R bb2`pBbb2K2Mi

R bb2`pBbb2K2Mi

RXR .J LQďH

.2pQB` R@ JûiB2` ¨ iBbb2` miQKiB[m2

2ti`Bi /m bmD2i /2 H #M[m2 Sh aA kyyk *Q``B;û T;2 8

X S`ûb2MiiBQM

G T`ûb2MiiBQM BMBiBH2 /m bmD2i 2bi /BbTQMB#H2 bm` KQM bBi2X

6+2 mt +QMi`BMi2b BKTQbû2b T` HǶ2MpB`QMM2K2Mi û+QMQKB[m2 /ǶmDQm`/Ƕ?mB- mM i2HB2` /2 /2Mi2HH2`B2 i`/BiBQMM2H KM[m2 2bb2MiB2HH2K2Mi /2 ~2tB#BHBiû ,

ě *?[m2 KûiB2` /QBi āi`2 û[mBTû /ǶmM D+[m`/ T`iB+mHB2`- /QMi H 7#`B+iBQM 2i H /mTHB+iBQM bQMi T`iB+mHBĕ`2K2Mi HQM;m2b 2i 7biB/B2mb2b , BH 7mi 2M 2z2i T2`7Q`2` H2b Hii2b /2 +`iQM mM2 T` mM2- TmBb H2b +Qm/`2 2Mi`2 2HH2bX G KQBM/`2 KQ/B}+iBQM /m KQ/ĕH2 /2 /2Mi2HH2 BKTQb2 H2 /ûKQMi;2 TmBb H2 `2KQMi;2 /m D+[m`/X

ě G /Bbi`B#miBQM /2 HǶûM2`;B2 Kû+MB[m2 mt /Bzû`2Mib KûiB2`b /ǶmM i2HB2` bǶ2z2+im2 ¨ T`iB` /ǶmM KQi2m` mMB[m2 m KQv2M /2 TQmHB2b 2i /2 +Qm``QB2b c H2 /BbTQbBiB7 2bi 2M+QK#`Mi- /M;2`2mt- 2i KM[m2 /2 bQmTH2bb2X

ě *2`iBMb +QKTQbMib Kû+MB[m2b T`ûb2Mi2Mi /2b bB;M2b /Ƕmbm`2- 2i bmTTQ`i2Mi KH H2b i2MiiBp2b /Ƕm;K2MiiBQM /2b +/2M+2bX

mbbB @i@QM +?QBbB H bi`iû;B2 bmBpMi2 TQm` KQ/2`MBb2` H2b KûiB2`b ,

ě *QMb2`piBQM /2 H T`iB2 Kû+MB[m2- [mB /QMM2 ;HQ#H2K2Mi biBb7+iBQM c [m2H[m2b KQ/B}+iBQMb /2 /ûiBH QMi T2`KBb /ǶûHBKBM2` /2b T`Q#HĕK2b /Ƕmbm`2 2t+2bbBp2 m MBp2m /2 +2`iBMb +QKTQbMibX ě _2KTH+2K2Mi /m D+[m`/ 2i /2 bQM /BbTQbBiB7 /2 H2+im`2 T` mM2 +QKKM/2 ûH2+i`QMB[m2 MmKû@

`B[m2X .2b ûH2+i`Q@BKMib- TBHQiûb T` mM KB+`Q@Q`/BMi2m`- bbm`2Mi H bûH2+iBQM /2b B;mBHH2bX JBb2 2M TH+2 /ǶmM2 KQiQ`BbiBQM miQMQK2 m KQv2M /ǶmM2 K+?BM2 bvM+?`QM2 miQTBHQiû2 UJaSV +QmTHû2 ¨ mM p`Bi2m` /2 pBi2bb2X *2i 2Mb2K#H2 2bi +QKKM/û 2M TQbBiBQM T` H2 KB+`Q@Q`/BMi2m`X G KQiQ`BbiBQM /m KûiB2` ¨ iBbb2` H /2Mi2HH2 /m Smv 2bi `ûHBbû2 T` mM KQi2m` +QKKmMûK2Mi TT2Hû2 KQi2m` Ŀ #`mb?H2bb ŀX *2 KQi2m` 2bi HBK2Miû T` mM p`Bi2m`X G +QKKM/2 /2 +2 ;`QmT2 KQiQ@p`Bi2m`

2i /2b B;mBHH2b 2bi TBHQiû2 T` mM2 +QKKM/2 MmKû`B[m2 UbvbiĕK2 SJ*V 2K#`[mû2 /Mb mM KB+`Q Q`/BMi2m`X GǶ`+?Bi2+im`2 /m bvbiĕK2 2bi /QMMû2 bm` H };m`2 RXRXR bmBpMi2 ,

GǶûim/2 M2 TQ`i2` [m2 bm` HǶMHvb2 /m TBHQi;2 /m KQi2m` Ŀ #`mb?H2bb ŀX G2 +QMi`ƬH2 /2 +2i t2 K2i 2M ƾmp`2 ,

ě mM KQi2m` Ŀ #`mb?H2bb ŀ HBK2Miû2 T` mM bvbiĕK2 /2 i`QBb 7Q`K2b /ǶQM/2b /2 i2MbBQMb Hi2`MiBp2b 7Qm`MB2b T` HǶQM/mH2m`X lM2 KQ/ûHBbiBQM T2`K2i /2 /ûp2HQTT2` mM2 +QKKM/2 bBKTH2 2M +Qm`Mi /QM+ 2M +QmTH2X *2ii2 KQ/ûHBbiBQM M2 7Bi Tb T`iB2 /m bmD2i KBb T2`K2i /2 TQb2` C(t) = K<sub>t</sub>·I(t) Uû[miBQM MHQ;m2 ¨ +2HH2 /ǶmM2 K+?BM2 ¨ +Qm`Mi +QMiBMmV c

ě mM p`Bi2m` MmKû`B[m2 /QMi H2 `ƬH2 2bi /Ƕbb2`pB` 2M +QmTH2 2i 2M pBi2bb2 H2 KQi2m` c

ě mM2 +QKKM/2 MmKû`B[m2 /QMi H2 `ƬH2 2bi /Ƕbb2`pB` 2M TQbBiBQM H2 KQi2m` 2M 7Qm`MBbbMi mM2

`û7û`2M+2 /2 pBi2bb2 m p`Bi2m`X

G2 bvbiĕK2 2bi MmKû`B[m2 2i MQM@HBMûB`2X *2T2M/Mi- H 7`û[m2M+2 `2HiBp2K2Mi ûH2pû2 /2 /û+QmT;2 2i /2 `7`ŗ+?Bbb2K2Mi /2b /Bzû`2Mi2b ;`M/2m`b BMbB [m2 HǶ?vTQi?ĕb2 /2 HBMû`Biû bm` H2 KQ/ĕH2 mt p`BiBQMb T2`K2i /2 KQ/ûHBb2` H2 bvbiĕK2 bQmb 7Q`K2 /2 aXGXAX UavbiĕK2 GBMûB`2 AMp`BMiV +QMiBMm /m i2KTbX PM miBHBb2` /QM+- /Mb H2 +/`2 /2 +2ii2 ûim/2- H i`Mb7Q`Kû2 /2 GTH+2 2i H `2T`ûb2MiiBQM T`

b+?ûKb #HQ+bX

R

R bb2`pBbb2K2Mi

6B+?B2` KQiB7 D+[m`/

*Q/2 /2

TBHQi;2 *XLX SJ*

JB+`Q Q`/BMi2m`

6Bb+2m /ǶûH2+i`QBKMib /2 +QKKM/2 /ǶB;mBHH2b

o`Bi2m`

JQ/mH2 /2

+QKKM/2 PM/mH2m` JQi2m`

"`mb?H2bb

*QKKM/2 /ǶB;mBHH2b

V_Ωref θ_ref

*XSX_

*XSX_X 4 *Ti2m` /2 SQbBiBQM /m _QiQ`

6B;m`2 RXRXR Ĝ `+?Bi2+im`2 /m bvbiĕK2

"X úim/2 /2 H #Qm+H2 /2 +Qm`Mi

G #Qm+H2 /2 +Qm`Mi U/QM+ /2 +QmTH2V 2bi T`ûb2Miû2 bm` H };m`2 RXRXkX

+− I_ref

K_i1 + T_i·p T_i·p _i

K_ond

U_c K_M

1 + T_e·p

U I K_t C

K_ci

*Q``2+i2m`C<sub>pi</sub> PM/mH2m` JQi2m`

*Ti2m` /2 +Qm`Mi

K_ond= 15c T_e= 2 ms-K_M= 0,2 V A⁻¹cK_t= 0,55 N m A⁻¹cK_ci= 1X 6B;m`2 RXRXk Ĝ a+?ûK #HQ+ /2 H #Qm+H2 /2 +Qm`Mi

6B;m`2 RXRXj Ĝ _ûTQMb2 i2KTQ`2HH2 ¨ HǶû+?2HQM mMB@

iB`2 /2 H #Qm+H2 /2 +Qm`Mi ZRX .QMM2` bQmb 7Q`K2 +MQMB[m2 2i HBiiû`H2 UbMb

7B`2 BMi2`p2MB` /2 pH2m`b MmKû`B[m2bV H 7QM+iBQM /2 i`Mb72`i 2M #Qm+H2 72`Kû2 F_i(p) = I(p)

I_ref(p) = KN_i(p)

D_i(p)X

PM b2 T`QTQb2 /2 /ûi2`KBM2` T<sub>i</sub> 2i K<sub>i</sub> ¨ T`iB`

/ǶmM KQ/ĕH2 bBKTHB}û /2F_i(p)Q#i2Mm 2M Mû;HB;2Mi H2 xû`Q /m MmKû`i2m`- bQBi F_i(p) = K 1

D_i(p)X ZkX .ûi2`KBM2` MmKû`B[m2K2Mi T<sub>i</sub> 2iK<sub>i</sub> TQm` Q#@

i2MB` H2 +QKTQ`i2K2Mi /ǶmM b2+QM/ Q`/`2 p2+ , ě mM +Q2{+B2Mi /ǶKQ`iBbb2K2Mim= 1c ě mM2 TmHbiBQM Mim`2HH2 Xω_ni= 6 000 rad s⁻¹X ZjX G `ûTQMb2 i2KTQ`2HH2 `û2HH2 /2 H #Qm+H2 /2 +Qm`Mi ¨ HǶû+?2HQM mMBiB`2 2bi `2T`ûb2Miû2 }@

;m`2 RXRXjX

k Gv+û2 *?`H2K;M2

R bb2`pBbb2K2Mi

ě .ûi2`KBM2` ;`T?B[m2K2Mi H2 /ûTbb2K2Mi . 2M WX ě *QM+Hm`2 [mMi ¨ HǶ?vTQi?ĕb2 ûKBb2 ¨ H [m2biBQM ZkX

PM +QMbB/ĕ`2 H MQmp2HH2 bi`m+im`2 /2 +Q``2+i2m` BMiû;`û /Mb H #Qm+H2 /2 +Qm`Mi T`ûb2Miû2 };m`2 RXRX9X

*2ii2 bi`m+im`2 2bi +QKKmMûK2Mi TT2Hû2 Ŀ +Q``2+i2m` /2 ivT2 AXS ŀX

+−

I_ref 1

T_i·p _i

+− K_i U_c K_ond K_M

1 + T_e·p

U I K_t C

K_ci

PM/mH2m` JQi2m`

*Ti2m` /2 +Qm`Mi

K_ond= 15cT_e= 2 ms- K_M= 0,2 V A⁻¹cK_t= 0,55 N m A⁻¹cK_ci= 1X 6B;m`2 RXRX9 Ĝ a+?ûK #HQ+ /2 H #Qm+H2 /2 +Qm`Mi@bi`m+im`2 AXSX

Z9X .QMM2` bQmb 7Q`K2 +MQMB[m2 2i HBiiû`H2 UbMb 7B`2 BMi2`p2MB` /2 pH2m` MmKû`B[m2V H 7QM+iBQM /2 i`Mb72`i 2M #Qm+H2 72`Kû2G_i(p) = I(p)

I_ref(p)X

Z8X *QKT`2`G_i(p) p2+ F_i(p) /2 H [m2biBQM ZRX SQm` H bmBi2- QM TQb2 G_i(p) = 1

1 +_ω^p

ni

p2+τi= 1 ω_niX

ZeX § [m2HH2b +QM/BiBQMb +2ii2 bBKTHB}+iBQM 2bi@2HH2 pH#H2 \

*X úim/2 /2 H #Qm+H2 /2 pBi2bb2

PM +QMb2`p2 H2 KQ/ĕH2 TT`Q+?û /m R<sup>2`</sup>Q`/`2 /2 H #Qm+H2 /2 +Qm`MiX G #Qm+H2 /2 pBi2bb2 2bi T`ûb2Miû2 bm` H };m`2 RXRX8XK<sub>can</sub>`2T`ûb2Mi2 H2 +QMp2`iBbb2m` MHQ;B[m2@MmKû`B[m2 U*XXLXV /2 HǶ2Mi`û2 /2 `û7û`2M+2 2M pBi2bb2 /m p`Bi2m`X lM }Hi`2 T2`K2i /2 HBbb2` H2b bmi /2 H MmKû`BbiBQMX mM +Q``2+i2m` C_Ω(p) 2bi TH+û /Mb H +?ŗM2 /B`2+i2X

K_an

Ω_ref 1

1 +τ_ω Ω_r2 +−

K_Ω1 + T_Ω·p T_Ω·p

_Ω 1

1 +τ_i·p I_ref

K_t

I 1

J·p

C Ω

K_cω m_Ω

*Q``2+i2m` C_Ω G_i(p)

*Ti2m` /2 pBi2bb2 }Hi`2

*XXLX

K_cω=4096

π c J = 1,5 kgm²-τ_i= 167ƒsc K_t= 0,55 N m A⁻¹cK_an= 10·πX 6B;m`2 RXRX8 Ĝ a+?ûK #HQ+ /2 H #Qm+H2 /2 pBi2bb2

ZdX .QMM2` H 7Q`K2 HBiiû`H2 /2 H 7QM+iBQM /2 i`Mb72`i 2M #Qm+H2 Qmp2`i2 B_Ω(p) = mΩ(p)

(p) /m bvbiĕK2

#Qm+Hû /2 H };m`2 RXRX8X

PM TQb2 p2+T_Ω=a·τ_i p2+a >1X

Gv+û2 *?`H2K;M2 j

R bb2`pBbb2K2Mi

PM bǶBMiû`2bb2 /Mb mM2 T`2KB2` i2KTb- ¨ H 7QM+iBQMT(p) =1 + T_Ω·p

1 +τ_i·p 2ti`Bi2 /2 H 7QM+iBQM /2 i`Mb72`i B_Ω(p)

Z3X 1tT`BK2` H2 KQ/mH2 2MdB 2i HǶ`;mK2Mi /2 H 7QM+iBQM /2 i`Mb72`i +QKTH2t2 T(j·ω)X ZNX JQMi`2` [m2 HǶ`;mK2Mi TQbbĕ/2 mM KtBKmK ΦM TQm` H TmHbiBQMω_m= 1

√a·τ_i 2i [mǶBH 2bi i2H [m2 sin (ΦM) = a−1

a+ 1X

ZRyX .ûi2`KBM2`a TQm` [m2ΦM= 62ê

ZRRX h`+2` p2+ bQBM bm` H +QTB2 2i 2M BM/B[mMi H2b pH2m`b `2K`[m#H2b-

ZRRX HǶHHm`2 /m /B;`KK2 bvKTiQiB[m2 /2 "Q/2 2M T?b2 /2B_Ω(p) UTH+2` ω_mV-

ZRR#X HǶHHm`2 /m /B;`KK2 bvKTiQiB[m2 /2 "Q/2 2M ;BM 2i 2M T?b2 /2B_Ω(p)- b+?Mi [m2 K_Ω 2bi i2H [m2 HǶt2 /2b 0 dBTbb2 T`ω_m U|B_Ω(j·ω_m)|= 1V

ZRkX .ûi2`KBM2` K_Ω 2M 7QM+iBQM a- τ_i- K_cΩ- J 2i K_t TQm` [m2 Dmbi2K2Mi- H +Qm`#2 /2 ;BM +QmT2 HǶt2 0 dB2M ω_m- 6B`2 HǶTTHB+iBQM MmKû`B[m2X

ZRjX .ûi2`KBM2` H 7QM+iBQM /2 i`Mb72`i 2M #Qm+H2 72`Kû2 F_Ω(p) = Ω(p) Ω_ref(p)

SQm` H bmBi2- QM bbBKBH2 H 7QM+iBQM /2 i`Mb72`i 2M #Qm+H2 72`Kû2F_Ω(p) ¨ mM T`2KB2` Q`/`2 G_Ω(p) = K_FΩ

1 + T_Ω·p= 4,82×10⁻² 1 1 + p

372 X

.X úim/2 /2 H #Qm+H2 /2 TQbBiBQM

PM +QMb2`p2 H2 KQ/ĕH2 TT`Q+?û /m R<sup>2`</sup>Q`/`2 /2 H #Qm+H2 /2 pBi2bb2X G #Qm+H2 /2 TQbBiBQM 2bi T`ûb2Miû2 };m`2 RXRXeX G2 ;BM K<sub>cna</sub> `2T`ûb2Mi2 H2 +QMp2`iBbb2m` MmKû`B[m2 MHQ;B[m2 /2 bQ`iB2 /2 H +QKKM/2 MmKû`B[m2 SJ*X

+− θ_ref

K_{θ θ}

K_cna U_c

G_Ω(p)

Ω_ref 1

p

Ω θ

K_cθ

*Q``2+i2m`C_θ

*Ti2m` /2 TQbBiBQM

K_cna= 1

3276cK_cθ = 4096 2·π X

6B;m`2 RXRXe Ĝ a+?ûK #HQ+/2 H #Qm+H2 /2 TQbBiBQM

ZR9X .QMM2` bQmb 7Q`K2 +MQMB[m2 H 7QM+iBQM /2 i`Mb72`i 2M #Qm+H2 72`Kû2 F_θ(p) = θ(p)

θref(p) UM2 7B`2 BMi2`p2MB` m+mM2 pH2m` MmKû`B[m2VX

ZR8X .ûi2`KBM2` K_θ /2 i2HH2 bQ`i2 [m2 H `ûTQMb2 ¨ mM û+?2HQM /2 TQbBiBQM bǶ2z2+im2 bMb /ûTbb2K2Mi 2i 2M mM i2KTb /2 `ûTQMb2 KBMBKmKX

9 Gv+û2 *?`H2K;M2