOAE?EAOe?E CA OAIITH AeENA?OAOe??

1. *aaai A., ?aaaaao A., ?aaaaao I. Aeai?eoi ?ac?aooieo eiiooaoe?eieo
?aaeeiia a aeaeo?iiaoai?/ieo nenoaiao. — Oe?aeineay eiioa?aioeey. —
Iiaeaee?iaaiea e enneaaeiaaiea onoie/eainoe nenoai. — Eeaa: 1996.
n.149.

2. *aaai I., ?aaaaao A., ?aaaaao I. Iioei?caoe?y ?ioi?a aeeiiaa/iai
aneio?iiiiai iioi?a. Proceedings of the 1-st International modelling
school. — Krym Autumn’96, — Rzeszow, 1996, p. 128-130.

3. *aaai A.E., ?aaaaao A., ?aaaaaa I. Iai?aiieueiaa iaoaiaoe/ia
iiaeaeue aeeiioaaeueiiai aneio?iiiiai iioi?a c ianeaiei ?ioi?ii. —
A?niee AeO “Euea?anueea iie?oaoi?ea’’ Aeie?iaaeueia oaoi?ea oa
iao?ieia?y, ? 53, Euea?a, 1998, n.130-131.

4. Tchaban V.‚ rababah A., rababah M. Calculation of inital condition
in electromechanical systems.- Proceeding of the 2-nd International
scientific and technical conference on unconventional electromech. and
electrotechn. systems. Szczecin, 1996, p. 627-630.

5. Aouae. ?., *aaai. I., ?aaaaao. I. Eiii’thoa?ia neioethaaiiy
aeaeo?iiaoai?/ieo i?ioean?a o oai??? aeaeo?ia?iaoiiai iiey. — Oe?aeineay
eiioa?aioeey: “Iiaeaee?iaaiea e enneaaeiaaiea onoie/eainoe nenoai”,
Eeaa, 1996, n. 42.

6. *aaai A., ?aaaaao I. Iaoaiaoe/ia iiaeaeue aaoiiiiii? nenoaie
aneio?iiieo iioi??a. — I?aoe? I?aeia?iaeiiai iaoeiai-i?aeoe/iiai
neiiic?oio “I?iaeaie noaeiiaoaeoaaiiy: noai, ?aea?, ??oaiiy”, Ieeiea?a,
1997.

7. The matematical model of three-phase actuating asynchronous motor
with massive ferromagnetic rotor. O. Tchaban, A. Rababah, M. Rababah, A.
Kovalchyk, V. Tchaban. — Materialy miendzynarodowego sympozium
metrologow, Rzeszow, 1997, ss. 233-236.

8. *aaai A., ?aaaaao I, *aaai. I. ??aiyiiy nenoaie aeeiiaa/eo
aneio?iiieo iioi??a c ianeaiei ?ioi?ii. — Aaoiiaoeea, aei??thaaiiy oa
ea?oaaiiy. — ? 324, Euea?a, 1998, n. 118- 120.

9. ?aaaaaa I., ?aaaaaa A. Iaoaiaoe/ia iiaeaeue aocea aeeaeaiiy
aeeiioaaeueieo aneio?iiieo iioi??a i?e?iaeaeo?iiaoai?/ieo nenoai. —
Iaoeiiciaanoai, 1998/8’98, c 20-23.

10. ??aiyiiy aocea aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a. Eia?a/ae
ss., *aaai I., ?aaaaaa I., ?aaaaaa A.- Oaoi?/i? a?no?, 1998/1 (6),
1998/2(7), c. 47-48.

11. *aaai A. E, Aeue ?aaaaaa I. N, *aaai I. A. ??aiyiiy nenoaie
aeeiiaa/eo aneio?iiieo iioi??a.- A?niee AeO ,, Euea?anueea iie?oaoi?ea’’
Aeaeo?iaia?aaoe/i? oa aeaeo?iiaoai?/i? nenoaie, ? 334, Euea?a, 1997, n.
139-141.

12. *aaai I., ?aaaaao A., ?aaaaao I. Iioei?caoe?y ?ioi?a aeeiiaa/iai
aneio?iiiiai iioi?a. Proceedings of the 1-st International Modelling
School, Krym, Autumn’96, Rzeszow, 1996, p. 83.

AIIOAOe?ss

Aeue ?aaaaaa Iaioi Noeaeiai. Aeine?aeaeaiiy ia?ao?aeieo i?ioean?a aocea
aeeaeaiiy aeeiiaa/eo aneio?iiieo iioi??a ye aeaiaioa nenoaie ea?oaaiiy.
— ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 05.13.05.- aeaiaioe oa i?eno?i? ia/enethaaeueii?
oaoi?ee oa nenoai ea?oaaiiy. — Aea?aeaaiee oi?aa?neoao «Euea?anueea
iie?oaoi?ea», Euea?a, 1998.

Aeena?oaoe?y i?enay/aia iiaoaeia? iaoaiaoe/ii? iiaeae?
aeaeo?iiaoai?/iiai noaio aocea aeeaeaiiy nenoai ea?oaaiiy aeeiiaa/eie
aneio?iiieie iioi?aie c ?ioi?aie oeio a?ey/i? ee?oee, nooe?eueieie
ii?iaeienoeie oa?i- oa iaia?iaoiei ?ioi?aie. Iaoiae aiae?co ??oioo?oueny
ia ii?aeiaii? iaoiae?a iae?i?eieo aeaeo?iia?iaoieo e?e oa
aeaeo?iia?iaoiiai iiey o iae?i?eiiio nooe?eueiiio ?ooiiiio na?aaeiaeu?.
?ic?iaeai? ae?i?eoie oa eiii’thoa?i? i?i??aie ?ic?aooieo ia?ao?aeieo
i?ioean?a ia?aaeaa/athoue no?eaeiiiae?ai? ci?ie eiiooaoe?eieo no?oi?a a
iaiioeao iaia?ia/oaaiiy. Iieacaii, ui aac a?aooaaiiy oeueiai yaeua
?ic?aooiie ia?ao?aeiiai i?ioeano noa? iaiiaeeeaei. I?eaiaeyoueny
?acoeueoaoe ?ic?aooieo ia?ao?aeiiai aeaeo?iiaoai?/iiai i?ioeano aocea
aeeaeaiiy /ioe?ueio aeeiiaa/eo aneio?iiieo iioi??a, caaeeaeaieo
ni?eueiei o?ainoi?iaoi?ii.

Eeth/ia? neiaa: nenoaia ea?oaaiiy, aeeiiaa/ee aneio?iiiee iioi?,
o?ainoi?iaoi?, aocie aeeaeaiiy, aeaeo?iia?iaoia iiea, ia?ao?aei?
i?ioeane.

AIIIOAOeEss

Aeue ?aaaaaa Iaioi Noeaeiai. Enneaaeiaaiea ia?aoiaeiuo i?ioeannia ocea
ieoaiey eniieieoaeueiuo aneio?iiiuo aeaeaaoaeae eae yeaiaioa nenoaiu
oi?aaeaiey. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05. 13. 05. — yeaiaiou e ono?ienoaa au/eneeoaeueiie
oaoieee e nenoai oi?aaeaiey. — Ainoaea?noaaiiue oieaa?neoao «Euea?anueea
iie?oaoi?ea», Eueaia, 1998.

Aeenna?oaoeey iinayuaia iino?iaieth iaoaiaoe/aneie iiaeaee
yeaeo?iiaoaie/aneiai ninoiyiey ocea ieoaiey nenoai oi?aaeaiey
eniieieoaeueiuie aneio?iiiuie aeaeaaoaeyie n ?ioi?aie a aeaea aaee/ueae
eeaoee, nieioiui ionoioaeui oa??i- e iaiaaieoiui ?ioi?aie.. Iaoiae
aiaeeca aace?oaony ia niaianoiii ni/aoaiee iaoiaeia iaeeiaeiuo
yeaeo?iiaaieoiuo oeaiae e yeaeo?iiaaieoiiai iiey a iaeeiaeiie nieioiie
iiaeaeaeiie n?aaea. ?ac?aaioaiua aeai?eoiu e eiiiuethoa?iua i?ia?aiiu
?an/aoa ia?aoiaeiuo i?ioeannia o/eouaatho nea/eiia?aciua eciaiaiey
eiiiooaoeeiiiuo oieia a iaiioeao iaiaaie/eaaiey. Iieacaii, /oi aac o/aoa
yoiai yaeaiey ?an/ao ia?aoiaeiiai i?ioeanna noaiiaeony iaaiciiaeiui.
I?eaiaeyony ?acoeueoaou ?an/aoa ia?aoiaeiiai yeaeo?iiaoaie/aneiai
i?ioeanna ocea ieoaiey /aou?ao eniieieoaeueiuo aeaeaaoaeae n ieoaieyi io
iauaai o?ainoi?iaoi?a.

Eeth/aaua neiaa: nenoaia oi?aaeaiey, eniieieoaeueiue anei

o?iiiue aeaeaaoaeue, o?ainoi?iaoi?, ocae ieoaiey, yeaeo?iiaaieoiia iiea,
ia?aoiaeiua i?ioeannu.

ABSTRACT

Al Rababaa Mamoun Suleiman. The investigation of transient processes of
power supply node of actuating induction motors as element of control
system. — Manuscript.

Thesis for a candidate’s degree by speciality 05.13.05 — units and
devices of computer technique and control systems.- State university
”Lviv polytechnic”, Lviv, 1998.

The thesis is devoted to the creation of the mathematical model of
electromechanical state of power supply node of the control system of
actuating induction motors with squirrel-cage rotors and massive hollow
ferromagnetic and nonmagnetic rotors. The method of analysis is based on
the combining the methods of nonlinear electromagnetic circuits and
electromagnetic field in nonlinear continuous movable medium. The
created algorithms and computer programs of transient processes
calculation account uneven changes of commutation currents in the
magnetization windings. The matter that the transient process
calculation is not available without accounting of such phenomenon is
shown. The results of computation of transient electromechanical process
of power supply node of four actuating induction motors supplied by
common transformer are given.

Key words: control system, actuating induction motor, transformer, power
supply node, electromagnetic field, transient processes.

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