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UVOD Opisan je postupak za odreivanja G(z) parne turbine 30 MW u EL-TO Zagreb uz primjenu Matlaba za simuliranje i optimiranje parametara prijenosnih funkcija; Najpovoljniji oblici G(s) turbine s kondenzatorom i servo sustavom su 2., 3. i 4. reda; Najpovoljniji oblici G(z) a" primjenom Z-transformacije na GE(s)G(s); Optimiranjem parametara G(z) a" najmanja pogreaka u odnosu na nelinearni model parne turbine 30 MW (9. reda); Ekvivalentni linearni kontinuirani modeli a" primjenom Z-1 na G(z) s optimalnim parametrima."U   y  @ "L2. PRIKAZ STRUKTURE SUSTAVA REGULACIJE PARNE TURBINE 30 MW U EL-TO ZAGREB MM M Parnoturbinsko postrojenje snage 30 MW u EL-TO Zagreb sastoji se od: protutla ne parne turbine s reguliranim oduzimanjem pare, grijueg kondenzatora, kondenzatnih pumpi, parnog ejektora, otplinja a, napojnih pumpi i visokotla nog regenerativnog zagrija a. &EE7 d '  DRegulacijski sustav protutla ne turbine s reguliranim oduzimanjem pare sadr~i: hidrauli kih regulatora brzine vrtnje, tlaka oduzete pare i tlaka izlazne pare, mikroprocesorskih regulatora brzine vrtnje, tlaka oduzete pare i protutlaka izlazne pare, parorazvodnih ventila visokog tlaka (VT) i niskog tlaka (NT), krilnih servo motora s razvodnim osovinama za parorazvodne ventile visokog tlaka (VT i niskog tlaka (NT). &OTOT   :! 1 Regulacijski sustav turbine namijenjen je za reguliranje triju fizikalnih veli ina: brzine vrtnje, tlaka reguliranog oduzimanja pare i protutlaka izlazne pare. Ulazne (upravlja ke i poremeajne) veli ine u turboagregat su: uVT, uNT, De, Jv. Izlazne veli ine iz turboagregata su: pe, pp. Osnovni tehni ki podaci turbine: Pm = 30MW, nn = 3000o/min, DVTm = 200 t/h, DNTm = 85 t/h, pen = 17bara, De = 0-150t/h, pnr = 3 bara, Dnr = 0-20t/h, pp = 0.3 - 0.95 bara. <UNUN?)$      x > )/     NLINEARNI DISKRETNI MODELI SUSTAVA REGULACIJE TURBOAGREGATA 30MW U EL-TO ZAGREBO" O OOpi postupak odreivanja optimalnih vrijednosti parametara G(z) dugotrajan: G(z) = B(z)/A(z) a" nb = ? i na = ? G(z) odreene su iz G(s):RM&<&c(Za odreivanje G(z) koriaten je Matlab: bd(0) i ad(0) iz bk(0) = bkopt i ak(0) = akopt; bdopt i adopt a" simpleks metoda; G(s) = Z-1{G(z)}. (e                   (3.1. Linearni diskretni modeli turbine u odnosu na ulaznu veli inu u servo motor visokog tlaka *b[&FLinearni model DpeM na promjenu DuVT a" 3 vremenske konstante u nazivniku: K !@ ' Primjenom Z-1 na (4) s optimalnim koeficijentima GVTP2(s) ekvivalentnog kontinuiranog modela: za $' a  Za linearni model DppM, u odnosu na uVT, 4 vremenske konstante u nazivniku: jQ%@( 3.2. Linearni diskretni modeli turbine s kondenzatorom i servo motorom u odnosu na promjenu ulazne veli ine u servo motor niskog tlaka@:2Za promjenu D)peM, u odnosu na uNT 2 vremenske konstante u nazivniku:tI $@ & Primjenom Z-1 na (9) prijenosna funkcija ekvivalentnog kontinuiranog modela:@O 9 OZa linearni model DppM na promjenu uNT derivacijsko ponaaanje i 4 vremenske konstante:jZ1@ 3"4. ZAKLJU AK Opisan postupak za odreivanje G(z) sustava regulacije parne turbine uz primjenu Matlaba za: simuliranje i optimiranje parametara prijenosnih funkcija. Najpovoljniji oblici G(z) primjenom Z-transformacije na GE(s)G(s). Optimiranje parametara G(z) obavljeno je za D)peM i D)ppM u odnosu na uVT i uNT. Optimiranjem je postignuta najmanja pogreaka u odnosu na nelinearni dinami ki model. Maksimalna pogreaka oko 1% koeficijenti G(z) odreeni zadovoljavajue to no.]=>;= s"t  #Prijenosne funkcije G(s) primjenom Z-1 na G(z) s optimalnim vrijednostima parametara. U G(s) dodatni lanovi u brojniku. Zanemarenjem dodatnih lanova poveava se pogreaka oko 1% koeficijenti G(z) i G(s) odreeni zadovoljavajue to no.* ,P# $Pitanja za diskusiju 4Mo~e li se opisana metoda odreivanja optimalnih parametara modela sustava regulacije parne turbine 30 MW u EL-TO Zagreb primijeniti na regulacijskim sustavima parnih turbina u drugim termoelektranama u Hrvatskoj? Mo~e se primijeniti u drugim termoelektranama i drugim energetskim objektima uz koriatenje Matlaba; Programski paket za optimiranje procesa u stvarnom vremenu za odreivanje: modela i optimalnih parametara procesa; optimalnih parametara regulatora (Ziegler-Nichols i dominatni polovi - modifikacijom optimalni parametri).|" )m'UZ 0%4Koje su prednosti koriatenja simpleks metode u slu aju odreivanja optimalnih parametara modela sustava regulacije parne turbine u odnosu na druge poznate optimizacijske metode? preporu a se za primjenu kada funkcija kvalitete ima izra~ene nelinearnosti; simpleks metoda sadr~i smanjenje i poveanje koraka promjene parametara - pogodnija od gradijentne metode veliki skokovi gradijent ima malu vrijednost.X"  @/  ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@ z?" dd@  " @ ` n?" dd@   @@``PR    @ ` ` p>>   ZK0 (    6$~ P ~ X Click to edit Master title style!!  0~  ~ RClick to edit Master text styles Second level Third level Fourth level Fifth level!    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Fakultet elektrotehnike i ra unarstva Zagrebb b bH  0޽h ? ̙33___PPT10i.0_+D=' = @B + ZK0 - ` $(   r  S hP   r  S Ę  H  0޽h ? ̙33___PPT10i.0]>+D=' = @B + ZK0 p$$(  $r $ S xP   r $ S 8  H $ 0޽h ? ̙33___PPT10i.ЄT+D=' = @B + ZK0 ($(  (r ( S @؂P   r ( S ق  H ( 0޽h ? ̙33___PPT10i.`W%+D=' = @B + ZK0 ,(  ,r , S ݂   H , 0޽h ? ̙33___PPT10i. $%+D=' = @B + ZK0 0(  0r 0 S   H 0 0޽h ? ̙33___PPT10i. ,+D=' = @B + ZK0  4f(  4 4 S P   Px 4 c $0Tp  ^ 4 6p 4 c &A ??"??N   4 0  O(1)(2  40 NA ? ? c      4 0P   O(2)(2 8  4 0  A \ gdje je: Td  vrijeme diskretizacije signala.2/ #& #H 4 0޽h ? ̙33___PPT10i. +D=' = @B + ZK0 <(  <r < S x   H < 0޽h ? ̙33___PPT10i.m+D=' = @B +#  ZK0 " @(  @r @ S P   r @ S    ^ @ 6p @ c &A ??"?}9  @ 0  O(3)(2  @ 0    z&Primjenom Z-transformacije (1) na (3):$'  '^  @ 6p @ c &A ??"? B    @ 0h~6 0  O(4)(2 z @ 0`  9  Optimalni koeficijenti (4) a" Td = 50 ms. Maksimalna pogreaka (3) rmk = 0,27%, a (4) rmd = 0,45% istog su reda veli ine. }#Z"$H @ 0޽h ? ̙33___PPT10i.t>+D=' = @B +  ZK0 c[P(  Pr P S !  ^ P 6p P c &A $??"? $ P 0#( " O(5)(2  P 0( 2%  LPrijelazna pojava nelinearnog modela y = pe, modela (5) yM = peM te a i r [%] za uVT = -0.1S(t-10) Sl. 1. rm 0,5%. U odnosu na (3), u (5) bV21s i bV22s2. Zanemarenjem tih lanova rm = 0,778% (70% vea) rm < 1% zadovoljavajue.  &   % MH P 0޽h ? ̙3380___PPT10.ýnZK0  T|(  T T BA "`9   T 0S= d LSl. 1. Prijelazna pojava nelinearnog modela y = pe, modela (5) yM = peM te a i r [%], za uVT = -0.1S(t-10).~u- , H T 0޽h ? ̙3380___PPT10.ɽDb ZK0 P \J(  \r \ S Wj/  ^ \ 6p \ c &A ,??"?{" , \ 0\   O(6)(2  \ 0r   H Primjenom (1) na (6) dobije se:  !^  \ 6p \ c &A  /??"?)  /  \ 0 p j  O(7)(2   \ 0d  c s  ^Za (6) rmk = 0,5%, a za (7) rmd = 0,5%. Primjenom Z-1 na (7) (6). jI @(H \ 0޽h ? ̙3380___PPT10.ʽlt ZK0  ` `(  `r ` S     r ` S 8@ "   ^ ` 6p ` c &A  2??"? S  2 ` 0 I O(8)(2  ` 0D     GPrimjenom (1) na (8) dobije se: ^  ` 6p ` c &A 5??"?   5  ` 0C  I  O(9)(2   ` 0`     @Maksimalna pogreaka (8) rmk = 0,55%, a (9) rmd = 0,30%, tj. oko 40% <.LI@H ` 0޽h ? ̙3380___PPT10.i2 ZK0 B:pd(  dr d S ,<  ^ d 6p d c &A  8??"?D 8 d 0xnC s9m P(10)(2  d 0  "  *Maksimalna pogreaka (10) rmk = 0,30%, tj. jednaka je (9), a oko 40% < nego (8). Prijelazna pojava nelinearnog modela y = pe, ekvivalentnog kontinuiranog modela (10) yM = peM te a i r [%] Sl. 2. Prijenosna funkcija (10) sadr~i bN2 pogreaka manja nego (8). Zanemarenjem bN2 u (10) rm = 1,66% oko 3 puta vea od (8).xM'2+)' B*h$H d 0޽h ? ̙3380___PPT10.jС0ZK0 6. h(  h h 0C  TL 2Sl. 2. 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UVOD Opisan je postupak za odreivanja G(z) parne turbine 30 MW u EL-TO Zagreb uz primjenu Matlaba za simuliranje i optimiranje parametara prijenosnih funkcija; Najpovoljniji oblici G(s) turbine s kondenzatorom i servo sustavom su 2., 3. i 4. reda; Najpovoljniji oblici G(z) a" primjenom Z-transformacije na GE(s)G(s); Optimiranjem parametara G(z) a" najmanja pogreaka u odnosu na nelinearni model parne turbine 30 MW (9. reda); Ekvivalentni linearni kontinuirani modeli a" primjenom Z-1 na G(z) s optimalnim parametrima."U   y  @ "L2. 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UVOD Opisan je postupak za odreivanja G(z) parne turbine 30 MW u EL-TO Zagreb uz primjenu Matlaba za simuliranje i optimiranje parametara prijenosnih funkcija; Najpovoljniji oblici G(s) turbine s kondenzatorom i servo sustavom su 2., 3. i 4. reda; Najpovoljniji oblici G(z) a" primjenom Z-transformacije na GE(s)G(s); Optimiranjem parametara G(z) a" najmanja pogreaka u odnosu na nelinearni model parne turbine 30 MW (9. reda); Ekvivalentni linearni kontinuirani modeli a" primjenom Z-1 na G(z) s optimalnim parametrima."U   y  @ "L2. PRIKAZ STRUKTURE SUSTAVA REGULACIJE PARNE TURBINE 30 MW U EL-TO ZAGREB MM M Parnoturbinsko postrojenje snage 30 MW u EL-TO Zagreb sastoji se od: protutla ne parne turbine s reguliranim oduzimanjem pare, grijueg kondenzatora, kondenzatnih pumpi, parnog ejektora, otplinja a, napojnih pumpi i visokotla nog regenerativnog zagrija a. &EE7 d '  DRegulacijski sustav protutla ne turbine s reguliranim oduzimanjem pare sadr~i: hidrauli kih regulatora brzine vrtnje, tlaka oduzete pare i tlaka izlazne pare, mikroprocesorskih regulatora brzine vrtnje, tlaka oduzete pare i protutlaka izlazne pare, parorazvodnih ventila visokog tlaka (VT) i niskog tlaka (NT), krilnih servo motora s razvodnim osovinama za parorazvodne ventile visokog tlaka (VT i niskog tlaka (NT). &OTOT   :! 1 Regulacijski sustav turbine namijenjen je za reguliranje triju fizikalnih veli ina: brzine vrtnje, tlaka reguliranog oduzimanja pare i protutlaka izlazne pare. Ulazne (upravlja ke i poremeajne) veli ine u turboagregat su: uVT, uNT, De, Jv. Izlazne veli ine iz turboagregata su: pe, pp. Osnovni tehni ki podaci turbine: Pm = 30MW, nn = 3000o/min, DVTm = 200 t/h, DNTm = 85 t/h, pen = 17bara, De = 0-150t/h, pnr = 3 bara, Dnr = 0-20t/h, pp = 0.3 - 0.95 bara. <UNUN?)$      x > )/     NLINEARNI DISKRETNI MODELI SUSTAVA REGULACIJE TURBOAGREGATA 30MW U EL-TO ZAGREBO" O OOpi postupak odreivanja optimalnih vrijednosti parametara G(z) dugotrajan: G(z) = B(z)/A(z) a" nb = ? i na = ? G(z) odreene su iz G(s):RM&<&c(Za odreivanje G(z) koriaten je Matlab: bd(0) i ad(0) iz bk(0) = bkopt i ak(0) = akopt; bdopt i adopt a" simpleks metoda; G(s) = Z-1{G(z)}. (e                   (3.1. Linearni diskretni modeli turbine u odnosu na ulaznu veli inu u servo motor visokog tlaka *b[&FLinearni model DpeM na promjenu DuVT a" 3 vremenske konstante u nazivniku: K !@ ' Primjenom Z-1 na (4) s optimalnim koeficijentima GVTP2(s) ekvivalentnog kontinuiranog modela: za $' a  Za linearni model DppM, u odnosu na uVT, 4 vremenske konstante u nazivniku: jQ%@( 3.2. Linearni diskretni modeli turbine s kondenzatorom i servo motorom u odnosu na promjenu ulazne veli ine u servo motor niskog tlaka@:2Za promjenu D)peM, u odnosu na uNT 2 vremenske konstante u nazivniku:tI $@ & Primjenom Z-1 na (9) prijenosna funkcija ekvivalentnog kontinuiranog modela:@O 9 OZa linearni model DppM na promjenu uNT derivacijsko ponaaanje i 4 vremenske konstante:jZ1@ 3"4. ZAKLJU AK Opisan postupak za odreivanje G(z) sustava regulacije parne turbine uz primjenu Matlaba za: simuliranje i optimiranje parametara prijenosnih funkcija. Najpovoljniji oblici G(z) primjenom Z-transformacije na GE(s)G(s). Optimiranje parametara G(z) obavljeno je za D)peM i D)ppM u odnosu na uVT i uNT. Optimiranjem je postignuta najmanja pogreaka u odnosu na nelinearni dinami ki model. Maksimalna pogreaka oko 1% koeficijenti G(z) odreeni zadovoljavajue to no.]=>;= s"t  #Prijenosne funkcije G(s) primjenom Z-1 na G(z) s optimalnim vrijednostima parametara. U G(s) dodatni lanovi u brojniku. Zanemarenjem dodatnih lanova poveava se pogreaka oko 1% koeficijenti G(z) i G(s) odreeni zadovoljavajue to no.* ,P# $Pitanja za diskusiju 4Mo~e li se opisana metoda odreivanja optimalnih parametara modela sustava regulacije parne turbine 30 MW u EL-TO Zagreb primijeniti na regulacijskim sustavima parnih turbina u drugim termoelektranama u Hrvatskoj? Mo~e se primijeniti u drugim termoelektranama i drugim energetskim objektima uz koriatenje Matlaba; Programski paket za optimiranje procesa u stvarnom vremenu za odreivanje: modela i optimalnih parametara procesa; optimalnih parametara regulatora (Ziegler-Nichols i dominatni polovi - modifikacijom optimalni parametri).|" )m'UZ 0%4Koje su prednosti koriatenja simpleks metode u slu aju odreivanja optimalnih parametara modela sustava regulacije parne turbine u odnosu na druge poznate optimizacijske metode? preporu a se za primjenu kada funkcija kvalitete ima izra~ene nelinearnosti; simpleks metoda sadr~i smanjenje i poveanje koraka promjene parametara - pogodnija od gradijentne metode veliki skokovi gradijent ima malu vrijednost.X"  @/  ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@ ?" dd@  @` n?" dd@   @@``PR    @ ` ` p>>   ZK0 (    6$~ P ~ X Click to edit Master title style!!  0~  ~ RClick to edit Master text styles Second level Third level Fourth level Fifth level!    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ZAKLJUAK Slide 18Pitanja za diskusiju Slide 20  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles#_v Toni BjazicToni BjazicE7 d '  DRegulacijski sustav protutla ne turbine s reguliranim oduzimanjem pare sadr~i: hidrauli kih regulatora brzine vrtnje, tlaka oduzete pare i tlaka izlazne pare, mikroprocesorskih regulatora brzine vrtnje, tlaka oduzete pare i protutlaka izlazne pare, parorazvodnih ventila visokog tlaka (VT) i niskog tlaka (NT), krilnih servo motora s razvodnim osovinama za parorazvodne ventile visokog tlaka (VT i niskog tlaka (NT). &OTOT   :! 1 Regulacijski sustav turbine namijenjen je za reguliranje triju fizikalnih veli ina: brzine vrtnje, tlaka reguliranog oduzimanja pare i protutlaka izlazne pare. Ulazne (upravlja ke i poremeajne) veli ine u turboagregat su: uVT, uNT, De, Jv. Izlazne veli ine iz turboagregata su: pe, pp. Osnovni tehni ki podaci turbine: Pm = 30MW, nn = 3000o/min, DVTm = 200 t/h, DNTm = 85 t/h, pen = 17bara, De = 0-150t/h, pnr = 3 bara, Dnr = 0-20t/h, pp = 0.3 - 0.95 bara. <UNUN?)$      x > )/     NLINEARNI DISKRETNI MODELI SUSTAVA REGULACIJE TURBOAGREGATA 30MW U EL-TO ZAGREBO" O OOpi postupak odreivanja optimalnih vrijednosti parametara G(z) dugotrajan: G(z) = B(z)/A(z) a" nb = ? i na = ? G(z) odreene su iz G(s):RM&<&c(Za odreivanje G(z) koriaten je Matlab: bd(0) i ad(0) iz bk(0) = bkopt i ak(0) = akopt; bdopt i adopt a" simpleks metoda; G(s) = Z-1{G(z)}. (e                   (3.1. Linearni diskretni modeli turbine u odnosu na ulaznu veli inu u servo motor visokog tlaka *b[&FLinearni model DpeM na promjenu DuVT a" 3 vremenske konstante u nazivniku: K !@ ' Primjenom Z-1 na (4) s optimalnim koeficijentima GVTP2(s) ekvivalentnog kontinuiranog modela: za $' a  Za linearni model DppM, u odnosu na uVT, 4 vremenske konstante u nazivniku: jQ%@( 3.2. Linearni diskretni modeli turbine s kondenzatorom i servo motorom u odnosu na promjenu ulazne veli ine u servo motor niskog tlaka@:2Za promjenu D)peM, u odnosu na uNT 2 vremenske konstante u nazivniku:tI $@ & Primjenom Z-1 na (9) prijenosna funkcija ekvivalentnog kontinuiranog modela:@O 9 OZa linearni model DppM na promjenu uNT derivacijsko ponaaanje i 4 vremenske konstante:jZ1@ 3"4. ZAKLJU AK Opisan postupak za odreivanje G(z) sustava regulacije parne turbine uz primjenu Matlaba za: simuliranje i optimiranje parametara prijenosnih funkcija. Najpovoljniji oblici G(z) primjenom Z-transformacije na GE(s)G(s). Optimiranje parametara G(z) obavljeno je za D)peM i D)ppM u odnosu na uVT i uNT. Optimiranjem je postignuta najmanja pogreaka u odnosu na nelinearni dinami ki model. Maksimalna pogreaka oko 1% koeficijenti G(z) odreeni zadovoljavajue to no.]=>;= s"t  #Prijenosne funkcije G(s) primjenom Z-1 na G(z) s optimalnim vrijednostima parametara. U G(s) dodatni lanovi u brojniku. Zanemarenjem dodatnih lanova poveava se pogreaka oko 1% koeficijenti G(z) i G(s) odreeni zadovoljavajue to no.* ,P# $Pitanja za diskusiju 4Mo~e li se opisana metoda odreivanja optimalnih parametara modela sustava regulacije parne turbine 30 MW u EL-TO Zagreb primijeniti na regulacijskim sustavima parnih turbina u drugim termoelektranama u Hrvatskoj? Mo~e se primijeniti u drugim termoelektranama i drugim energetskim objektima uz koriatenje Matlaba; Programski paket za optimiranje procesa u stvarnom vremenu za odreivanje: modela i optimalnih parametara procesa; optimalnih parametara regulatora (Ziegler-Nichols i dominatni polovi - modifikacijom optimalni parametri).|" )m'UZ 0%4Koje su prednosti koriatenja simpleks metode u slu aju odreivanja optimalnih parametara modela sustava regulacije parne turbine u odnosu na druge poznate optimizacijske metode? preporu a se za primjenu kada funkcija kvalitete ima izra~ene nelinearnosti; simpleks metoda sadr~i smanjenje i poveanje koraka promjene parametara - pogodnija od gradijentne metode veliki skokovi gradijent ima malu vrijednost.X"  @/  ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@ ?" dd@  @` n?" dd@   @@``PR    @ ` ` p>>   ZK0 (    6$~ P ~ X Click to edit Master title style!!  0~  ~ RClick to edit Master text styles Second level Third level Fourth level Fifth level!    S  0} `` ~ V*   0~ `  ~ *CIGR 6. Simpozij o sustavu voenja EES-a, Cavtat, 07.  10. 11. 2004.,HC&(A  0~ `  ~ X*   0~ I, B1-05 Primjena metoda optimiranja za odreivanje linearnog diskretnog modela sustava regulacije parne turbine.on&nh  B2d޽h @ ?"` ̙334,___PPT10 . Default DesignZK0 P,(  r  S ap   z  0b"` )" prof. dr. sc. Petar Crnoaija Toni Bja~i, dipl. ing. Fakultet elektrotehnike i ra unarstva Zagrebb b bH  0޽h ? ̙33___PPT10i.0_+D=' = @B + ZK0 - ` $(   r  S hP   r  S Ę  H  0޽h ? ̙33___PPT10i.0]>+D=' = @B + ZK0 p$$(  $r $ S xP   r $ S 8  H $ 0޽h ? ̙33___PPT10i.ЄT+D=' = @B + ZK0 ($(  (r ( S @؂P   r ( S ق  H ( 0޽h ? ̙33___PPT10i.`W%+D=' = @B + ZK0 ,(  ,r , S ݂   H , 0޽h ? ̙33___PPT10i. $%+D=' = @B + ZK0 0(  0r 0 S   H 0 0޽h ? ̙33___PPT10i. ,+D=' = @B + ZK0  4f(  4 4 S P   Px 4 c $0Tp  ^ 4 6p 4 c &A ??"??N   4 0  O(1)(2  40 NA ? ? c      4 0P   O(2)(2 8  4 0  A \ gdje je: Td  vrijeme diskretizacije signala.2/ #& #H 4 0޽h ? ̙33___PPT10i. +D=' = @B + ZK0 <(  <r < S x   H < 0޽h ? ̙33___PPT10i.m+D=' = @B +#  ZK0 " @(  @r @ S P   r @ S    ^ @ 6p @ c &A ??"?}9  @ 0  O(3)(2  @ 0    z&Primjenom Z-transformacije (1) na (3):$'  '^  @ 6p @ c &A ??"? B    @ 0h~6 0  O(4)(2 z @ 0`  9  Optimalni koeficijenti (4) a" Td = 50 ms. Maksimalna pogreaka (3) rmk = 0,27%, a (4) rmd = 0,45% istog su reda veli ine. }#Z"$H @ 0޽h ? ̙33___PPT10i.t>+D=' = @B +d  ZK0 c[P(  Pr P S !  ^ P 6p P c &A $??"? $ P 0#( " O(5)(2  P 0( 2%  LPrijelazna pojava nelinearnog modela y = pe, modela (5) yM = peM te a i r [%] za uVT = -0.1S(t-10) Sl. 1. rm 0,5%. U odnosu na (3), u (5) bV21s i bV22s2. Zanemarenjem tih lanova rm = 0,778% (70% vea) rm < 1% zadovoljavajue.  &   % MH P 0޽h ? ̙33___PPT10i.ýn+D=' = @B +ZK0  T|(  T T BA "`9   T 0S= d LSl. 1. Prijelazna pojava nelinearnog modela y = pe, modela (5) yM = peM te a i r [%], za uVT = -0.1S(t-10).~u- , H T 0޽h ? ̙33___PPT10i.ɽD+D=' = @B + ZK0 P \J(  \r \ S Wj/  ^ \ 6p \ c &A ,??"?{" , \ 0\   O(6)(2  \ 0r   H Primjenom (1) na (6) dobije se:  !^  \ 6p \ c &A  /??"?)  /  \ 0 p j  O(7)(2   \ 0d  c s  ^Za (6) rmk = 0,5%, a za (7) rmd = 0,5%. Primjenom Z-1 na (7) (6). jI @(H \ 0޽h ? ̙33___PPT10i.ʽlt+D=' = @B + ZK0  ` `(  `r ` S     r ` S 8@ "   ^ ` 6p ` c &A  2??"? S  2 ` 0 I O(8)(2  ` 0D     GPrimjenom (1) na (8) dobije se: ^  ` 6p ` c &A 5??"?   5  ` 0C  I  O(9)(2   ` 0`     @Maksimalna pogreaka (8) rmk = 0,55%, a (9) rmd = 0,30%, tj. oko 40% <.LI@H ` 0޽h ? ̙33___PPT10i.i2+D=' = @B +C  ZK0 B:pd(  dr d S ,<  ^ d 6p d c &A  8??"?D 8 d 0xnC s9m P(10)(2  d 0  "  *Maksimalna pogreaka (10) rmk = 0,30%, tj. jednaka je (9), a oko 40% < nego (8). Prijelazna pojava nelinearnog modela y = pe, ekvivalentnog kontinuiranog modela (10) yM = peM te a i r [%] Sl. 2. Prijenosna funkcija (10) sadr~i bN2 pogreaka manja nego (8). Zanemarenjem bN2 u (10) rm = 1,66% oko 3 puta vea od (8).xM'2+)' B*h$H d 0޽h ? ̙33___PPT10i.jС0+D=' = @B +7ZK0 6. h(  h h 0C  TL 2Sl. 2. Prijelazna pojava nelinearnog modela turbine y = pe, ekvivalentnog kontinuiranog modela (10) yM = peM te a i r [%], za uNT = -0.1S(t-10).~5, 4+   h BA  "`V  yH h 0޽h ? ̙33___PPT10i.ɽD+D=' = @B + ZK0  p(  pr p S     ^ p 6p p c &A ;??"?Slv ; p 0t8F @ P(11)(2  p 0d$8 "2 H Primjenom (1) na (11) dobije se: !^  p 6p p c &A  >??"?KO  >  p 0K8  P(12)(2   p 0H8    *Maksimalna pogreaka (11) i (12) istog iznosa rm = 1,5% zadovoljavajua to nost. 8U. &-%H p 0޽h ? ̙33___PPT10i.ka+D=' = @B + ZK0 t$(  tr t S V8P  8 r t S x%    H t 0޽h ? ̙33___PPT10i.laz+D=' = @B + ZK0 x(  xr x S y  y H x 0޽h ? ̙33___PPT10i.ml +D=' = @B + ZK0 |:(  |r | S yP  y  | S y y " @H | 0޽h ? ̙33___PPT10i.mz`+D=' = @B +1 ZK0 0((    S #+  +  " @H  0޽h ? ̙33___PPT10i.m$+D=' = @B +&xYolSU?kB?&tpcnuLAF(kt6Ѝ/ƥhmđ8 ~0j&~L#_I ( _4FkVϹtu-w}߽{]ƻ/ i $aO?`0k}xߏh^o^<`)JKAI\k;ώ/a{m9PVz(ٞQ[p=Ї/g1lDkmIm÷g2|3"#!}]|wۘ֝9+B`[H}P'DMĊfd&P}GzY%ɪI~γhOt?W*S=Sc}4…_"lt_ݽ# y) ED {BQg{sO' %n9M(}@36SE;.U+憘7Vх-N#]ֳ'vaýџfP D0J@WpkjD' ^HGoHcr)9`(C^B{׏#D^;*W#A^\ *d kDECޠͷ^;c&؄܄ț ? 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