Modelo Matematico y Control De...

 

JIHAFI JDXAJÄXLCI \ CIOXRIF HA QO SLSXAJD HA GFQLHIS ^DQFD DOHRAD IRXLP WDFAOCLD  @ISÌ FAIODRHI RDJÊRAP ACKDWDRRÊD FIRAOD CDRHIOD RAOHÓO

 

   

Irtlz Wdfaocld, ^dufd Dohrad Jihafi jdtajätlci y ciotrif ha uo slstajd ha gfulhis / ^dufd Dohrad Irtlz Wdfaocld, @isì Faiodrhi Rdjêraz Ackdvdrrêd,

              

Firaod Cdrhiod2>44. Raohóo5 ahltird Slfvld Loìs @ljìoaz Mójaz.-- 4ª ah. -- Jahaffêo0 Lostltuti Xacoi Xacoifómlci fómlci Jatripifltdoi, 4 14 318 7> • Gdx0 88> 12 12 www.ltj.ahu.ci Jahaffêo – Cifijbld

Fds iplolioas, irlmlodfas y cltdclioas haf taxti sio ha fd raspiosdblflhdh ha fis dutiras. Af Lostltuti sdfvd cudfqular ibflmdclóo harlvdhd haf flbri qua sa pubflcd. ^ir fi tdoti, affd racdarä ðolcd y axcfuslvdjaota a xcfuslvdjaota sibra fis dutiras.

 

CIOXAOLHI

L OXRIHQCCLÓO ................................................................................................. .................................................. ............................................... 4= 4.

JIHAFDHI HA SLSXAJDS ................................................. ................................................................... .................. 23

4.4 4.4.4 4.4.2 4.4.3

Hlsaôi axparljaotdf..................................................... ....................................................................... .................. 21 Wdrldbfas ha hlsaôi ....................................................... ......................................................................... .................. 27 Saôdf ha axcltdclóo....................................................... ......................................................................... .................. 2= Fdzi carrdhi ....................................................... ................................................................................... ............................ 33

4.4.8 4.4.1

Cdotlhdh hdtis ......................................................... ........................................................................... .................. ^arêihi hahajuastrai ....................................................................... ..................................................... .................. 33 38

4.2 4.2.2 4.2.3 4.2.8

Safacclóo ha fd astructurd haf jihafi ............................................ 31 Cijpfa`lhdh haf jihafi ....................................................... ................................................................ ......... 31 Cisti haf jihafi................................................ ............................................................................ ............................ 3= Qsi qua sa fa hdrä df jihafi................................................. .......................................................... ......... 3;

4.3 4.3.4 4.3.2

Safacclóo haf crltarli ha d`usta y astljdclóo ha pdräjatris .......... 84 Jloljlzdclóo ha fis arriras ha prahlcclóo .................................... 88 Jdrci astdhêstlci pdrd fd astljdclóo ha pdräjatris ...................... 87

4.3.3 4.3.8

D`usta ha ciaglclaotas ha iha y dpflcdclioas aspacldfas ................ 8; Wdflhdclóo ....................................................................................... .................................................. ..................................... 8<

2.

HLSAÔI HA CIOXRIFDHIRAS CFÄSLCIS ................................................ ................................................ 13

2.4 2.2 2.2.4 2.2.2

D`usta ha fis ciotrifdhiras p, pl y plh ........................................... 18 Slotiolzdclóo ha ciotrifdhiras pir af jìtihi ha Plamfar-Olckifs 1= Jìtihi ha mdodocld fêjlta .................................................... ............................................................. ......... 1; Jìtihi ha fd curvd ha radcclóo ..................................................... 7>

 

2.2.3 2.2.8

Ramufdhir plh jahldota af fumdr maijìtrlci ha fds rdêcas ............. 74 Ciotrif pir af jìtihi ha Xruxdf-Rdmdzzlol................................... 78

3.

HLSAÔI HA CIOXRIFDHIRAS LOXAFLMAOXAS .......................................... .......................................... 7<

3.4 3.4.4 3.4.2 3.4.3 3.2 3.2.4 3.2.2 3.2.3 3.2.8

Rahas oauriodfas .................................................... ............................................................................ ........................ 7< Cdrdctarêstlcds maoardfas ha fds rahas oauriodfas .......................... =4 Guoclioas ha dctlvdclóo .................................................. ................................................................. ............... =3 Dpraohlzd`a .................................................. .................................................................................... .................................. =1 Fómlcd hlgusd ................................................ .................................................................................. .................................. =1 Cio`uotis hlgusis ................................................... ........................................................................... ........................ =; Wdrldbfas flomöêstlcds y tìrjlois flomöêstlcis ................................ =; Ramfds a logaraocld hlgusds ......................................................... ............................................................. .... =; Ciotrif hlgusi......................................................... ................................................................................. ........................ =<

8.

RQABDS  \  RASQFXDHIS  AO  AF  CDSI  HA  ASXQHLI. FD  ^FDOXD  HA  GFQLHIS  ^ HAF L OSXLXQXI XACOIFÓMLCI JAXRI^IFLXDOI , LXJ ....... .............. ............. ............. ......... ;4

8.4 8.4.4 8.4.2

Hascrlpclóo ha fd pfdotd qua sa vd d ciotrifdr ............................... ;4 Maoardflhdhas ........................................................ ................................................................................. ......................... ;2 Lostrujaotdclóo ..................................................... .............................................................................. ......................... ;8

8.2 8.2.4 8.2.4.4 8.2.4.2

Ibtaoclóo haf jihafi jdtajätlci ha fd pfdotd ha gfulhis ............ 2 8.2.4.7 Crltarli ha d`usta y astljdclóo ha pdräjatris .............................. 4>3 8.2.4.= Wdflhdclóo haf jihafi .................................................... .................................................................. .............. 4>< 8.2.2 Jihafi oi floadf ................................................... .......................................................................... ....................... 4>< 8.2.2.4 Hlsaôi axparljaotdf ....................................................... ..................................................................... .............. 4><

 

8.2.2.2 Astructurd haf jihafi ................................................... ................................................................... ................ 448 8.2.2.3  Crltarli ha d`usta y astljdclóo ha pdräjatris .............................. 44< 8.2.2.8  Wdflhd dflhdclóo clóo haf jiha ....... .............. ............. ............. .............. .............. ............. ............. .............. ............ ..... 424 8.3 8.3.4 8.3.2 8.3.3 8.3.8 8.3.1

Hlsaôi Hlsaôi haf haf ciotrif ciotrif ciovaocliodf pir af jìtihi.................................................. haf tdotai ................................ 427 427 Plamfar-Olckifs, mdodocld fêjlta .................................................. 42; Plamfar-Olckifs, curvd ha radcclóo .............................................. 42< Hlsaôi haf ciotrif usdohi af jìtihi haf fumdr maijìtrlci ha fds rdêcas (fmr) ................................................ ....................................................... ....... 42< Hlsaôi haf ciotrif usdohi af jìtihi ha Rdmdzzlol ..................... 437

8.8 8.8.4 8.8.2

Ciotrif hlgusi..................................................... ............................................................................... .......................... 43< Haglolclóo ha fds aotrdhds ..................................................... ............................................................ ....... 43< ^drtlclioas birrisds .................................................... ..................................................................... ................. 43<

8.8.3 8.8.8 8.8.1 8.8.7 8.1 8.7

Guoclioas ha partaoaocld ............................................................. ...................................................... ....... 43< Ramfds ha logaraocld ..................................................................... .................................................... ................. 484 Hacihlglcdclóo ................................................... ............................................................................. .......................... 484 Sljufdclóo haf ciotrif hlgusi ...................................................... 482 Ciotrif cio rahas oauriodfas ................................................ ....................................................... ....... 481 Doäflsls cijpdrdtlvi ha fds tìcolcds ha ciotrif usdhds ............... 412

1.

D OA[I 4. K ARRDJLAOXD AO JDXFDB®/SLJQFLOE  ^DRD AF ASXQHLI HA FD  ^FDOXD HA GFQLHIS HAF L OSXLXQXI XACOIFÓMLCI JAXRI^IFLXDOI , LXJ . ...................................................................................................... ................................................ ...................................................... 411

1.4 1.4.4 1.4.2 1.4.3 1.4.8 1.4.1 1.2 1.3 1.3.4 1.3.2

Raquarljlaotis haf......................................................... slstajd................................................... .......................................................... ....... 411 Slstajd ipardtlvi ......................................................................... ................ 411 ^ricasdhir ................................................. .................................................................................... ................................... 411 Aspdcli ao af hlsci ....................................................... ....................................................................... ................ 411 Jajirld rdj ...................................................... ................................................................................ .......................... 417 Jdtfdb® .................................................... ....................................................................................... ................................... 417 Lostrucclioas ha lostdfdclóo ................................................. ......................................................... ........ 417 Cóji utlflzdr Kajagfu................................................. ................................................................. ................ 47> Lhaotlglcdclóo ha pdräjatris e4 y e2 ........................................... 474 Ciotrif plh ................................................. ................................................................................... .................................. 473

 

1.3.3 1.3.8

Ciotrif Rdmdzzlol.................................................. ......................................................................... ....................... 477 Ciotrif Lotaflmaota ................................................ ....................................................................... ....................... 4=>

7.

D OA[I 2. JDOQDF BÄSLCI HA I^ARDCLÓO HA FD ^FDOXD HA GFQLHIS  HAF L OSXLXQXI XACOIFÓMLCI JAXRI^IFLXDOI ,

LXJ ....... .............. .............. .......... ... 4=3

7.4 7.4.4 7 .4.2

Ciohlclioas lolcldfas ha fis aqulpis............................................ 4=3 Lospacclóo vlsudf ................................................... .......................................................................... ....................... 4=8 ^ricahljlaoti pdrd fd puastd ao jdrckd ...................................... 4=8

   

BLBFLIMRDGÊD ................................................. ................................................................................. ................................ 4;4

 

Ê OHLCA OHLCA HA GLMQRDS GLMQRD 4

^ricasi pdrd af jihafdhi ha uo slstajd ................................... 21

GLMQRD 2  Raprasaotdclóo mräglcd ha fd saôdf ljpufsi ............................... 2; GLMQRD 3  Raprasaotdclóo mräglcd ha fd saôdf ascdfóo uoltdrli .................. 3> GLMQRD 8  Raspuastd df ascdfóo têplcd ha uo slstajd ha prljar irhao cio ratdrhi ..................................................... ....................................................................... .................. 34 GLMQRD 1  Hldmrdjd ha vdflhdclóo ha uo jihafi ...................................... 1> GLMQRD 7  Raspuastd haf slstajd cudohi fd mdodocld haf ciotrifdhir as lmudf d fd mdodocld ðftljd  E u y af parêihi ðftlji as Xu ...  ...... ... 1< GLMQRD =  Dfmirltji ha ciotrif pdrd af ramufdhir ^LH (FMR ) ....... ............. ............. .......... ... 73 GLMQRD ;  Asquajd bäslci ha uo slstajd ha ciotrif radfljaotdhi............ 78 GLMQRD   Oauriod drtlglcldf ..................................................... ....................................................................... .................. =3 GLMQRD 44 GLMQRD 42 GLMQRD 43 GLMQRD 48 GLMQRD 41 GLMQRD 47 GLMQRD 4= GLMQRD 4; GLMQRD 4< GLMQRD 2> GLMQRD 24

Guoclioas ha dctlvdclóo .................................................... ............................................................. ......... =8 Drqultacturd ha uo slstajd ha ciotrif hlgusi ............................ ;> ^fdotd ha gfulhis haf LXJ ................................................... ............................................................ ......... ;4 Hldmrdjd ha lostrujaotis pdrd af ciotrif ha gfu`i.................... ;3 Hldmrdjd ha lostrujaotis pdrd af ciotrif ha olvaf ................... ;3 Wdrldhir ha vaficlhdh ....................................................... ................................................................ ......... ;1 Hldmrdjd ha cioaxlóo haf vdrldhir ha vaficlhdh...................... ;7 Xrdosjlsir ha gfu`i Sltrdos ^ ha Slajaos ................................. ;= Xrdosjlsir ha olvaf ................................................. ................................................................... .................. ;< ^dotdffd ha ipardclóo ao ]loCC .................................................. .................................................. = Saôdf dpflcdhd d fd vdrldbfa jdolpufdhd (vdrldhir ha vaficlhdh) ........................................................... ........................................... ................ 44> GLMQRD 2 Saôdf ha raspuastd pdrd af olvaf ao af tdoqua 2 (tdoqua jatäflci) ................................................................................................. ........................................................ ......................................... 442 GLMQRD 34 Saôdf ha raspuastd pdrd af cduhdf T4   (hasha af tdoqua jatäflci df tdoqua dcrêflci) ........................... 443 GLMQRD 32 Saôdf ha raspuastd pdrd af cduhdf T3   (hasha af tdoqua dcrêflci df tdoqua jatäflci) ........................... 448 GLMQRD 33 Bfiqua ha Sljufloe ® cio af jihafi haf slstajd ..................... 422 GLMQRD 38 Hldmrdjd haf lotarlir haf bfiqua cio af jihafi haf slstajd ... 423 GLMQRD 31 Wdfiras hdhis d fds vdrldbfas haf jihafi ................................ 423 GLMQRD 37 Hldmrdjd haf lotarlir haf bfiqua ciostdotas ha rastr rastrlcclóo lcclóo ha fd Glmurd 3= ................................ 428 GLMQRD 3= Hldmrdjd haf lotarlir haf bfiqua tdoqua 4 ha fd Glmurd 38 ..... 428 GLMQRD 3; Hldmrdjd haf lotarlir haf bfiqua tdoqua 2 ha fd Glmurd 38 ..... 428 GLMQRD 3< Warlglcdclóo aotra af vdfir radf y astljdhi pdrd E 4 ................ .................. 421 GLMQRD 8> Warlglcdclóo aotra af vdfir radf y astljdhi pdrd E 2 ................ .................. 427 GLMQRD 84  Raspuastd ao sljufdclóo haf slstajd ciotrifdhi cio uo ciotrif tdoqua 2) .................... 42= ^LH (olvaf ha dmud ao af tdoqua GLMQRD 82  Saôdf ha ciotrif pdrd af slstajd slstajd ha olvaf ciotrifdhi cio uo ciotrif ^LH ..................................................................... ........................................................ ............. 42= GLMQRD 83 Hldmrdjd ha biha pdrd af slstajd ha tarcar irhao cio ratdrhi .............................................................................. 42< GLMQRD 88 Raspuastd haf slstajd ................................................ ............................................................. ............. 43> GLMQRD 81 Lomrasi ha fis raquarljlaotis ha hlsaôi .................................. 434 GLMQRD 87 Ärad ha hlsaôi haf ciotrifdhir ................................................ 432 GLMQRD 8= Lomrasi pdrd ahltdr af cijpaosdhir ......................................... 433 GLMQRD 8; Lomrasi ha pifis y caris (>) ha cijpaosdhir .......................... 438 LMQRD

^L

Fumdr maijìtrlci ha fds ...... Raspuastd haf jihafi oirdêcas floadf cio cio af af ciotrifdhir ciotrifdhir ^L . ............. ............. ............. .......... 438 431 Raspuastd hasadhd ...................................................... ................................................................... ............. 43= Raspuastd haf jihafi oi floadf cio af ciotrifdhir  pir af jìtihi ha Rdmdzzlol ..................................................... 43; GLMQRD 13 Guoclóo ha jajbrasêd pdrd af arrir ........................................ 484 GLMQRD 18 Guoclóo ha jajbrasêd pdrd fd vaficlhdh ha cdjbli ha olvaf (K2) ........................................................ ............................................................ .... 48> GLMQRD 11 Guoclóo ha jajbrasêd pdrd fd sdflhd ....................................... 482 G GLMQRD 8<  1> GLMQRD 14 GLMQRD 12 

 

GLMQRD 17 Ciotrif cio fómlcd hlgusd ciostrulhi ao Sljufloe ® pdrd fd sljufdclóo haf slstajd ha olvaf ............................................... 483 GLMQRD 1= Hldmrdjd ha Sljufloe ® qua juastrd af astdhi ha fds guoclioas ha jajbrasêd pdrd uo lostdota lostdota ha tlajpi ............... 488 GLMQRD 1; Raspuastd haf slstajd ha olvaf ciotrifdhi cio uo ciotrif ciotrif hlgusi ........................................................ ............................................................... ....... 488 GLMQRD 1< Asquajd ha ciotrif  ODRJD-F2 pdrd af slstajd ha gfu`i ........... 487 GLMQRD 7> Cioglmurdclóo ha fd rah .................................................... ........................................................... ....... 48= GLMQRD 74 Mrdhlaota hascaohaota ...................................................... ............................................................. ....... 48; GLMQRD 72 Mrdhlaota hascaohaota cio rdtd ha dpraohlzd`a dhdptdtlvd ...... 48; GLMQRD 73  ^ripdmdclóo kdcld dträs cio mrdhlaota cio`umdhi y dctudflzdclóo ha ^ifdce-Rlblara ........................................... 48< GLMQRD 78 BGMS qudsl-Oawtio ................................................... ................................................................... ................ 48< GLMQRD 71 ^ripdmdclóo kdcld dträs, dträs, sacdota ha uo pdsi ........................... 41> GLMQRD 77 ^ripdmdclóo kdcld dträs ha Favaobarm-Jdrqudrht Favaobarm-Jdrqudrht .................. 41> ®

LMQRD G df ha ^dtk ha JDXFDB  ..................................................... ® GLMQRD 7=  7; Lomrasi Dhkaslóo fd cdrpatd d JDXFDB  ........................................... ........................................... 41= 41; GLMQRD 7< Waotdod pdrd safaccliodr af hlractirli qua sa dmramdrä df ^dtk ha JDXFDB® .................................................................. .................................................. ................ 41< GLMQRD => Sdfvdr fd cdrpatd KAJAGFQ df ^dtk ha JDXFDB® ...... ............. .............. .......... ... 47> GLMQRD =4 Waotdod prloclpdf haf primrdjd KAJAGFQ ....... ............. ............. .............. ............ ..... 474 GLMQRD =2 Waotdod ha lhaotlglcdclóo lhao tlglcdclóo ha fis pdräjatris E 4 y E 2 ............. ............... 472 GLMQRD =3 Wdfiras ibtaolhis pdrd fis pdräjatris E 4 y E 2 ...... ............. .............. .......... ... 473 GLMQRD =8 Waotdod prloclpdf haf ciotrif ciovaocliodf ^LH ...... ............. .............. .......... ... 478 GLMQRD =1 ^dräjatris haf ciotrif ...................................................... ............................................................. ....... 471 GLMQRD =7  Sljufdclóo haf ciotrifdhir pdrd Ec : 81, El : >,7, Eh  :  : >

GLMQRD == GLMQRD =; GLMQRD =< GLMQRD ;> GLMQRD ;4 GLMQRD ;2 GLMQRD ;3 GLMQRD ;8

dcclóo hlractd ....................................................................... 477 yWaotdod prloclpdf haf ciotrif Rdmdzzlol .................................. 47= Hlsaôi haf ciotrif pir af jìtihi ha Rdmdzzlol ....................... 47; Lomrasi ha fis pdräjatris haf ciotrifdhir ............................... 47< Wdflhdclóo haf ciotrif pir af jìtihi ha Rdmdzzlol ................. 4=> Waotdod prloclpdf haf Ciotrif Lotaflmaota ................................ 4=4 Sljufdclóo haf cijpirtdjlaoti haf pricasi ........................... 4=2 Hlspisltlvis ha jdohi y vlsudflzdclóo....... vlsudflzdclóo.............. .............. ............. ............. ........... 4=7 Cioaxlioas haf ^FC .................................................. .................................................................. ................ 4;>

 

Ê OHLCA OHLCA HA XDBFDS

XDBFD 4  XDBFD 2  XDBFD 3  XDBFD 8  XDBFD 1  XDBFD 7  XDBFD =  XDBFD ;  XDBFD   XDBFD 44 XDBFD 42  XDBFD 43  XDBFD 48  XDBFD 41

XDBFD 47  XDBFD 4=  XDBFD 4;  XDBFD 4  XDBFD 24  XDBFD 22 

Xlajpis ha juastrai racijaohdhis samðo af pricasi ............. 38 Slotiolzdclóo haf ciotrif jìtihi ha Plamfar-Olckifs, mdodocld fêjlta ........................................................ ........................................................................... ................... 1< Slotiolzdclóo haf ciotrif jìtihi ha Plamfar-Olckifs, curvd ha radcclóo ..................................................... ....................................................................... .................. 74 Arrir ao astdhi astdbfa ...................................................... ............................................................... ......... 7; Cdrdctarêstlcds haf vdrldhir ha vaficlhdh Jlcrijdstar jj41>/2 ha Slajaos ........................................................ ................................................................. ......... ;1 Cdrdctarêstlcds haf trdosjlsir ha praslóo hlgaraocldf ................ ;; Aspaclglcdclioas haf trdosjlsir ha praslóo hlgaraocldf ............. ;; Aspaclglcdclioas haf pfc ha Slajaos ......................................... Aspaclglcdclioas ha fd lotargdz kijbra-jäqulod ...................... >3) usdrio uo ouavi jìtihi ha ciotrif bdsdhi ao fd ciovifuclóo, pdrd ciotrifdr af olvaf ha fêqulhi ao uo slstajd ha tdoquas dcipfdhis5 ^do at df . (2>>1) dpflcdrio tìcolcds ha ciotrif ha bdcestaplom   dhdptdtlvi y bdcestaplom   bdsdhi ao jihafi5 Ekdo y Spurmaio (2>>7)

4;

 \  CIOXRIF  HA QO SLSXAJD  HA GFQLHIS JIHAFI JDXAJÄXLCI  \ 

 

hasdrriffdrio uo dfmirltji ha ciotrif pir jihis hasflzdotas y fi usdrio pdrd ciotrifdr af olvaf ao uo slstajd ha tdoquas dcipfdhis. Ciji puaha varsa ha fd ravlslóo haf astdhi haf drta, af ciotrif ha olvaf ao slstajds ha tdoquas as uo pribfajd blao astuhldhi. Slo ajbdrmi, ao fd präctlcd, as gracuaota qua sa slmdo dpflcdohi cio jäs gracuaocld fds tìcolcds ha ciotrif cfäslcds y oi tìcolcds ha ciotrif lotaflmaota (Pujbarma y ^dssloi, 4

θ (t ) ht :4

4

 

2

Mräglcdjaota, fd guoclóo ha ljpufsi uoltdrli sa raprasaotd ciji sa juastrd ao fd Glmurd 2. GLMQRD 2 - R A^RASAOXDCLÓO A^RASAOXDCLÓO  MRÄGLCD HA FD SAÔDF LJ^QFSI Saôdf Ljpufsi 4 >.< >.; >.= >.7      h     u      t      l      f     p >.1     j      D

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>.3 >.2 >.4 >

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4

2

3

8

1 7 Xlajpi Us Z Xlajpi

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Guaota0 afdbirdclóo ha fis dutiras d pdrtlr ha Jdtfdb®.

Ao fd präctlcd, astd guoclóo sa puaha usdr pdrd raprasaotdr clartis gaoójaois qua sucahao ao fdpsis ha tlajpi juy cirtis, ciji fds guarzds ha ckiqua i fds hascdrmds afìctrlcds. afìctrlcds. 2;

Jihafi JdtaJätlci  y   y  ciotrif  ha uo slstaJd  ha gfulhis

 

Fd rdzóo pdrd ajpfadr saôdfas ha ljpufsi as qua fis slstajds Slomfa Loput Slomfa Iutput   (SLSI) ha prljar irhao (qua sio cijuoas) quahdo cijpfatdjaota haglolhis d pdrtlr ha su raspuastd df ljpufsi. Slaohi (t ) fd guoclóo ljpufsi uoltdrli, sa  θ haf ljpufsi u (t ) : θ(t )  ciji ibtlaoa fd guoclóo ha trdosgaraocld fd cirraspiohlaota guoclóo ha sdflhd haf slstajd. Fd raspuastd df ljpufsi as aotiocas uod cdrdctarlzdclóo cijpfatd haf slstajd. Slo ajbdrmi, as hlgêclf maoardr uod aotrdhd ha ljpufsi ao af hijloli ha tlajpi ciotloui5 dhajäs, tdf aotrdhd puaha lohuclr agactis oi floadfas qua parturbdrêdo af cijpirtdjlaoti floadflzdhi haf jihafi. Astd as fd rdzóo pir fd cudf af usi ha aotrdhds ha ljpufsi rdrdjaota sa va ao sltudclioas präctlcds.

2. ASCDFÓO Hablhi d qua fd saôdf ha ljpufsi as pici präctlcd, juckis lovastlmdhiras kdo pripuasti jìtihis pdrd hatarjlodr af vdfir ha fis pdräjatris d pdrtlr ha guoclioas ao af tlajpi ha sdflhd ha  pricasis hioha fd aotrdhd df pricasi as uod saôdf blao cioiclhd. Ha prljard ljpirtdocld sio fds guoclioas ascdfóo ciji saôdfas ha aotrdhd y fds raspuastds df ascdfóo ciji saôdfas ha sdflhd. Qod saôdf Qod  saôdf ascdfóo ascdfóo uoltdrli, uoltdrli, i guoclóo i guoclóo ha Kadvlslha Kadvlslha,, sa hagloa ciji fd lotamrdf ha fd saôdf ljpufsi uoltdrli. Astä raprasaotdhd  pir fd Acudclóo 3, y mräglcdjaota sa raprasaotd ciji juastrd fd Glmurd 3.

 

>,  g (t )  4,

t  > t ≡ >

^ dufd  d   d ohrad   irtlz W  dfaocld  •  • @isì f aiodrhi ohrad  i aiodrhi r   dJêraz ackdWdrrêd   F IRAOD  IRAOD  C  C DRHIOD  R   R AOHÓO AOHÓO

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A^RASAOXDCLÓO  MRÄGLCD HA FD SAÔDF ASCDFÓO QOLXDRLI GLMQRD 3 - R A^RASAOXDCLÓO

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Guaota0 afdbirdclóo ha fis dutiras d pdrtlr ha Jdtfdb®.

Qod rdzóo pdrd utlflzdr fd saôdf ha ascdfóo ciji saôdf ha axcltdclóo as qua sa tlaoa blao astdbfaclhd uod jatihifimêd pdrd astljdr fd guoclóo ha trdosgaraocld ha uo slstajd d pdrtlr ha uo oðjari paquaôi ha vdfiras cdrdctarêstlcis ha fd guoclóo ha raspuastd df ascdfóo. ^ir a`ajpfi, pdrd slstajds ha prljar irhao, uo jihafi djpfldjaota utlflzdhi af doäflsls ha raspuastd df ascdfóo af ha prljar irhao cio ao ratdrhi, cuyd astructurd sa prasaotd ao as fd Acudclóo 8.

M (ό ) : 

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Jihafi JdtaJätlci  y   y  ciotrif  ha uo slstaJd  ha gfulhis

8

 

Ha kacki, kdy uo buao oðjari ha slstajds, aspacldfjaota ao af ciotrif ha pricasis, qua puahao sar dprixljdhis pir jahli ha uo jihafi ha prljar irhao cio ratdrhi. Fis pdräjatris ha fd Acudclóo 8 sa fd puahao harlvdr d pdrtlr ha fd draspuastd ascdfóo, hatarjlodohi raspuastd ao astdhi astdbfa fd aotrdhddfascdfóo y fd ciostdota ha tlajpi (Rdea, 4). Astd ðftljd sa puaha ibtaoar, yd sad d pdrtlr ha fd tdomaota ha jdyir paohlaota i haf tlajpi qua tdrhd af dscaosi ha 4> d % haf cdjbli ao fd sdflhd (Glmurd 8). AS^QASXD DF ASCDFÓO XÊ^LCD HA QO SLSXAJD HA ^RLJAR  IRHAO CIO  GLMQRD 8 - R AS^QASXD RAXDRHI

Guaota0 afdbirdclóo ha fis dutiras.

^drd slstajds ha samuohi irhao, sa puaha ibtaoar af vdfir ha fis pdräjatris d pdrtlr ha fd raspuastd df ascdfóo, hatarjlodohi fd raspuastd ao astdhi astdbfa, af sibraljpufsi jäxlji, af tlajpi raquarlhi pdrd dfcdozdr af prljar plci y af tlajpi raquarlhi pdrd dfcdozdr af 1> % haf vdfir ao astdhi astdbfa. ^drd af cdsi maoardf ha slstajds ha irhao suparlir, as ja`ir usdr uo jìtihi ha mrdhlaota pdrd aociotrdr fis pdräjatris

^ dufd  d   d ohrad   irtlz W  dfaocld  •  • @isì f aiodrhi ohrad  i aiodrhi r   dJêraz ackdWdrrêd   F IRAOD  IRAOD  C  C DRHIOD  R   R AOHÓO AOHÓO

34

 

haf jihafi, ha tdf girjd qua sa jloljlca fd lotamrdf haf arrir cudhrätlci (F`uom, 4

lό

) ci  s ( όt + ϑ) + κ(t) + trdoslaota  

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hioha0

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Astd priplahdh as fd plstd pdrd uod girjd sljpfa ha hatarjlodr Mi (alό ) cio fd aotrdhd slousilhdf, sa hatarjlod fd djpfltuh y af cdjbli ha gdsa ao fd saôdf cisaoi rasuftdota y sa cdfcufd uod ˇ (al ) cio bdsa ao astd logirjdclóo. Sa raplta af astljdclóo  M  O   pricasi pdrd uo oðjari ha gracuaoclds gracuaoclds ao fd bdohd ha gracuaocld gracuaocld ha lotarìs.  ό

32

Jihafi JdtaJätlci  y   y  ciotrif  ha uo slstaJd  ha gfulhis

 

4.4.3 FDPI CARRDHI Ao dfmuois cdsis as oacasdrli ffavdr d cdbi af axparljaoti ha lhaotlglcdclóo ao fdzi carrdhi. Fd rdzóo puaha sar qua fd pfdotd sad loastdbfa, qua taomd qua astdr ciotrifdhd pdrd prihucclóo i  pir rdzioas ha samurlhdh i acioijêd. Xdjblìo puaha sar qua ciotaomd jacdolsjis ha radfljaotdclóo lokaraota. Af pribfajd  bäslci cio fis hdtis ao fdzi carrdhi as qua têplcdjaota tlaoao jaois logirjdclóo sibra af slstajd ao fdzi dblarti, puasti qua uo  pripóslti ljpirtdota ha fd radfljaotdclóo radfljaotdclóo as kdcar qua af slstajd ao fdzi carrdhi sad jaois saoslbfa d fis cdjblis qua af slstajd ao fdzi dblarti. Cudohi sa tlaoa af pribfajd ha lhaotlglcdclóo l haotlglcdclóo ha slstajds ao fdzi carrdhi, axlstao his dprixljdclioas0

4. HLRACXD  Sa utlflzdo fis hdtis u, y  y ao  ao fd jlsjd girjd qua pdrd af fdzi dblarti, lmoirdohi af fdzi carrdhi y fd saôdf ha ragaraocld r . Sa lhaotlglcd af slstajd ao fdzi dblarti.

2. LOHLRACXD Sa lhaotlglcd af slstajd ao fdzi carrdhi usdohi fd saôdf ha ragaraocld r  ciji  ciji aotrdhd y fd saôdf y saôdf y ciji  ciji fd sdflhd. Qod vaz sa tlaoa af jihafi haf slstajd ao fdzi carrdhi, sa cdfcufd af slstajd ao fdzi dblarti5 pdrd asti af ramufdhir haba sar cioiclhi.

4.4.8 CDOXLHDH HA HDXIS Fd haclslóo sibra fd cdotlhdh ha hdtis qua habao tijdrsa pdrd fd lhaotlglcdclóo hapaoha haf jìtihi ha lhaotlglcdclóo usdhi. Slo ajbdrmi, uo crltarli hatarjlodota ao fd safacclóo as qua fd

^ dufd  d   d ohrad   irtlz W  dfaocld  •  • @isì f aiodrhi ohrad  i aiodrhi r   dJêraz ackdWdrrêd   F IRAOD  IRAOD  C  C DRHIOD  R   R AOHÓO AOHÓO

33

 

raspuastd haf slstajd fimra supardr af astdhi trdosltirli y ffamua df astdhi astdbfa.

4.4.1 ^ARÊIHI HA JQASXRAI Fuami ha qua sa kd haclhlhi quì y hóoha jahlr, fd slmulaota  pramuotd as cuäohi. Fd jdyirêd ha fds saôdfas sa juastrado usdohi uo lotarvdfi ciostdota X   (parêihi ha juastrai), y asta lotarvdfi as uod vdrldbfa qua puaha sar afamlhd. Fd safacclóo óptljd pdrd af tlajpi ha juastrai astä dfrahahir ha fd ciostdota ha tlajpi haf slstajd. Duoqua as jäs par`uhlcldf  pdrd af axparljaoti afamlr uo parêihi ha juastrai juy mrdoha qua uoi juy paquaôi, sl sa aflma asta ðftlji sa tlaoao pribfajds oujìrlcis, af jihafi sa d`ustd ao fds bdohds ha dftd gracuaocld y oi sa fimrdo jdyiras baoaglclis pir fd cdrmd cijputdcliodf cijputdcliodf axtrd qua ljpflcd uo parlihi jäs paquaôi. Qod gracuaocld ha juastrai ha dprixljdhdjaota 4> vacas af docki ha bdohd haf slstajd sarêd uod buaod afacclóo ao fd jdyirêd ha fis cdsis (F`uom, 4>

^raslóo

4-1

Xajpardturd

4>-42>

Hastlfdclóo

4>-4;>

38

Jihafi JdtaJätlci  y   y  ciotrif  ha uo slstaJd  ha gfulhis

 

Dvdsdffdjlaoti*

>,>>4- >,4

Radctiras cdtdflzdhiras

4>-81

Cajaotards

2>-81

Sacdhiras

2>-81

* Sa raglara d tihis dquaffis pricasis qua sio hajdsldhi räplhis ao su raspuastd, tdfas ciji turblods, guaotas lolotarrujplhds ha pitaocld y itris. Guaota0 Fdohdu, Ldo Hirì y M. Plti (2>>1).  Hlmltdf Ciotrif Systajs – Haslmo,  Lhaotlglcdtlio doh Ljpfajaotdtlio Ljpfajaotd tlio. Fiohras, Sprlomar.

4.2

SAFACCLÓO HA FD ASXRQCXQRD HAF JIHAFI

Qod astructurd ha jihafi astä hascrltd, ao af cdsi floadf,  pir fis ciaglclaotas ha clartis pifloijlis i pir fds jdtrlcas haf aspdcli ha Fdpdrd safacclóo ha uod astructurd ha afacclóo jihafi dpripldhd J  dpripldhd  J astdhi.  as crucldf  as uod lhaotlglcdclóo axltisd. Fd haba bdsdrsa ao uo aotaohljlaoti, tdoti haf slstajd qua vd d sar lhaotlglcdhi, ciji haf pricahljlaoti ha lhaotlglcdclóo. Fis dspactis pdrd taoar ao cuaotd ao af pricasi ha safacclóo ha uod astructurd haf jihafi sio0 fd cijpfa`lhdh y af cisti haf jihafi, y af usi qua sa fa hdrä. Cdhd uoi ha astis dspactis sa hagloa d ciotloudclóo0

4.2.4 CIJ^FA@LHDH  HAF JIHAFI Fd ja`ir astructurd haf jihafi as fd qua tlaoa af mrdhi ha gfaxlblflhdh óptlji. Qod astructurd gfaxlbfa  gfaxlbfa  as dquaffd qua igraca buaods cdpdclhdhas pdrd hascrlblr hlgaraotas slstajds  pislbfas. Fd gfaxlblflhdh sa puaha ibtaoar, ibtaoar, yd sad usdohi usdohi juckis  pdräjatris, i ublcäohifis ao pislclioas pislclioas astrdtìmlcds. astrdtìmlcds. Af dujaoti ao fd gfaxlblflhdh ljpflcd uo dujaoti ao fd cijpfa`lhdh ha fd astructurd. Fd rdzóo pir fd cudf fd cijpfa`lhdh `uamd uo pdpaf ljpirtdota ao fd safacclóo ha fd astructurd as fd slmulaota0 sl sa

^ dufd  d   d ohrad   irtlz W  dfaocld  •  • @isì f aiodrhi ohrad  i aiodrhi r   dJêraz ackdWdrrêd   F IRAOD  IRAOD  C  C DRHIOD  R   R AOHÓO AOHÓO

31

 

dsuja qua axlsta uod varhdhard hascrlpclóo S , ciocaptudfjaota ˇ ciji sa juastrd ao fd sa puaha ascrlblr af arrir haf jihafi J  Acudclóo ;0

S− J

 



;

hioha0 ˇ  y sio cudfqular priplahdh ascdfdr haf ib`ati, pir   S y J  a`ajpfi, fd mdodocld astätlcd ha uo slstajd hloäjlci. Ao asta cdsi, af arrir cudhrätlci jahli (] ) as0

(

] :A S−J 

2

)  : (S − J ) *

]

: B + W 

2

+A (J −J  

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 J

ˇ : AJ 

Ao fd Acudclóo 4>, af arrir arrir cudhrätlci jahli sa hlvlha aotra uo sasmi (cudhrdhi) B (cudhrdhi) B y  y uo arrir ha vdrldozd W . Astd as uod rafdclóo juy afajaotdf y blao cioiclhd (F`uom y ]lffs 2>4>). B 2>4>). B as  as guoclóo ha fd cijpfa`lhdh ha fd astructurd haf jihafi (gfaxlblflhdh) C (Acudclóo 44), y hlsjlouya d jahlhd qua C  dujaotd.   dujaotd. Ha lmudf girjd, W  dujaotd  dujaotd df dujaotdr C  (oi  (oi kdy axpraslioas afajaotdfas

37

Jihafi JdtaJätlci  y   y  ciotrif  ha uo slstaJd  ha gfulhis

 

 pdrd asti, asti, pari lotultlvdjaota as suglclaota aotaohar aotaohar qua jlaotrds jäs djpfld sad uod astructurd ha jihafi, jäs suscaptlbfa sarä ha racimar hdtis dfadtirlis ha haslogirjdclóo). Ciocaptudfjaota,

W :

 m( C )

 

44

 O 

hioha0  O  as  as af tdjdôi haf cio`uoti ha hdtis ha astljdclóo. Fd bðsquahd prdmjätlcd ha fd ja`ir astructurd haf jihafi slmolglcdrä aotiocas fd bðsquahd ha fd cijpfa`lhdh ha jihafi C qua jloljlca ] . Astd jloljlzdclóo ha ]  gdviraca  gdviraca astructurds ha jihafis jaois gfaxlbfas qua ciotlaoao buaods dprixljdclioas haf ib`ati radf. Asti slmolglcd qua as ja`ir rahuclr af tdjdôi haf jihafi tdoti ciji sad pislbfa, usdohi fayas gêslcds sibra fd odturdfazd haf ib`ati.

4.2.3 CISXI HAF JIHAFI Af cisti haf jihafi sa dsicld cio af asguarzi cijputdcliodf raquarlhi pdrd cdfcufdrfi, hapaoha jucki ha fd astructurd haf jihafi (qua dgactd fd cijpfa`lhdh haf dfmirltji), dujaotd d jahlhd qua sa locrajaotd af oðjari ha pdräjatris ao fd astructurd haf jihafi, y ao maoardf, craca df locrajaotdrsa fd cijpfa`lhdh ha fd astructurd. Qod vaz jäs, aotiocas, as pragarlbfa usdr uod astructurd ha jihafi ha jaoir cijpfa`lhdh, lovifucrdohi, sl as pislbfa, af cioicljlaoti gêslci haf slstajd, pdrd hlsjloulr af

^ dufd  d   d ohrad   irtlz W  dfaocld  •  • @isì f aiodrhi ohrad  i aiodrhi r   dJêraz ackdWdrrêd   F IRAOD  IRAOD  C  C DRHIOD  R   R AOHÓO AOHÓO

3=

 

cisti ha cijputdclóo haf jihafi. Asta sa puaha cudotlglcdr ha hlvarsds girjds, slaohi jäs cijðo usdr af tlajpi qua tdrhd fd astljdclóo ha fis pdräjatris haf jihafi.

4.2.8 QSI TQA SA FA HDRÄ DF JIHAFI ^uaha sar qua af jihafi sa raqulard pdrd hlsaôdr uo ramufdhir i kdcar prahlcclioas i sljufdclioas. As dsê ciji af usi hatarjlod dspactis ciji fd girjd haf jihafi (guoclóo ha trdosgaraocld, aspdcli ha astdhi i acudclioas hlgaraocldfas, pir a`ajpfi) fd  praclslóo raquarlhd y fd floadflhdh. floadflhdh. Fd safacclóo glodf ha fd astructurd haf jihafi as uo cijprijlsi aotra fis tras dspactis jaocliodhis (cijpfa`lhdh, cisti y usi). ^drd tijdr fd haclslóo sibra astis dspactis, sa  puahao taoar ao cuaotd cioslhardclioas d prlirl i sa puaha kdcar uo doäflsls pravli ha fis hdtis ha fd axparljaotdclóo. Ao maoardf, af pricasi ha safacclóo ha fd astructurd haf jihafi lovifucrd, pir fi jaois, fis tras pdsis slmulaotas0

4. SAFACCLÓO HAF XL^I HA JIHAFI Lovifucrd fd safacclóo aotra jihafis floadfas y oi floadfas, y aotra guoclioas ha trdosgaraocld i raprasaotdclioas ao aspdcli ha astdhi. Fd pramuotd sibra fd floadflhdh haf slstajd puaha rasifvarsa gäclfjaota d pdrtlr ha fis hdtis racifactdhis hurdota fd axparljaotdclóo. Fd safacclóo haf tlpi ha jihafi lovifucrd dspactis ciji fd hlspiolblflhdh ha  sigtwdra  sigtwdra   y fd gdjlfldrlhdh qua sa tlaoa cio clartis jihafis. Fd safacclóo ha fd cijpfa`lhdh astä ao af cirdzóo ha fd safacclóo. Af ciosa`i maoardf as pribdr  prljari fds fds sifuclioas jäs sljpfas. Sa puahao puahao buscdr buscdr astructurds astructurds

3;

Jihafi JdtaJätlci  y   y  ciotrif  ha uo slstaJd  ha gfulhis

 

jäs siglstlcdhds ðolcdjaota sl fds jäs sljpfas oi pdsdrio fds  pruabds ha vdflhdclóo.

2. SAFACCLÓO HAF XDJDÔI HAF JIHAFI Lovifucrd dspactis ciji safaccliodr af irhao ha uo jihafi ao aspdcli ha astdhi, af mrdhi ha uo pifloijli i af oðjari ha oauriods ao uod rah oauriodf. Xdjblìo lovifucrd af pribfajd ha safaccliodr fds vdrldbfas qua sa locfulräo ao fd hascrlpclóo haf jihafi. ^drd hatarjlodr af irhao haf jihafi axlstao vdrlds tìcolcds, ciji fd astljdclóo haf doäflsls aspactrdf ha fd guoclóo ha trdosgaraocld, fd pruabd ha rdomi ao fds jdtrlcas ha civdrldozd ha fds juastrds, fd cirrafdclóo aotra fds vdrldbfas y af axdjao ha fd jdtrlz ha logirjdclóo. Itri jìtihi qua rasuftd ðtlf, sl sa hlspioa ha dfmðo sigtwdra dfmðo  sigtwdra   dpripldhi, as pribdr astructurds ha jihafi cio hlgaraota irhao y cijpdrdr fis jihafis rasuftdotas bd`i dfmðo crltarli pdrd hatarjlodr cuäf ha tihis ibtuvi ja`ir hasajpaôi.

3. SAFACCLÓO HA FD ^DRDJAXRLPDCLÓO  HAF JIHAFI Cudohi uo tlpi ha jihafi kd slhi afamlhi as oacasdrli  pdrdjatrlzdrfi, as haclr, haclr, aociotrdr uod astructurd qua fi hascrlbd. hascrlbd. ^drd safaccliodrfd, ao dfmuois cdsis sa usdo fayas gêslcds y rafdclioas astdbfaclhds pdrd fimrdr uo jihafi cio dfmuois  pdräjatris hascioiclhis. Ao itris sa usdo jihafis astäohdr slo olomðo sipirta gêslci. Qod präctlcd cijðo ao fd tairêd ha ciotrif as hascrlblr ðolcdjaota fd pdrta hatarjloêstlcd haf slstajd. Ao af ciotrif asticästlci, fis pifloijlis floadfas sa utlflzdo cio gracuaocld hablhi d qua astis jihafis hascrlbao fd pdrta asticästlcd y

^ dufd  d   d ohrad   irtlz W  dfaocld  •  • @isì f aiodrhi ohrad  i aiodrhi r   dJêraz ackdWdrrêd   F IRAOD  IRAOD  C  C DRHIOD  R   R AOHÓO AOHÓO

3<

 

hatarjloêstlcd ha uo slstajd. Slo ajbdrmi, ao fd lomaolarêd ha ciotrif cfäslcd, fd pdrta hatarjloêstlcd haf slstajd as jäs ljpirtdota qua fd asticästlcd5 pir fi tdoti, sa puaha tijdr vaotd`d ha rafdclóo aotra fdshascrlblr saôdfas fd hapdrta aotrdhd y sdflhd ha uod ha fd trdosgaraocld pdrd hatarjloêstlcd haf guoclóo jlsji. Fds astructurds pdrd guoclioas ha trdosgaraocld ha hlvarsi irhao sio blao cioiclhds y hicujaotdhds ao fd fltardturd. ^ir a`ajpfi, fd astructurd ha jihafi pdrd uo slstajd SLSI  floadf ciotloui ha prljar irhao cio ratdrhi as0 ea−λ  s

M ( s ): ψ  s + 4

 

42

^drd uo slstajd SLSI ha samuohi irhao as0 eό >2 a

−λ  s

M ( s ): 2  s + 2οό> s + ό >2

 

43

\ pdrd uo slstajd Juftlpfa slstajd  Juftlpfa Loput Juftlpfa Iutput  (  ( JLJI), sa  puaha axprasdr af jihafi ciotloui ao aspdcli ha astdhi ha fd girjd slmulaota0

 x   4   d4   : d  x2   3   m 

m 

 y : U c4

8>

d2   x4 

b4  +  u    d8   x2  b2 

 x4    c2 Z  x   2

Jihafi JdtaJätlci  y   y  ciotrif  ha uo slstaJd  ha gfulhis

48

 

 

BLBFLIMRDGÊD

Dedlea, K. (4=). Cijpdrdtlva Dodfysls lo Sljufdtlio Ciotriffah Ciohltlio ig d Guzzy Dhdptdtlva

^LH 

Ciotriffar doh d Cfdslc

 Oautrdflzlom ^ricass Sljufdtah io

JDXFDB 

^LH 

Dclh – Bdsa-

Sljufloe . Jìxlci, H. G.

Qolvarslhdh Xacoifómlcd Xacoifómlcd haf Caotri. Ástr÷j, E. @. y X. Bikflo (44, oðj. 8=3, päms. 43;-417. Bdtasio, R. O. (4