Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Ndipapasha isahluko sokuqala seentetho kwithiyori yolawulo oluzenzekelayo, emva koko ubomi bakho soze bufane.

Iintetho kwikhosi "Ulawulo lweeNkqubo zoBugcisa" zinikezelwa ngu-Oleg Stepanovich Kozlov kwiSebe le "Nuclear Reactors kunye neZityalo zaMandla", i-Faculty ye "Power Mechanical Engineering" ye-MSTU. N.E. Bauman. Endimbulela ngayo kakhulu.

Ezi ntetho zisalungiselelwa ukupapashwa njengencwadi, kwaye njengoko kukho iingcali ze-TAU, abafundi, kunye nabo banomdla nje kweso sifundo, nakuphi na ukugxekwa kwamkelekile.

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

1. Iingcamango ezisisiseko zethiyori yokulawula iinkqubo zobugcisa

1.1. Iinjongo, imigaqo yolawulo, iintlobo zeenkqubo zolawulo, iinkcazo ezisisiseko, imizekelo

Uphuhliso kunye nokuphuculwa kwemveliso yemizi-mveliso (amandla, ezothutho, ubunjineli boomatshini, ubuchwephesha basemajukujukwini, njl.njl.) kufuna ukwanda okuqhubekayo kwemveliso yoomatshini kunye neeyunithi, ukuphucula umgangatho wemveliso, ukunciphisa iindleko kwaye, ngakumbi kumandla enyukliya, ukunyuka okubukhali kwimveliso. ukhuseleko (inyukliya, ukusasazeka kwemitha, njl.njl.) .d.) ukusebenza kwemizi-mveliso yamandla enyukliya kunye nofakelo lwenyukliya.

Ukuphunyezwa kweenjongo ezimiselweyo akunakwenzeka ngaphandle kokungeniswa kweenkqubo zokulawula zanamhlanje, kubandakanywa zombini ngokuzenzekelayo (ngokuthatha inxaxheba komqhubi womntu) kunye ngokuzenzekelayo (ngaphandle kokuthatha inxaxheba komqhubi womntu) iinkqubo zokulawula (CS).

Ingcaciso: Ulawulo ngumbutho wenkqubo ethile yezobuchwepheshe eqinisekisa ukufezekiswa kwenjongo emiselweyo.

Ithiyori yokulawula lisebe lenzululwazi nobuchwepheshe bale mihla. Isekelwe (esekelwe) kuzo zombini iinkalo ezisisiseko (inzululwazi ngokubanzi) (umzekelo, imathematika, i-physics, i-chemistry, njl.) kunye nezifundo ezisetyenzisiweyo (i-electronics, iteknoloji ye-microprocessor, inkqubo, njl.).

Nayiphi na inkqubo yolawulo (automatic) iqulathe ezi zigaba zilandelayo (elementi):

  • ukufumana ulwazi malunga nomsebenzi wokulawula;
  • ukufumana ulwazi malunga nesiphumo solawulo;
  • uhlalutyo lolwazi olufunyenweyo;
  • ukuphunyezwa kwesigqibo (impembelelo kwinto yokulawula).

Ukuphumeza iNkqubo yoLawulo, inkqubo yolawulo (CS) kufuneka ibe:

  • imithombo yolwazi malunga nomsebenzi wolawulo;
  • imithombo yolwazi malunga neziphumo zolawulo (iinzwa ezahlukeneyo, izixhobo zokulinganisa, ii-detectors, njl.);
  • izixhobo zokuhlalutya ulwazi olufunyenweyo kunye nokuphuhlisa izisombululo;
  • ii-activators ezisebenza kwi-Control Object, equlethe: umlawuli, ii-motor, izixhobo zokuguqula i-amplification, njl.

Ingcaciso: Ukuba inkqubo yolawulo (CS) iqulethe zonke ezi ndawo zingasentla, ngoko ivaliwe.

Ingcaciso: Ukulawulwa kwento yobugcisa usebenzisa ulwazi malunga neziphumo zolawulo kuthiwa ngumgaqo wempendulo.

Ngokwezicwangciso, inkqubo yolawulo enjalo inokumelwa ngolu hlobo:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.1.1 — Ubume benkqubo yolawulo (MS)

Ukuba inkqubo yokulawula (CS) inomzobo webhloko, ifom ehambelana neFig. 1.1.1, kunye nemisebenzi (imisebenzi) ngaphandle kokuthatha inxaxheba komntu (umqhubi), ngoko kuthiwa inkqubo yolawulo oluzenzekelayo (ACS).

Ukuba inkqubo yokulawula isebenza kunye nokuthatha inxaxheba komntu (umqhubi), ngoko kuthiwa inkqubo yolawulo oluzenzekelayo.

Ukuba uLawulo lubonelela ngomthetho onikiweyo wokutshintsha into ngexesha, kungakhathaliseki ukuba zithini na iziphumo zolawulo, ngoko ulawulo olunjalo lwenziwa kwilophu evulekileyo, kwaye ulawulo ngokwalo lubizwa ngokuba. inkqubo ilawulwa.

Iinkqubo ezivulelekileyo zibandakanya oomatshini boshishino (imigca yokuhambisa, imigca ejikelezayo, njl.njl.), oomatshini bokulawula amanani ekhompyuter (CNC): jonga umzekelo kwi-Fig. 1.1.2.

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Umzobo.1.1.2 - Umzekelo wolawulo lwenkqubo

Isixhobo esiyintloko sinokuba, umzekelo, "umkhupheli".

Ekubeni kulo mzekelo akukho zinzwa (iimitha) esweni inxalenye eyenziwayo, ukuba, umzekelo, i-cutter ifakwe ngokungalunganga okanye iphukile, ngoko injongo emiselweyo (ukuveliswa kwenxalenye) ayikwazi ukufezekiswa (ifezekiswe). Ngokuqhelekileyo, kwiinkqubo zolu hlobo, ulawulo lwemveliso luyafuneka, oluya kurekhoda kuphela ukuphambuka kwemilinganiselo kunye nokuma kwenxalenye evela kwinto oyifunayo.

Iinkqubo zolawulo oluzenzekelayo zahlulwe zibe ziindidi ezi-3:

  • iinkqubo zolawulo oluzenzekelayo (ACS);
  • iinkqubo zolawulo oluzenzekelayo (ACS);
  • iinkqubo zokulandelela (SS).

I-SAR kunye ne-SS zizinto ezincinci ze-SPG ==> Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa.

Inkcazo: Inkqubo yokulawula ngokuzenzekelayo eqinisekisa ukugcinwa kwanoma yimuphi ubungakanani bomzimba (iqela lobuninzi) kwinto yokulawula ibizwa ngokuba yinkqubo yokulawula ngokuzenzekelayo (ACS).

Iinkqubo zolawulo oluzenzekelayo (ACS) lolona hlobo luqhelekileyo lweenkqubo zolawulo oluzenzekelayo.

Umlawuli wokuqala wehlabathi ozenzekelayo (inkulungwane ye-18) ngumlawuli weWatt. Esi sikimu (jonga umfanekiso 1.1.3) siphunyezwe nguWatt eNgilani ukugcina isantya esiqhubekayo sokujikeleza kwevili le-injini ye-steam kwaye, ngokufanelekileyo, ukugcina isantya esiqhubekayo sokujikeleza (intshukumo) ye-pulley yokuhambisa (ibhanti ).

Kwesi sicwangciso izinto ezinovakalelo (abenzi boluvo bokulinganisa) “ziisisindo” (iingqukuva). “Ubunzima” (iingqukuva) “zinyanzelise” ingalo yerocker kunye nevalve ukuba ihambe. Ngoko ke, le nkqubo inokuchazwa njengenkqubo yokulawula ngokuthe ngqo, kwaye umlawuli unokuchazwa njenge umlawuli obambeleyo othe ngqo, ekubeni ngexesha elifanayo lenza imisebenzi yazo zombini "imitha" kunye "nomlawuli".

Kubalawuli ababambeleyo ngokuthe ngqo umthombo owongezelelweyo akukho mandla afunekayo ukuhambisa umlawuli.

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.1.3 — Watt automatic regulator circuit

Iinkqubo zokulawula ezingathanga ngqo zifuna ubukho (ubukho) be-amplifier (umzekelo, amandla), i-actuator eyongezelelweyo equkethe, umzekelo, i-motor electric, i-servomotor, i-hydraulic drive, njl.

Umzekelo wenkqubo yokulawula ngokuzenzekelayo (inkqubo yokulawula ngokuzenzekelayo), ngokwengqiqo epheleleyo yale nkcazo, yinkqubo yokulawula eqinisekisa ukuqaliswa kwe-rocket kwi-orbit, apho ukuguqulwa okulawulwayo kunokubakho, umzekelo, i-angle phakathi kwe-rocket. i-axis kunye nesiqhelo kuMhlaba ==> bona i-Fig. 1.1.4.a kunye nomkhiwane. 1.1.4.b

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.1.4(a)
Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.1.4 (b)

1.2. Ulwakhiwo lweenkqubo zolawulo: iinkqubo ezilula kunye nezininzi

Kwithiyori yoLawulo lweeNkqubo zezobuGcisa, nayiphi na inkqubo idla ngokuhlulwa ibe yisethi yezixhumanisi eziqhagamshelwe kwizakhiwo zenethiwekhi. Kwimeko elula kakhulu, inkqubo iqulethe ikhonkco enye, igalelo layo linikezelwa ngesenzo sokufaka (igalelo), kunye nempendulo yenkqubo (imveliso) ifunyenwe kwigalelo.

Kwithiyori yoLawulo lweeNkqubo zoBugcisa, iindlela ezi-2 eziphambili zokumela amakhonkco eenkqubo zolawulo zisetyenziswa:

— kwizinto eziguquguqukayo “zegalelo-imveliso”;

— kwiimeko eziguquguqukayo (ukufumana iinkcukacha ezithe vetshe, bona amacandelo 6...7).

Ukubonakaliswa kwiinguqu ze-input-output ngokuqhelekileyo zisetyenziselwa ukuchaza iinkqubo ezilula kakhulu ezine "input" enye (isenzo sokulawula esinye) kunye "nesiphumo" esinye (i-variable controlled variable, jonga uMzobo 1.2.1).

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.2.1 – Umelo olucwangcisiweyo lwenkqubo yolawulo elula

Ngokuqhelekileyo, le nkcazo isetyenziselwa ubugcisa obulula beenkqubo zokulawula ngokuzenzekelayo (iinkqubo zokulawula ngokuzenzekelayo).

Kutshanje, ukumelwa kwiinguqu zombuso kuye kwasasazeka, ngakumbi kwiinkqubo ezintsonkothileyo zobugcisa, kubandakanywa iinkqubo zolawulo oluzenzekelayo ezizii-multidimensional. KwiFig. 1.2.2 ibonisa ukumelwa kweskim senkqubo yolawulo oluzenzekelayo oluyi-multidimensional, apho u1(t)...um(t) -izenzo zokulawula (i-vector yokulawula), y1(t)...yp(t) — iiparamitha ezihlengahlengiswayo ze-ACS (i-vector yemveliso).

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.2.2 — Ukumelwa okucwangcisiweyo kwenkqubo yolawulo ebanzi

Makhe siqwalasele ngokubanzi isakhiwo se-ACS, esimelelwe kwiinguqu ze "input-output" kunye nenye igalelo (igalelo okanye i-master, okanye isenzo sokulawula) kunye nesiphumo esisodwa (isenzo sokuphuma okanye esilawulwayo (okanye esilungelelanisiweyo) esiguquguqukayo).

Makhe sicinge ukuba umzobo webhloko we-ACS enjalo iqukethe inani elithile lezinto (izixhumanisi). Ngokwenza amaqela amakhonkco ngokwemigaqo esebenzayo (into eyenziwa ngamakhonkco), umzobo wesakhiwo we-ACS unokuncitshiswa ube yile fomu ilandelayo:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.2.3 - Umzobo weBlock wenkqubo yokulawula ngokuzenzekelayo

Uphawu ε(t) okanye ukuguquguquka ε(t) ibonisa ukungahambelani (impazamo) kwimveliso yesixhobo sokuthelekisa, esinokuthi "sisebenze" kwindlela yayo yomibini imisebenzi elula yothelekiso lwe-arithmetic (ubukhulu becala ukuthabatha, ukongezwa okuncinci) kunye nemisebenzi ethelekisayo entsokothileyo (iinkqubo).

ukususela y1(t) = y(t)*k1phi k1 yinzuzo, ngoko ==>
ε(t) = x(t) - y1(t) = x(t) - k1*y(t)

Umsebenzi wenkqubo yolawulo (ukuba izinzile) "ukusebenza" ukuphelisa ukungahambelani (impazamo) ε(t), okt. ==> ε(t) → 0.

Kufuneka kuqatshelwe ukuba inkqubo yokulawula ichaphazeleka zombini iimpembelelo zangaphandle (ukulawula, ukuphazamisa, ukuphazamiseka) kunye nokuphazamiseka kwangaphakathi. Uphazamiso luyahluka kwimpembelelo yobume bestochasticity (ngokungacwangciswanga) kobukho bayo, ngelixa impembelelo iphantse isoloko imisela.

Ukumisela ulawulo (ukusetha isenzo) siya kusebenzisa nokuba x (t), okanye u (m).

1.3. Imithetho esisiseko yolawulo

Ukuba sibuyela kumfanekiso wokugqibela (umzobo webhloko we-ACS kwi-Fig. 1.2.3), ngoko kuyimfuneko "ukucacisa" indima edlalwa yi-amplification-converting device (yiyiphi imisebenzi eyenzayo).

Ukuba isixhobo sokuguqula i-amplification (ACD) songeza kuphela (okanye sinciphise) isignali engafanelekanga ε(t), eyile: Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisaphi Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa- i-proportionality coefficient (kwimeko ethile Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa = Const), ngoko ke imowudi yolawulo yenkqubo yolawulo oluzenzekelayo ebizwa ngokuba yimowudi ulawulo olulinganayo (P-control).

Ukuba iyunithi yolawulo yenza isignali yemveliso ε1(t), ngokuhambelana nemposiso ε(t) kunye nendibaniselwano ye ε(t), i.e. Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa, ke le ndlela yolawulo ibizwa ngokuba ngokomlinganiselo-ukudibanisa (Ulawulo lwePI). ==> Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisaphi b - i-proportionality coefficient (kwimeko ethile b = Const).

Ngokuqhelekileyo, ulawulo lwe-PI lusetyenziselwa ukuphucula ulawulo (umgaqo) ukuchaneka.

Ukuba iyunithi yolawulo yenza isignali yemveliso ε1(t), ngokomlinganiselo wemposiso ε(t) kunye nephuma kuyo, ngoko le ndlela ibizwa ngokuba. пропорционально-дифференцирующим (Ulawulo lwePD): ==> Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Ngokuqhelekileyo, ukusetyenziswa kolawulo lwePD kwandisa ukusebenza kwe-ACS

Ukuba iyunithi yolawulo yenza isignali yemveliso ε1(t), ngokomlinganiselo wemposiso ε(t), idirivative yayo, kunye nendibaniselwano yemposiso ==> Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa, ke le ndlela ibizwa ngokuba le ndlela yokulawula ibizwa imo yolawulo edibeneyo-edibeneyo-eyahlukileyo (Ulawulo lwePID).

Ulawulo lwe-PID luhlala lukuvumela ukuba unikeze ngokuchaneka kolawulo "olulungileyo" ngesantya "esilungileyo".

1.4. Ukuhlelwa kweenkqubo zolawulo oluzenzekelayo

1.4.1. Ukuhlelwa ngokodidi lwenkcazo yemathematika

Ngokusekwe kudidi lwenkcazo yemathematika (equations of dynamics and statics), iinkqubo zolawulo oluzenzekelayo (ACS) zahlulwe zaba umgca и nonlinear iinkqubo (izibhamu eziziqhubela phambili okanye i-SAR).

I-"subclass" nganye (i-linear ne-nonlinear) yohlulwe ngokwenani lee-"subclasses". Ngokomzekelo, izibhamu eziziqhubela phambili (i-SAP) zineeyantlukwano kuhlobo lwenkcazo yemathematika.
Ukusukela ukuba le semester iyakuthathela ingqalelo iipropathi eziguquguqukayo zolawulo oluzenzekelayo oluzenzekelayo (ulawulo), apha ngezantsi sibonelela ngohlelo ngokohlobo lwenkcazo yemathematika kwiinkqubo zolawulo oluzenzekelayo (ACS):

1) Iisistim zolawulo oluzenzekelayo zomgama ezichazwe kwigalelo-imveliso eguquguqukayo ngomlinganiso oqhelekileyo weequation (ODE) kunye ngokusisigxina i-coefficients:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

apho x (t) - impembelelo yegalelo; y (x) - impembelelo yesiphumo (ixabiso elinokulungiswa).

Ukuba sisebenzisa ifom yomsebenzisi (“compact”) yokubhala i-ODE yomgca, i-equation (1.4.1) inokumelwa ngolu hlobo lulandelayo:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

phi, p = d/dt — umsebenzi wokwahlulahlula; L(p), N(p) ngabasebenzisi bomda abahambelanayo, abalingana no:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

2) Iisistim zolawulo oluzenzekelayo ezizihambelayo ezichazwe ngomgca olungelelaniso weequation eziqhelekileyo (ODE) nge ezahlukeneyo (ngexesha) i-coefficients:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Kwimeko eqhelekileyo, ezo nkqubo zinokuhlelwa njengeenkqubo ezizenzekelayo ezizenzekelayo (i-NSA).

3) Iisistim zolawulo ezizenzekelayo ezizihambelayo ezichazwe ngokweequation zomahluko womgca:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

apho f(…) - umsebenzi ohambelanayo weengxoxo; k = 1, 2, 3... - amanani apheleleyo; Δt - isithuba sobungakanani (isithuba sesampulu).

I-equation (1.4.4) inokumelwa kwinqaku elithi “compact”:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Ngokuqhelekileyo, le nkcazo ye-linear automatic control systems (ACS) isetyenziswe kwiinkqubo zokulawula idijithali (usebenzisa ikhompyutha).

4) Iinkqubo zolawulo oluzenzekelayo ngokulibaziseka:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

apho L(p), N(p) - abaqhubi abahlukeneyo bomgca; τ - ixesha lag okanye lag rhoqo.

Ukuba abaqhubi L(p) и N(p) yehla (L(p) = 1; N(p) = 1), ngoko i-equation (1.4.6) ihambelana nenkcazo yemathematika ye-dynamics yekhonkco lokulibaziseka elifanelekileyo:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

kunye nomfanekiso womzobo weempawu zayo uboniswe kwiFig. 1.4.1

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.4.1 — Iigrafu zegalelo kunye nesiphumo sekhonkco lokulibaziseka elifanelekileyo

5) Iisistim zolawulo oluzenzekelayo zomgama ezichazwe ngolungelelwaniso lomgca oluhlukileyo kwi izinto eziphuma ngokuyinxenye. Imipu enjalo eziqhubayo idla ngokubizwa ngokuba isasazwe iinkqubo zolawulo. ==> Umzekelo "ongekhoyo" wenkcazelo enjalo:

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Inkqubo ye-equations (1.4.7) ichaza i-dynamics yenkqubo yokulawula ngokuzenzekelayo, okt. ubungakanani obulawulwayo buxhomekeke kungekuphela nje kwixesha, kodwa nakwindlela enye yolungelelwaniso lwesithuba.
Ukuba inkqubo yolawulo yinto "yesithuba", ngoko ==>

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

apho Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa kuxhomekeke kwixesha kunye nolungelelwaniso lwesithuba olugqitywe yiradius vector Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

6) izibhamu eziziqhubelayo ezichazwe iinkqubo Ii-ODE, okanye ii-systems ze-equations umahluko, okanye ii-systems of partial differential equations ==> njalo njalo...

Ulwahlulo olufanayo lunokucetywa kwiinkqubo ezizenzekelayo zokulawula ezizenzekelayo (SAP)...

Kwiisistim zomgca ezi mfuno zilandelayo ziyafezekiswa:

  • umgca weempawu ezimileyo ze-ACS;
  • umgca we-dynamics equation, okt. izinto eziguquguqukayo zibandakanyiwe kwi-equation ye-dynamics kuphela kwindibaniselwano yomgca.

Uphawu olumileyo luxhomekeke kwisiphumo kubungakanani bempembelelo yegalelo kwisimo esizinzileyo (xa zonke iinkqubo ezidlulayo zifile).

Kwizixokelelwano ezichazwe ngemigca yeequation ezahluka-hlukeneyo ezinee-coefficient ezingaguqukiyo, uphawu olungatshintshiyo lufumaneka kwi-dynamic equation (1.4.1) ngokumisela onke amagama angengawo amileyo ukuya ku-zero ==>

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Umzobo 1.4.2 ubonisa imizekelo yeempawu ze-static zomgca kunye nezingahambelaniyo zeenkqubo zokulawula ngokuzenzekelayo (umgaqo).

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.4.2 - Imizekelo yomgca omileyo kunye neempawu ezingenayo

Ukungahambelani kwamagama aqulathe izinto eziphuma kwixesha kwii-equations eziguquguqukayo kunokuvela xa kusetyenziswa imisebenzi yemathematika engekho mgca (*, /, Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa, Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa, isono, ln, njalo njalo). Ngokomzekelo, xa kuqwalaselwa i-dynamics equation yompu oziqhubayo “ongekhoyo”

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa

Qaphela ukuba kule nxaki, kunye neempawu ezimile zomgca Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa ikota yesibini neyesithathu (imiqathango eguqukayo) kwicala lasekhohlo leequation zi nonlinear, ngoko ke i-ACS echazwe nge-equation efanayo nonlinear kwi ngamandla isicwangciso.

1.4.2. Ukuhlelwa ngokohlobo lweempawu ezigqithisiweyo

Ngokusekwe kubume beempawu ezithunyelwayo, iinkqubo zolawulo oluzenzekelayo (okanye ummiselo) zahlulwe zibe:

  • iinkqubo eziqhubekayo (iinkqubo eziqhubekayo);
  • iisistim zokuhanjiswa kwe-relay (iinkqubo zeentshukumo zokudluliselwa);
  • iinkqubo ezicacileyo (i-pulse kunye nedijithali).

Inkqubo ngokuqhubekayo isenzo sibizwa ngokuba yi-ACS, kwikhonkco ngalinye apho ngokuqhubekayo utshintsho kwisignali yegalelo ekuhambeni kwexesha ihambelana nokuqhubekayo utshintsho kwisignali yokuphuma, ngelixa umthetho wokutshintsha kwisignali yokuphuma unokuba yinto engafanelekanga. Ukuze i-self-propelled gun ibe yinto eqhubekayo, kuyimfuneko ukuba iimpawu ezimileyo zazo zonke amakhonkco ayeqhuba.

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.4.3 - Umzekelo wenkqubo eqhubekayo

Inkqubo udluliselo isenzo sibizwa ngokuba yinkqubo yokulawula ngokuzenzekelayo apho ubuncinci kwikhonkco enye, kunye noshintsho oluqhubekayo kwixabiso legalelo, ixabiso lemveliso ngexesha elithile lenkqubo yokulawula litshintsha "gxuma" kuxhomekeke kwixabiso lophawu lokufaka. Uphawu olungatshintshiyo lwekhonkco elinjalo iindawo zokuqhawula okanye ukwaphuka ngokugqabhuka.

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.4.4 - Imizekelo yeempawu zerelay static

Inkqubo ecacileyo isenzo yinkqubo apho ubuncinci kwikhonkco elinye, ngotshintsho oluqhubekayo kubungakanani begalelo, ubungakanani bemveliso uhlobo lweempembelelo zomntu ngamnye, ebonakala emva kwexesha elithile.

Ikhonkco eliguqula umqondiso oqhubekayo kwisignali ecacileyo ibizwa ngokuba yi-pulse link. Uhlobo olufanayo lweempawu ezithunyelwayo lwenzeka kwinkqubo yokulawula ngokuzenzekelayo ngekhompyutha okanye umlawuli.

Ezona ndlela ziqhele ukuphunyezwa (i-algorithms) zokuguqula isiginali yegalelo eqhubekayo ibe sisignali ephumayo yepulsed zezi:

  • i-pulse amplitude modulation (PAM);
  • Ukumodareyitha kobubanzi be-Pulse (PWM).

KwiFig. Umzobo 1.4.5 ubonisa umzobo we-algorithm ye-pulse amplitude modulation (PAM). Phezulu kweFig. ukuxhomekeka kwexesha kubonisiwe x (t) - umqondiso emnyango kwicandelo lempembelelo. Umqondiso wesiphumo sebhloko yepulse (ikhonkco) y (x) - ulandelelwano lwe-pulses yoxande oluvela kunye esisigxina ixesha lobungakanani Δt (jonga inxalenye esezantsi yomfanekiso). Ubude bexesha lemibhobho iyafana kwaye ilingana no-Δ. I-pulse amplitude kwimveliso yebhloko ilingana nexabiso elihambelanayo lomqondiso oqhubekayo x (t) kwigalelo lale block.

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.4.5 — Ukuphunyezwa kwe-pulse amplitude modulation

Le ndlela yokuguqulwa kwe-pulse yayixhaphake kakhulu kwisixhobo sokulinganisa i-elektroniki sokulawula kunye nokukhusela iinkqubo (CPS) zezityalo zamandla enyukliya (NPP) kwi-70s ... i-80 yekhulu lokugqibela.

KwiFig. Umzobo 1.4.6 ubonisa umzobo womzobo we-algorithm ye-pulse width modulation (PWM). Phezulu kweFig. 1.14 ibonisa ukuxhomekeka kwexesha x (t) -umqondiso kwigalelo kwikhonkco le-pulse. Umqondiso wesiphumo sebhloko yepulse (ikhonkco) y (x) - ukulandelelana kwee-pulses ezixande ezibonakala kunye nexesha lokulinganisa rhoqo Δt (jonga phantsi kweFig. 1.14). I-amplitude yazo zonke ii-pulses iyafana. Ubude be-Pulse Δt kwimveliso yebhloko ilingana nexabiso elihambelanayo lomqondiso oqhubekayo x (t) kwigalelo lebhloko ye-pulse.

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.4.6 — Ukuphunyezwa kokumodareyitha kobubanzi be-pulse

Le ndlela yokumodareyitha ipulse okwangoku yeyona ixhaphakileyo kwisixhobo sokulinganisa sombane solawulo nokhuseleko (CPS) lwezixhobo zamandla enyukliya (NPP) kunye ne-ACS yezinye iinkqubo zobugcisa.

Ukuqukumbela eli candelwana, kufuneka kuqatshelwe ukuba ukuba uphawu lwexesha luhlala kwezinye iikhonkco zezibhamu eziziqhubela phambili (SAP) kakhulu ngakumbi Δt (ngemiyalelo yobukhulu), ngoko inkqubo yepulse inokuthathwa njengenkqubo yolawulo oluzenzekelayo eqhubekayo (xa usebenzisa zombini i-AIM kunye ne-PWM).

1.4.3. Ukuhlelwa ngokwendalo yolawulo

Ngokusekelwe kubume beenkqubo zolawulo, iinkqubo zolawulo oluzenzekelayo zahlulwe zibe zezi ntlobo zilandelayo:

  • iinkqubo zokulawula ngokuzenzekelayo, apho umqondiso wegalelo unokudibaniswa ngokungathandabuzekiyo kunye nomqondiso wokuphuma (kunye nokunye);
  • stochastic ACS (yamanani, okunokwenzeka), apho i-ACS "iphendula" kumqondiso wegalelo elinikiweyo. random (stochastic) isignali yemveliso.

Isiphumo sophawu lwestochastic luphawulwa:

  • umthetho wolwabiwo;
  • ulindelo lwemathematika (ixabiso eliphakathi);
  • ukusasazeka (ukutenxa okusemgangathweni).

Ubume be-stochastic yenkqubo yokulawula ngokuqhelekileyo ibonwa kwi ngokusisiseko i-ACS engahambelaniyo zombini ukusuka kwindawo yokujonga iimpawu ze-static, kwaye ukusuka kwindawo yokujonga (nokuba kumlinganiselo omkhulu) wokungahambelani kwemigqaliselo eguquguqukayo kwi-equations ye-dynamics.

Intshayelelo kwithiyori yolawulo oluzenzekelayo. Iingcamango ezisisiseko zethiyori yolawulo lweenkqubo zobugcisa
Irayisi. 1.4.7 — Ukuhanjiswa kwexabiso lemveliso yestochastic inkqubo yolawulo oluzenzekelayo

Ukongeza kwiindidi eziphambili ezingentla zokuhlelwa kweenkqubo zolawulo, kukho ezinye iindidi. Ngokomzekelo, ulwahlulo lunokwenziwa ngokwendlela yokulawula kwaye lusekelwe ekusebenzisaneni kunye nokusingqongileyo kwangaphandle kunye nokukwazi ukulungelelanisa i-ACS kwiinguqu kwimimiselo yokusingqongileyo. Iinkqubo zohlulwe zibe ziindidi ezimbini ezinkulu:

I-1) Iinkqubo zokulawula eziqhelekileyo (ezingezilungeleyo) ngaphandle kokulungelelanisa; Ezi nkqubo ziphantsi koluhlu lwezinto ezilula ezingatshintshi isakhiwo sazo ngexesha lolawulo. Zezona ziphuhliswe kakhulu kwaye zisetyenziswa ngokubanzi. Iinkqubo zolawulo eziqhelekileyo zohlulwe kwii-subclasses ezintathu: i-open-loop, i-closed-loop kunye neenkqubo zokulawula ezidibeneyo.

2) Iinkqubo zokulawula ukuzilungisa (adaptive). Kwezi nkqubo, xa iimeko zangaphandle okanye iimpawu zento elawulwayo zitshintsha, utshintsho oluzenzekelayo (lungamiselwanga kwangaphambili) kwiparameters yesixhobo solawulo lwenzeka ngenxa yotshintsho kwindlela yokulawula i-coefficients, ubume benkqubo yolawulo, okanye ukungeniswa kwezinto ezintsha. .

Omnye umzekelo wokuhlela: ngokwesiseko se-hierarchical (inqanaba elinye, inqanaba ezimbini, inqanaba elininzi).

Ngabasebenzisi ababhalisiweyo kuphela abanokuthatha inxaxheba kuphando. Ngena, ndiyacela.

Qhubeka nokupapasha iintetho kwi-UTS?

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  • 7,5%No10

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Bangama-133 abasebenzisi abavotileyo. Abasebenzisi abali-10 abakhange.

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