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+− E(p)

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(p) S(p) ^ε(p) =E(p)−S(p)

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1

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BO(p) =Cd(p)

lO

# VX *b /m `2iQm` MQM mMBiB`2

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C_d(p)

(p) S(p)

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1

1+C_d(p)·Cr(p)

E(p) q3, C,C -

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ġ α≥0- I ,Icc3 0n cwcjěL3.

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# VX *H+mHb T`ûH#H2b

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p^α·D(p) E(p)

ε(p) = ^pα·D(p)

p^α·D(p) +K·N(p)^E(p)

kz

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p→0

p p^α·D(p)

p^α·D(p) +K·N(p)^E(p)

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p→0

p^α+1 p^α+KE(p)

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p→0

p^α+1 p^α+KE(p)

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ε_i = lim

p→0

p^α+1 p^α+K

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p

=lim

p→0

p^α

p^α+KE0

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p→0

p⁰

p⁰+KE0

= ¹

1+KE0

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+RLL3 Uaā,ā03LL3Nj

ε_t = lim

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p→0

p^α+1 p^α+KE(p)

kS

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ε_t = lim

p→0

p^α+1 p^α+K

A0

p²

= lim

p→0

A0· ^pα−1 p^α+K

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= +∞

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ε_t= lim

p→0

A0· ^pα−1 p^α+K

=0

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p³

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= lim

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= ²·A0

K avbiĕK2 /2 +Hbb2 >2 Uα>^2V

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p→0

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=0

kl

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K t

εa = +∞

α=2 t

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α>2 t

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t εt=0

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kk

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1+F1(p)·F2(p)·R(p)

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1+F1(p)·F2(p)·R(p)

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ε_p(p) =− ^F2(p)

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εp(p) =−^K2·N2(p)

p^α2·D2(p)· ¹ 1+ ^K1·N1(p)

p^α1·D1(p)· ^K2·N2(p) p^α2 ·D2(p)

·^R0 p

εp(p) =− ^K2·N2(p)·p^α1·D1(p)

p^α1·D1(p)·p^α2 ·D2(p) +K1·N1(p)·K2·N2(p)· ^R0 p

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ε_p= lim

t→∞(ε(t)) = lim

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εp = lim

p→0

−p· ^K2·p^α1

p^α1 ·p^α2+K1·K2 ·^R0 p

k:

q3,Ni(0) =Di(0) =1

εp= lim

p→0

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=−^R0 K1

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QN ,RNcjj3 $C3N. \n3 UInc I $N03 UccNj3 n<L3Nj3. UInc I3 j3LUc 03 aāURNc3 0CLCNn3Y /Nc I3c nja3c ,c. I3c ,I,nIc cRNj UInc ,RLUI3u3c. NRnc NRnc ICLCj3aRNc 0RN, © LRNja3a cNc 0āLRNcjajCRN \n3 URna nN cwcjěL3 0n c3,RN0 Ra0a3. I a3IjCRN 3Nja3 I $N03 UccNj3 3j I3 j3LUc 03 LRNjā3 3cj 03 LćL3 Njna3Y

TRna IȕāqIn3a. NRnc IIRNc ājn0C3a I3 ,c 0n cwcjěL3 0n c3,RN0 Ra0a3 © a3jRna nNCjCa3 ,CA03ccRncY

+−

(p) _K

p·(1+p)

E(p) S(p) H 7i#7 cȕā,aCj -

BF(p) = ¹ 1+_K^p + ^p_K² Ta C03NjC~,jCRN q3, I 8RaL3 ,NRNC\n3 RN R$jC3Nj -

ġ ωn=√

k. I UnIcjCRN UaRUa3 d

ġ z= ¹

2·√

K. I3 ,R3|,C3Nj 0ȕLRajCcc3L3NjY

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kf

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10⁻¹ 10⁰ 10¹

−60

−50

−40

−30

−20

−10 0 10

0#

a0gc

K=0.3 K=1 K=10

−3dB bp3

bp2

bp1

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t K=10

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tm1 tm2 tm3

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Δfc

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Correcteur 1

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Δx KS

Soupape

Δq KT

1 +τp Turbine

ΔPm +− f0

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Δf

ΔPc ΔPcht

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03 ,@a<3

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p

[SY /āj3aLCN3a I 8RN,jCRN 03 jaNc83aj HP(p) = ^ΔPm(p)

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k4

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$Rn,I3 CNj3aN3 03 aā<nIjCRN LāICRa3AjA3II3 I aUC0Cjā ]

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1+ ¹ Ti·p

Y

0,1 1 10

1 10

100 t_r5%·ω₀

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cC ,3jj3 $Rn,I3 03 aā<nIjCRN 3cj cj$I3 3j Uaā,Cc3Y [n3 U3njARN 0Ca3 0n j3LUc 03 aāA URNc3 ]

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[:Y KRNja3a \n3 0Nc ,3c ,RN0CjCRNc. I 8RN,jCRN 03 jaNc83aj HP(p) U3nj ćja3 UUaR,@ā3 Ua nN3 8RN,jCRN 03 jaNc83aj cCLUIC~ā3 0RNj RN Uaā,Cc3a I3c UaLěja3cY

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ΔPcs(p) cȕā,aCj cRnc I 8RaL3 - HP(p) = ¹+Ti·p

T_i·τ·p²+2·T_i·p+1Y

QN 0RNN3 I3c ,RNcjNj3cTa =10 s3jKri =10⁸W sY

[9Y /āj3aLCN3a I 8RN,jCRN 03 jaNc83aj 3N $Rn,I3 Rnq3aj3Hf o(p) = ^Δf(p)

εf(p) ^URnaΔPc(p)3jΔP_chtNnIcY bna I ~<na3 fYlO cRNj ja,āc I3c 0C<aLL3c 03 #R03 03 I 8RN,jCRN 03 jaNc83aj 3N $Rn,I3 Rnq3aj3 URnaTi =10·τ3jTi =0,1·τY

[fY TRna ,3c 03nu 8RN,jCRNc 03 jaNc83aj. UI,3a cna I3c 0C<aLL3c - [fY Taā,Cc3a I Iā<3N03Y

[f$Y TI,3a I3c UnIcjCRNc 1 τ. 1

Ti

3j 1

√T·τY

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[eY ia,3a I3c 0C<aLL3c 03 #R03 cwLUjRjC\n3 03Hf o(p) = ^Δf(p) ε_f(p)

[4Y 2N ccCLCINj I3 ja,ā 03 #R03 aā3I 0n <CN © cRN cwLUjRj3. ,I,nI3a I La<3 03 U@c3Y +RN,Ina3 cna I3c ,aCjěa3c 03 cj$CICjā 3j 03 Uaā,CcCRN 0n ,@C3a 03c ,@a<3cY

2N njCICcNj Iȕ3uUa3ccCRN UUaR,@ā3 -HP(p) = ¹

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[SSY pāaC~3a IRac I3 ,aCjěa3 03 aUC0Cjā 0n ,@C3a 03c ,@a<3cY

kO

10⁻³ 10⁻² 10⁻¹ 10⁰ 10¹

−40

−20 0 20 40 60 0#

a0gc

10⁻³ 10⁻² 10⁻¹ 10⁰ 10¹

−270

−225

−180

−135

−90

−45 0

◦

a0gc

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2u3a,C,3 9 A Taā,CcRN 3j UaLěja3c

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+− ΘeVUW

C(p) (p)

G(p) U(p) Θ(p)

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dt² + (4+α)·^dθ

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H aā<nIjCRN ,RLUIěj3 3cj a3Uaāc3Njā3 Ua I3 c,@āL $IR, ,C ,RNja3Y ġ Θe(p)- I jaNc8RaLā3 03 HUI,3 03 I j3LUāajna3 03 ,RNcC<N3θe(t)d ġ Θ(p)3jU(p)I3c jaNc8RaLā3c 03 HUI,3 03θ(t)3ju(t)d

ġ C(p)- I3 aā<nIj3naY

/Nc nN Ua3LC3a j3LUc. RN ,@RCcCj nN aā<nIj3na UaRURajCRNN3I -C(p) =KpY [SY /āj3aLCN3a I 8RN,jCRN 03 jaNc83ajG(p)Y

[lY /āj3aLCN3a I 8RN,jCRN 03 jaNc83aj 3N $Rn,I3 83aLā3GF(p) = ^Θ(p)

Θ_e(p)Y K3jja3 cRnc 8RaL3 ,NRA NC\n3Y

:z

[kY H3 cwcjěL3 3cjACI cj$I3 ]

[:Y /āj3aLCN3a FU URna R$j3NCa nN ,R3|,C3Nj 0ȕLRajCcc3L3NjzF>0, 5Y

[9Y /āj3aLCN3a Iȕ3aa3na CN0C,C3II3 URna nN ā,@3IRN 03 j3LUāajna3 03 Θ0 = 20^◦C3N 8RN,jCRN 0n UaLěja3αY +RN,Ina3 cna I Uaā,CcCRNY

QN ,@RCcCj LCNj3NNj nN aā<nIj3na UaRURajCRNN3I CNjā<aI -C(p) =Kp1+Ti·p T_i·p Y [fY /āj3aLCN3a I 7i#Q URna I3c qI3nac cnCqNj3c 03Ti3jαd

ġ Ti =1/20.Ti =1/16 ġ α=^20.α=¹⁶

[eY ¨ UajCa 0n ja,ā 03c 0C<aLL3c 03 #R03 03 I 7i#Q URna ,@,nN 03c ,c VRN Ua3N0Kp = 1W.

0āj3aLCN3a I3 ,RnUI3 Ti,Kp

j3I \n3 I La<3 03 U@c3 VMpW cRCj cnUāaC3na3 ©45ï URna jRnj3c I3c qI3nac 03αY

[4Y /āj3aLCN3a Iȕ3aa3na CN0C,C3II3 URna nN ā,@3IRN 03 j3LUāajna3 03Θ0 =20^◦CY 2u3a,C,3 f A Taā,CcCRN 3j cj$CICjā

+RaaC<ā U<3 :O bRCj I3 cwcjěL3 0ā,aCj Ua I3 c,@āL $IR, -

H1(p) Yre f(p)

+− U(p)

H2(p)

ε(p) Y(p)

H3(p) KVUW

H1(p) = (1+16·p)⁵·(1+33·p) ^H2(p) = ¹⁵·k

p(1+p) ^H3(p) = ¹ 1+0.1·p yre f(t) =Yo 3cj nN3 ,RNcC<N3 ,RNcjNj3 Vā,@3IRNWY

[SY /āj3aLCN3a I 8RN,jCRN 03 jaNc83ajO(p) = ^M(p)

ε(p) ^UnCcF(p) = ^Y(p) U(p) ^Y [lY /āj3aLCN3a I 8RN,jCRN 03 jaNc83ajG(p) = ^Y(p)

Yre f(p) ^Y

[kY /āj3aLCN3a I qI3na ~NI3 03Y(t)URnak=0,1.k =0,5.k =13jk =5Y 2u3a,C,3 e A 2uRc\n3I3jj3 URna I3 LNC3L3Nj 03 ,@a<3c

2ujaCj 03 ++b ibB lzSe +RaaC<ā U<3 9z

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~N 03 cȕccna3a 03 LCNCLCc3a Iȕ3aa3na Ua aUURaj © ,3jj3 ,RNcC<N3. RN LRNja3 \n3 ,3I a3qC3Nj © a3cU3,j3a nN3 Uaā,CcCRN © I 8RCc URna nN ā,@3IRN. nN3 aLU3 3j nN3 ,,āIāajCRNY

H3 ,@C3a 03c ,@a<3c 3cj 0ā,aCj ,CA03ccRnc -

:S

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ajC,nIjCRNc 03c ,@3qCII3c

TC30c k 3j kȕ

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ԣ UbV ᅭϵφU`/V

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;āa3a I3 LRnq3A L3Nj q3ajC,I

Taā,CcCRN cjjC\n3 03 I $Rn,I3 0ȕcc3aqCcc3L3Nj 03 URcCjCRN

3aa3na 03 URcCjCRN J SX

3aa3na 03 jaţN<3 J SX

3aa3na 0ȕ,,āIāajCRN J SX

b3IRN I3 ,@C3a 03c ,@a<3c. URna ccna3a nN3 $RNN3 cwN,@aRNCcjCRN 03c u3c. Iȕ3uC<3N,3 03 UaāA ,CcCRN cjjC\n3 cnCj3 © nN3 3Njaā3 03 jwU3 ā,@3IRN. 03 jwU3 aLU3 Rn 03 jwU3 ,,āIāajCRN 0RCj ćja3 CN8āaC3na3 © SXY

H3 Ua3LC3a LR0ěI3 0ā~NC ~<na3 fYkl 3cj 0RUjā URna ,@\n3 u3Y MRjjCRNc

:l

+− Θ_mC(p)

K1

ε(p)

+− Ω_mC(p)

C_Ω(p) ^CmC(p) Mc(p) ^Cm(p)+− 1 J·p+f

1 p

Ωm(p) Θm(p) Cr(p)

7ϔόЛЁζ fYklY Ģ Ta3LC3a LR0ěI3

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Cr(p) ,RnUI3 aācCcjNj U3ajna$j3na VqaC$I3 j3LURa3II3 -cr(t)3N MLW

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j3na

f ,R3|,C3Nj 03 8aRjj3L3Njc qCc\n3nu ā\nCqI3Nj URna Iȕ3Nc3L$I3 3N LRnq3L3Nj H3 ,Raa3,j3na 03 Iȕcc3aqCcc3L3Nj 03 qCj3cc3 3cj 03 I 8RaL3C_Ω(p) =K2·

1+ ¹ Ti·p

q3,Tiaā<Iā

~N 03 ,RLU3Nc3a I3 UǃI3 0RLCNNj URna I cCjnjCRN ,Raa3cURN0Nj © IȕCN3ajC3 LRw3NN3.Ti = ^J fY Hȕā,aj 3cj 0ā~NC Ua I qaC$I3ε(t) =θ_mC(t)−θ_m(t)Y

H Uaā,CcCRN cjjC\n3 0n cwcjěL3 3cj 0ā~NC3 Ua I3c UaLěja3c cnCqNjc - ġ 2aa3na 03 URcCjCRN -εp = lim

t→∞(ε(t)cnCj3 © nN3 3Njaā3 03 jwU3 ā,@3IRN nNCjCa3θmC(t) =H(t)Y ġ 2aa3na 03 jaţN<3 -εv = lim

t→∞(ε(t)cnCj3 © nN3 3Njaā3 03 jwU3 ā,@3IRN nNCjCa3θmC(t) =t· H(t)Y ġ 2aa3na 3N ,,āIāajCRN - εa = lim

t→∞(ε(t) cnCj3 © nN3 3Njaā3 03 jwU3 ā,@3IRN nNCjCa3 θmC(t) = t²· H(t)Y

q3,H(t)I 8RN,jCRN 03 ?3qCcC03Y

QN aUU3II3 I jaNc8RaLā3 03 HUI,3 03tⁿ· H(t)^{- n}

pⁿ⁺¹ URnan>^1Y

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[SY 2uUaCL3aH_Ω(p) = ^Ωm(p)

Ωmc(p) 3N 8RN,jCRN 03J.K23j pY [lY 2uUaCL3aε(p)3N 8RN,jCRN 03Θmc(p).H_Ω(p).K13jpY

[kY /āj3aLCN3a Iȕ3aa3na 03 URcCjCRNεp UnCc Iȕ3aa3na 03 jaţN<3εv+RN,Ina3 cna I qI3na 03K1URna cjCc8Ca3 © Iȕ3uC<3N,3 0ȕ3aa3na 3N jaţN<3Y

[:Y /āj3aLCN3a Iȕ3aa3na 3N ,,āIāajCRNεa3j ,RN,Ina3 \nNj n a3cU3,j 0n ,@C3a 03c ,@a<3cY

~N 03 cjCc8Ca3 Iȕ3uC<3N,3 0ȕnN3 3aa3na 3N ,,āIāajCRN CN8āaC3na3 © SX. QN ,@RCcCj 0ȕCNcjII3a nN3 ,Raa3,jCRN Ua NjC,CUjCRN 03 I qCj3cc3 V~<na3 fYkkW 3cj 0RUjāY

TRna ,3jj3 UajC3. RN Ua3N0 -H_Ω(p) = ¹

1+T·p q3,T=33 msY [9Y /āj3aLCN3aH2Θ(p) = ^Θm(p)

Θ_mC(p)Y H 8RN,jCRN 03 jaNc83aj 3cjA3II3 cj$I3Y ] [fY 2uUaCL3aε(p)3N 8RN,jCRNΘ_mC(p).T.K1.K33jpY

:k

+− Θ_mC(p)

K1

ε(p) ++ H_Ω= ¹

1+T·p

Ω_mC(p) ₁

p

Ωm(p) Θm(p) K3·p

7ϔόЛЁζ fYkkY Ģ c3,RN0 LR0ěI3

[eY H3 LR0ěI3 Ua NjC,CUjCRN AjACI nN3 CNn3N,3 cna Iȕ3aa3na 03 URcCjCRNεpY

[4Y 2uUaCL3a Iȕ3aa3na 03 jaţN<3 3j 0āj3aLCN3a I qI3na 03K3U3aL3jjNj IȕNNnI3a ,3jj3 3aa3naY [OY 2uUaCL3a 3j 0āj3aLCN3a Iȕ3aa3na 0ȕ,,āIāajCRNεa3N Ua3NNj I3c qI3nac 03K33j 03K10āj3aLCNā3c Uaā,ā03LL3NjY +RN,Ina3 \nNj n a3cU3,j 0n ,@C3a 03c ,@a<3cY

MRnc qRNc ,RNcC0āa3a nA03ccnc. \n3 I3 ,RnUI3 aācCcjNj 3cj Nā<IC<3$I3. RN ,RNcC0ěa3 LCNj3NNj

\n3cr(t) =Cr0· H(t)q3,Cr0nN ,RnUI3 aācCcjNj ,RNcjNjY

[SzY /āj3aLCN3aΘm(p)cRnc I 8RaL3Θm(p) =H_Θ·ΘmC(p) +HCr(p)·Cr(p)Y [SSY /āj3aLCN3a lim

t→∞(θm(t))^URnaθ_mC(t) =Θ0H(t)^3jcr(t) =Cr0· H(t)^Y

::