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Elettrovalvole

Accumulatore

Alimentazione

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Motoreelettrico

Cambio

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RP

valvolafrizione

attuatorefrizione

dischi frizione

sistema dicontrollo

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Va − E = RaIa + LadIadt

E = Kmω

Cm − Cmp = bmω + Jmdωdt

Cm = Iaω

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Cmp − Cr − bωpsgn(ωp) = bpωp + Jp

dωp

dt

Cr = (Pl −R)Kp

Qu = Qp − αr(Pl −R)

Qp = ωpKp

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6

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Cr

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25S>S>4@A�-0?>-\/`_ 2h6>694V2h698<?>-5b��C-\/`_ 2h6>694V2h698<?>-®S9OV69?>8;:52uO1D�R�8<S>O1[0O18<D@-�E0-0DH69?925/1-°s wax�-./18S>OZ:C4@8</1-|S>R�8<Sm6I25?>-�2�S>O1D@O1Sm69?92'O1D¶R�8<S>O1[0O18<D@-�s`½<xGf�S>OZB@-=:H-jE08</1/1-0eH25?>-°/k2'Ei25A�-0?92��25/1/k2uR@?>-0S>S>O18<D@-UB@O�25/1O1Aj-0DH6I25[0O18<D@-\-U/k2�Ei25A�-0?92 é 25/1/k2uR@?>-0S>S>O18<D@-MB@O�S>Ei2h?9OQE08@bÆ�_ 2h6>694V2h698<?>-�S>OVS>Rr8<Sm6G2t­T4@O1D@B@O7:H-0?>S>8uS>O1D@O1Sm69?92MRr-0?>A�-=6>69-0D@B@8u/`_ 4769O1/1OQ[0[08MB@-0/1/k2Uno-B@-0/1/k2qn>n�Ag25?>E0Ok27zh2®­T4@-0Sm698\R@4@DH698�S>-dE0OHS>O<:C4@8</1-�?>O1Rr8<?m6I25?>-ZO1DtR�8<S>O1[0O18<D@-ZE0-0DH69?925/1-s waxj¬3D@-0E0-0S>S925?>O18%E08</1/1-0eH25?>--0DT69?925A°p�- /1-�Ei25A�-0?>-)� - é 25/1/k2�R@?>-0S>S>O18<D@-3B@O25/1O1A�-0DH6I25[0O185D@-5fHE08<S>O1E0EGF@µ./k2tB@OQÅ¡-0?>-0D@[i2uB@O�25?>-i2gsYEi254@S92h6I2uBV25/1/1-®R@?>-0S>-0D@[i2°S>4@/1/k2S>O1D@O1Sm69?92B@-0O�p@O1E0EGF@O1-0?>O1D@OZO1D�E08</18<?>-|:<-0?>B@-5fZ2E08<DT6I2h6>698E08<DJ/`_ -0/1-0A�-0DH698?>8<S>S>8TxX{2%S>R�8<Sm6I25?>-�/`_ 2h6>694V2h698<?>-¶O1D�R�8<S>O1[0O18<D@-¶E0-0DH69?925/1-5b/O E08<S±´�R�8<S>S>O1p@O1/1-3O1D@S>-0?>O1?>-/k2�n>n>n°- /k2�nÂc Ag25?>E0Ok27b��C- BV25/1/k2¶Rr8<S>O1[0O18<D@-�E=-0DT69?925/1-�E0O�S>O�:C4@8</1-�S>Rr8<Sm6I25?>-D@-0/1/k2MR�8<S>O1[0O18<D@-�B@-0Sm69?92's{¾HxGfTp@OQS985e<DV2tE08</1/1-0eH25?>-®/k2MEi25A�-0?92 é 25/1/k2UR@?>-0S>S>O18<[email protected]@O25/1O1A�-0DH6I25[0O185D@-°-°/k2P� 25/1/18gS>Ei25?>O1E08@b�·o-0?M?>O1R�8<?m6I25?>S>O�O1D¶R�8<S>O1[0O18<D@-°E0-0DH69?925/1-|S>O8<R�-0?92jE08<A�-MS>-tE0O�S>O�69?>8a:h25S>S>-uO1DRr8<S>O1[0O18<D@-MS>O1D@O1Sm69?927b�C-�S>O®B@-0E0O1B@-B@OqO1D@S>-0?>O1?>-�/k2¶Ã\Lå¬D@-=E0-0S>SI25?>O18�E08</1/1-0eH25?>-'/1-�Ei2hA�-0?>-KÎ-

�Î25/1/18ÄS>Ei25?>O1E08¸- /k2 é 25/1/k2�R@?>-0S>S>O18<D@-3B@O\25/1O1Aj-0DH6G2h[0O18<D@-5fqE08<S±´tO��VD@-3E08<?>S92:H-0?>B@OqR�8<S>S>8<D@8�S>E08<?>?>-0?>-'�VD@8�25B)25?>?>OQ:h25?>-�23E08<DH6I2h6>698¶E08<D*/k2 RV25?>-=69-�B@-0Sm69?92-j/`_ 2h6>694V2h698<?>-°R@4���S>E08<?>?>-0?>-|�VD@8�25/1/`_ -0Sm69?>-0Ag2'B@-0Sm69?92JsY¿TxGb|·�-0?tO�D@8<Sm69?>OZS>E08<R@O?>O1S>4@/Q6I2UO1DT4769O1/1-lE08<D@S>O1B@-0?925?>-�/k2\R�8<S>S>O1p@O1/1OQ6I¹.B@OVO1D@S>-0?>O1?>-q/k2MÃ\LÄf<?>O1S>4@/Q69-0?9¹U­T4@O1D@B@O25S>S>-0DT69-'D@-0OlA�8TB@-0/1/1OZ�VS>O1E0OW-gS>O1A|4@/k2h6>OQ:COd25DV25/1O1[0[i2h69O�O1D¸S>-0e<4@OQ698@b Æ�_ 2h6>694V2h698<?>-R@4���E08<S±´o-0S>S>-0?>-�S>-0A�R@/1OQ�VEi2h698|E08<Aj-tO1D�voO1e@b@¾7bQwa½Cbn±/oA�8TB@-0/1/18gAg2h69-0Ag2h69OQE08gE08<S>?>4@OQ698'S>Oo?>OQX{¹'25/1/18�S>EGF@-=Ag2�S>-0A�R@/1OQ�VEi2h698gB@-0/1/k2

S>-0/1-0[0O18<D@-5f�O1/1/Q4@S>69?92h698�O1D�voO1e@b�¾7bQwa½CbtÉ.D¶e<-0D@-0?>O1E08�-0/1-0A�-0DH698�S>8<e<e<-=6>698�25B¶4@DV2R@?>-0S>S>O18<D@-

PB@OQ:<-0?>S92�BV2

0S>4@p@O1S>E0-�4@DV2XY8<?>[i2

FRV25?>Od25/1/k2'R@?>-0S>S>O18<D@-�Rr-0?u/k2

S>4V2g25?>-i2AB@O�E08<DT6I2h6>698@fVe<-0D@-0?>O1Ei25A�-0DH69-tS>O�FV2�­T4@O1D@B@O�EIF@-

F = APblK\R@R@/1O^]

Ei25D@B@8'6I25/1-�-0­T4V25[0O18<D@-|e<-=D@-0?925/1-|25/oS>O1Sm69-0Ag2gO1/1/Q4@Sm69?92h698gO1D¶voO1e@b�¾7bQwa½Cf¡/k2�XY8<?>[i2Fpsx

-0S>-0?>E0OQ6I2h6I2gBV25/1/k2�R@?>-0S>S>O18<D@-°D@-=/1/k2�Ei25A�-0?92gB@O�S>O1D@O1Sm69?92Psx

S>4@/1/`_ -0/1-0A�-0DH698A�8<p@O1/1-5f7B@O�25?>-i2

Asx = Asel + Abic

1 + sgn(xs)

2B@8a:<-5yAsel

¬ /`_ 25?>-i2ÄB@-0/1/`_ -0/1-0Aj-0DT698Ä?>8<S>S>8@fAbic

/{_ 25?>-i2ÄB@-0/\p@O1E0EIF@O1-0?>O1D@8JE08<? ]?>O1S>R�8<D@B@-0DH69-%-

xsO1D@B@O1Ei2º/18�S>R�8<Sm6I25A�-0DH698�B@-0/1/`_ 2h6>694V2h698<?>-JBV25/1/k2)R�8<S>O1[0O18<D@-

ñ�� ï&�����C�{�{�W���C�q�<���J�������C���a�l���C�q�<�V�¶ðo�Y�

1

1 2

2

B

BB

BA

A

A

A

Xs

voO1e<4@?92q¾7bQwa½Cy��CEIF@-0Ag2®S>-0A�R@/1OQ�VEi2h698qB@-0/1/`_ 2h6>694V2h698<?>-oB@OHS>-0/Q-0[0O18<D@-�S>-0D@[i2�/k2qRV25?m69-D@-0E0-0S>S925?>Ok2�25/1/`_ OQD@S>-0?>O1A�-0DH698|B@-0/1/k2|Ã\LÄbE0-0DH6I?925/Q-5fV¬

Fpsx= PsxAsx

25DV25/18<eH25A�-0DH69-UD@-0/1/k2°Ei25A�-0?92|B@O�B@-0Sm69?92Fpdx

= PdxAdx

E08<D 25?>-i2Adx = Asel + Abic

1− sgn(xs)2Æ�2°XY8<?>[i2j4769O1/1-UEIF@-u25e<O1S>E0-tS>4@/1/`_ 2h6>694V2h698<?>-jsY-0/1-0A�-=DT698j?>8<S>S>8Txl?>O1S>4@/Q6I2°­T4@O1D@B@O`y

Fu =(

Fpsx− Fpdx

) s{¾7bǽ<x25/1/12�­T4V25/1-Mp@O1S>8<e<DV2|R�-0?Q�jS>856>69?925?>?>-M/1-UXY8<?>[0-M?>-0S>O1Sm69-0DH69O�B@8a:C4769-u2he</1O�2h6>69?>OQ69O

:CO1S>E08<S>8b-tE08<4@/18<A°p@Ok25D@8

bcs

Fattriti = b xs + bcssgn(xs)

ñ�òK<%ï&�����C�{�Y�J���C�{�Y� (@�V�*(����Y� �3���Tó��{�W�7�i�a���7�;�r�h�l���ML��C�Y��,T�Y����� ñ�îL�-=6>69-0D@B@8�69476>698�25S>S>O1-0A�-MS9O�8h6969O1-=D@-tO1/¡S>-0e<4@-0DT69-uS>O1Sm69-0Ag2|B@O�-0­T4V25[0O18<D@O`y

Fpsx= PsxAsx

Fpdx= PdxAdx

msdxs

dt= Fu −K(xs)− Fattriti

Fattriti = b xs + bcssgn(xs)B@8a:<-5yPsx

?925R@R@?>-0S>-0DH6I2�/k2°R@?>-0S>S>O18<D@-tD@-0/1/k2°Ei25A�-0?92|B@O�S>O1D@O1Sm69?927zPdx

?925R@R@?>-0S>-0DH6I2�/k2°R@?>-0S>S>O18<D@-tD@-0/1/k2°Ei25A�-0?92|B@O�B@-0Sm69?927zAsx(xs)

?925R@R@?>-0S>-0DH6I2�/`_ 25?>-i2°D@-0/1/k2°Ei25A�-0?92|B@O�S>O1D@O1Sm69?92�XY4@D@[0O18<D@-B@-0/1/k2°R�8<S>O1[0O18<D@-UB@-0/1/`_ 2h6>694V2h698<?>-5z

Adx(xs)?925R@R@?>-0S>-0DH6I2�/`_ 25?>-i2°D@-0/1/k2°Ei25A�-0?92|B@O�B@-0Sm69?92|XY4@D@[0O18<D@-MB@-0/1/k2R�8<S>O1[0O185D@-MB@-0/1/`_ 2h6>694V2h698<?>-5z

K(xs)?925R@R@?>-0S>-0DH6I2�/`_ O1DH69-0?925[0O18<D@-\XY?92|/`_ 2h6>694V2h698<?>-U-t/1-MS>4@Rr-0?m�VE0O�B@OE08<DH6I2h6>698�2|�VD@-tE08<?>S92jB@-0/1/`_ 2a69694V2h698<?>-5z

Fattriti?925R@R@?>-0S>-0DH6I2�/`_ 2h6>69?>O^698°:CO1S>E08<S>8�-ME08<4@/18<A|p@O125D@8|S>4@/�A�85698|B@O69476>69O�e5/1O�-0/1-0A�-0DH69O�O1De<O18CE08@z

ms

?925R@R@?>-0S>-0DH6I2j/k2|Ag25S>S92°B@-0/1/1-MRV25?m69O�O1D�A�8a:CO1A�-0DH698°E08<D@D@-0S>S>-E08<D�/`_ 2h6>694V2h698<?>-UB@O�S>-0/1-0[0O18<D@-5z

íU25/1/1-\-0­T4V25[0O18<D@O�R@?>-0E0-=B@-0DT69O�¬MSm6I2h698jE=?9-02h698j4@D�A�8TB@-0/1/18|·Wêtë|f7A�8<Sm69?I2a6I8O1D�voO1e@b@¾7bQw;¾7bO BV2D@856I25?>-jEIF@-j/18S>EIF@-0Ag2�¬jp@O1B@O1A�-0D@S>O18<DV25/Q-5f�O1D7X{2h6>69OZ/k2':h25?>Ok25p@O1/Q-j· ¬

4@DV2gAg2h69?>O1E0-t-�?925R@R@?>-0S>-0DH6I2'S>Ok2j/k2�R@?>-0S>S>O18<D@-�D@-0/1/k2jEi25A�-0?92�B@O�B@-0Sm69?92gEGF@-�O1D­T4@-0/1/k2|B@O�S>O1D@O1Sm69?927b

P =

[

Psx

Pdx

]

�_ -0/1-0A�-0DT698As

?925R@R@?>-0S>-0DH6I2U/k2�Ag2h69?>O1E0-dB@OT69?925SmXY8<?>Ag25[0O18<D@-dBV25/CEi25A�R�8\O1B@?9254C]/1O1E08j25/�Ei25A�Rr8jA�-0E0Ei25D@O1E08@f@E08<DH69O1-0D@-tE0O18C¬M/1-t25?>-0-tB@-0e</1O�2h6>694V2h698<?>O`b

As =[

Asel + Abic1+ sgn(Xs)

2−(Asel + Abic

1− sgn(Xs)2

)]

ñ�� ï&�����C�{�{�W���C�q�<���J�������C���a�l���C�q�<�V�¶ðo�Y�

P

Ql

As- -

ATs

¾ ¾

Fu - ¾

1

mss+b

?

?

xs¾ - - -

bcs sgn()

6

6

¾ ¾

- -6

1s

6

K(xs)

6

xs

¾ ¾ 0

xs

voO1e<4@?92t¾7bQw;¾7yZL�8CB@-0/1/18u·Wêtë B@-0/VS9OQS>69-0A�2tB@Or2h6>694V25[0O18<D@-�B@-0/1/k2US>-0/1-0[0O18<[email protected]@-0/1/k2Ag25?>E0Ok27bÆ�2¶XY8<?>[i2Ä4769O1/1-

FuE08<S±´M856>69-0DT476I2ÄB@-0/1/`_ -0­T4V25[0O18<D@-Js{¾7bǽ<x|¬�­T4@-0/1/k2�EGF@-�X{2

S>R�8<Sm6I25?>-t/`_ 2h6>694V2h698<?>-t2°:<-0/18CE0OQ6I¹xs69?925A�OQ69-U/k2°B@O1DV25A�OQEi2

[

1

mss+b

]

Æ�2 Ag2h69?>O1E0-gB@-0/1/1-�:H-0/18TE0OQ6I¹ B@OqS>Rr8<Sm6I25A�-0DT698¶A�8</Q69OQR@/QOQEi2h6I2�R�-0?|/k2 Ag2h69?>O^]E0-�69?925S>R�8<Sm6I2)B@-0/1/1-�25?>-0-

As

XY8<?>D@O1S>E0-�/1-�R�8<?m6I2h69-Ä25S>S>8<?>p@OQ69-�D@-0/tE08<A�R@/1-0S>S>8BV25/1/`_ 2h6>694V2h698<?>-\BV25/1/1-UB@4@-u-0/1-=6>69?>8;:525/Q:<8</1-UB@O�B@-0Sm69?92�-MB@O�S>O1D@O1Sm69?927b

Ql =

[

Qsx

Qdx

]

R��-S.�m� T.§\£\�¡� ¢d£\¨W©���£Wª7¢«¤\��¥ ¥ �VUo¨d¥ Ud¢d¥ �&¤\�|�C��¥ ���¡� ¢d£\�Æ�-\:h25/Q:<8</1-\B@O�S>-0/1-0[0O18<D@-\S>8<D@8°B@O1S>R�8<S>OQ69OQ:COrR@?>8<R�8<?>[0O185DV25/1OrO1DgR�8<?m6I2h6I27fCE0O18T¬.XY8<? ]D@O1S>E08<D@8u4@DV2u­T4V25DH69OQ6I¹MB@OrR�8<?m6I2h6I2MB@O1?>-=6>6I25A�-0DH69-�R@?>8<R�8<?>[0OQ8<DV25/1-�25/1/k2UE08<?>?>-0DH69-EGF@-t/1-t25/1O1Aj-0DH6I27b�Æ�_ -0­T4V25[0O18<D@-tEi25?92h6>69-0?>O1Sm69O1Ei2°B@-0/1/1-U:h25/Q:H8</1-U¬5y

Q = KmI2√

4P

B@8a:<- 4P = Pl − Psx8

Pl − Pdx¬�/k23B@OQÅ¡-0?>-0D@[i2¶B@OqR@?>-0S>S>O18<D@-25OqEi25R@O

B@-0/1/k2 :525/Q:<8</k23E0O18C¬�/k2¶R@?>-0S>S>O18<D@-�2¶A�8<DT69-�A�-0D@8�/k23R@?>-0S>S>O18<D@- 23:525/1/1-5bI¬

/k2�E08<?>?>-0DH69-�EGF@-�25/1O1A�-0DH6I2'O1/�B@OQS9Rr8<S>OQ69OQ:<8-Km

4@DV2E08<Sm6I25DT69-jEi25?92h6>69-0?>O1Sm69O1Ei2

ñ�ò!>Jï&�����C�{�Y�J���C�{�Y� (@�V�*(����Y� �3���Tó��{�W�7�i�a���7�;�r�h�l���q�{�����C�=�;� ñrñB@-0/1/k2g:525/Q:<8</k27b°É.DÄRr8<S>S>O1p@O1/1-°A�8CB@-0/1/18�·Wêtë EIF@-jB@-0S>E0?>OQ:<-�O1/�XY4@D@[0O18<DV25A�-0DH698B@-0/1/k2:525/Q:<8</k2�¬gO1/1/14@Sm69?92h698�O1D¸voO1e@b�¾7bQwi¿@fZB@8;:H-

Cm?925R@R@?>-0S>-0DT6I23/k2�Ei25RV25E0OQ6I¹

O1B@?9254@/1O1Ei2�B@O�E08<A�R@?>-0S>S>O18<D@-tB@-0/�S>O1Sm69-0Ag2|B@O�2h6>694V25[0O185D@-5b

[

1− sgn(I)2

1+ sgn(I)2

]′

−Qr

Qv

[

1− sgn(I)2

1+ sgn(I)2

]

Pl

R- ¾

KmI2√∆P

?

?

Q

¾ -

¾ -

C−1m

1s

6

6

6

[

Pa

Pb

]

- ¾

voO1e<4@?92|¾7bQwi¿@ydL�8CB@-0/1/18j·Wêtë�B@-0/1/1-U:525/Q:<8</1-UB@O�S>-0/1-0[0O18<D@-tB@-0/1/k2°Ag25?>E0Ok27b

ÐgÑ�W ÓÕÔ�æ�Ø®Ú=Ú0Ô�æ�Ø®Ú=Ú=ØX.MátÚ0.°ÔuÚ=Ø ØPæ�Ø®èuÚ=Û�átÖ�Ö�àáMÖ�Ôt×oÛ�æ�ÛÛ0ÞÞ�ØM��Ö�Ô

·o-0?|Ei25R@O1?>-'O1/WE08<?>?>-=6>6983XY4@D@[0O18<DV25A�-0DH698¶B@-0/qp@/18TE0E08¶B@OqO1D@D@-0Sm698¶¬�D@-0E0-0S>S925?>O18Ei25R@O1?>D@-�O1/lS>O1e<D@OQ�VEi2h698@b%L�-0DH69?>-O1/lp@/18CE0E08¶B@OqS>-0/1-0[0O18<D@-�B@-=:H-S>8</18¶A°4@8;:H-0?>S>OR�-0?�S>-0/1-0[0O18<DV25?>-M/k2|Ag25?>E0Ok27fC-0S>S>8gB@-=:<-5y

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ωprim

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R�-0?�/1-MB@OQ:<-0?>S>-tAg25?>E0-5bE08<R@R@Ok27fZ8</Q69?>-jEGF@-'?>O1B@4@?>?>-�/k2�B@OQÅ¡-0?>-0D@[i2 B@Od:<-0/18CE0OQ6I¹7f�X{2 ?>4@856I25?>-g/`_ -0/Q-0A�-0DT698í�?>O1S>R�-=6>69825BÄK«E08<S±´lBV2�O1A�Rr-0B@O1?>-°/`_ 2i:525D@[i25A�-0DH698�B@O�K�:<-0?>S>8�O1/ZE08<A�R@/1-G6I8O1D@e<?925DV25A�-0DT698�B@-0/1/k2�Ag25?>E0Ok27b ³U4V25D@[email protected]@4@- -0/1-0A�-0DH69O.í -0B�¼«S>8<D@8%25/1/12Sm69-0S>S92�:<-0/18CE0OQ6I¹7fT/k2tS>4@R�-0?m�VE0O1-Uí S>Or?>Ok25/1/QOQD@-i2tE08<Dg/1-.S>4@R�-0?m�VE0O¡K -0B�¼¸E08<S±´�EIF@-O1/�Ag25D@O1E0856>698K R�8<S>S92�E08<DH69O1DC4V25?>-j/k2S>4V2�E08<?>S92�-0BJO1D@e<?925DV25?>-jOdB@-0DH69OWB@-0e</1O-0/1-0A�-0DT69O@í�-0Bg¼®f<O1D|A�8TB@8MBV2ME0?>-i25?>-®4@D�E08</Q/1-0eH25A�-0DH698\XY?92M/`_ 25/Qp�-0?>8UR@?>O1Ag25?>OQ8-g/`_ 25/1pr-0?>8S>-0E08<D@BV25?>O18@b é 8<A�-�R�-0?u/k2S>-0/1-0[0O18<D@-5f�/`_ -0/1-0A�-0DH698�A�8<p@O1/Q-|B@-0/1/`_ 2h6m]694V2h698<?>-5fVE08</1/1-0eH2h698|E085D�O1/�S>O1D@E0?>8<D@O1[0[i2h698<?>-�sY-0/1-0A�-0DT698j?>8<S>S>8�B@-0/1/12jvoO1e@b@¾7bQwJ=HxGf¬MS>8<e5e<-=6>698j25/1/k2tB@OQÅ¡-0?>-0D@[i2°B@O�XY8<?>[0-Ue<-0D@-0?92h69-UD@-0/1/1-\Ei25A�-0?>-UB@-0Sm69?92°-US>O1D@O1Sm69?927fS>O�FV2�­T4@O1D@B@O�EIF@-j/k2gXY8<?>[i2�4769O1/Q-°¬

Fu = Fpsx− Fpdx

B@8;:<-Fpsx

= PsxAsx

-Fpdx

= PdxAdx

b é 8<D%O1/WA�85698 B@-0/1/`_ O1D@D@-0Sm6983O1DH69-0?925e<O1S>E08<D@8325D@EGF@-'/`_ -0/1-0A�-0DC]698\� -�/12�?>-i25[0O18<D@-�:CO1D@E08</k25?>-�B@-0/�E08<DH6I2h6>698�XY?92�/1-S>4@R�-=?>�VE=O\í -0B�¼�B@-0/1/k2voO1e@bC¾7bQwJ=7b�Æ�_ -0/1-0A�-0DT698]��e5-0D@-0?92°4@DV2uXY8<?>[i2�sYE04@?m:52°p@/14�v�O1e@bC¾7bǽ<½<xdEIF@-\69-0D@B@-2:CO1D@E08</k25?>-�O1/�Ag25D@O1E0856>698K O1DÄR�8<S>O1[0O18<D@-jE0-0DT69?925/1-5bÆ�2�?>-i25[0O18<D@-j:CO1D@E08</k25?>-¬XY4@D@[0O18<D@-B@-0/1/18�S>Rr8<Sm6I25A�-0DH6I8Ä-B@-0/1/k2¶B@OQÅ¡-0?>-0D@[i2�e<O1?>O`fdO1D7X{2h6>69Oq/k2¶?>-i25[0OQ8<D@-O1D@O1[0Ok2�25/¡E08<DH6I2h6>698°XY?92°/1-\B@4@-MS>4@R�-0?m�VE0O�-\69-0?>A�O1DV2�­T4V25D@B@8|/k2�B@OQÅ¡-0?>-0D@[i2°XY?92�Oe<O1?>OrB@-0OV:525?>O�-0/1-=A�-0DT69Or¬.4@e<4V25/1-5fCBV2h698�EIF@-U2uB@OQÅ¡-0?>-0D@[i2ue<O1?>O^Iue</1OV-0/1-0A�-0DH69OrK�fí«-0Bļ�B@-0/1/k2'voO1e@b¡¾7bQwJ=g?>O1S>4@/Q6I25D@8�25/1/1OQD@-i2h69O{bMN�25/1-�XY8<?>[i2g:CO1-0D@-°O1D@B@O1Ei2h6I2gE08<DFsinc

(

xi,4ω

) b�n±D@8</Q69?>-5f�25/1/18�S>R�8<Sm6I25A�-0DH698�B@-0/1/`_ 2h6>694V2h698<?>-°S>O�8<R@R�8<D@e<8<D@8e</1O2h6>69?>OQ69Oo:CO1S>E08<S>8�-|E08<4@/18<A|p@O125D@8@f�O1D@B@O1Ei2h69OoE08<D

Fattriti = bxi + k sgn(xi)bjn±D

6I25p�-0/1/1-�¾7bǽMS>8<D@8uO1D@B@O1Ei2h69O@OV:h25?>Or?925R@Rr8<?m6IO@B@OV69?925SmXY8<?>Ag25[0O18<D@-qXY?92MO1/VDT4@A�-0?>8uB@Oe<O1?>O�B@-0/¡R@?>O1Ag25?>OQ8u-UB@-0/¡S>-0E08<D@BV25?>O18|2�S>-0E08<D@BV2|B@-0/¡?925R@Rr8<?m698°O1D@S>-0?>OQ698@bd³U4V25DC]B@84@DV2Ag2h?9E=Ok2'?>O1S>4@/Q6I2gO1D@e<?925DV2h6I27f�O1/oR@?>O1Ag25?>OQ8'-0BÄO1/oS>-0E08<D@BV25?>O18@f�69?925A�OQ69-�O1/?925R@R�8<?m698MB@O7Ei25A°p@O18@f5e<O1?925D@8M25/1/1OQD@-i2h69O{z<Ag2\­T4V25D@B@8MS>O@B@-0E0O1B@-®B@O7-=Å¡-=6>694V25?>-®4@DEi25A|p@Ok25Aj-0DT698uB@O¡?925R@R�8<?m698@f7O�e<O1?>O�B@-0O¡B@4@-M25/1p�-0?>O�?>O1S>4@/Q6I25D@8�B@O1S925E0E08<R@R@Ok2h69O`fTO1D­T4V25DT698|-0?925D@8j25/1/1OQD@-i2h69OrE08</�:H-0E0EIF@O18j?925R@Rr8<?m698|B@O¡Ei25A°p@O18@bd³U4@-0Sm6I2°B@OQÅ¡-0?>-0D@[i2B@OVe<O1?>O7B@-=:�_ -0S>S9-0?>-U25D@DT4@/1/k2h6I2\R�-0?dRr8569-0?d-=Å¡-=6>694V25?>-�4@DV2MEi25A°p@Ok2h6I27b�n±/VE08<A�R@OQ698

<^� ï&�����C�{�{�W���C�q�<���J�������C���a�l���C�q�<�V�¶ðo�Y�B@-0/7?>Ok25/1/QOQD@-i25A�-0DH698\B@-0/1/1-W:<-0/18TE0OQ6I¹\S>R�-=6>6I2M25/CS>O1D@E0?>8<D@O1[0[i2h698<?>-5bZ¼�S>S>8U69?925S>A�-=6>69-4@DV2jE08<R@R@Ok2|B@O�2h6>69?9O^6I8

Csinc = Fsync(xi,∆ω)K4syncsgn(4ω)

EGF@-t?>Ok25/1/QOQD@-i2°/1-U:<-0/18CE0OQ6I¹7f7B@8;:H-5yCsync

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K4sync?925R@R@?>-0S>-0DH6I2uO1/@RV25?925A�-=69?>[email protected]?92h6>69-0?>O1[0[i2M/k2U69?925SmXY8<?>Ag25[0O18<D@-qBV25/1/k2

XY8<?>[i2Fsinc

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Jp?>4@856I22':<-0/18CE0OQ6I¹

ωp-0BĬjS>8<e<e<-=6>698

25/1/k2tE08<R@R@Ok2 −Csync A�-0DT69?>-\O1/�S>-0E08<D@BV25?>O18°R@?>-0S>-0DH6G2CfVO1D@-0?>[0Ok2 Js E08<R@R@Ok2 Csync:H-0/Q8CE0OQ6I¹ωsb

ps ωω CsincCsinc

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Jpωp = −Csync − bpωp

Jsωs = Csync − bsωs

4ω = ωp − ωs

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Fpsx= PsxAsx

Fpdx= PdxAdx

Fu = Fpsx− Fpdx

F = Fu − Fb(xi)− Fsinc(

xi,4ω

)

− Fattriti

Fattriti = b xi + k sgn(xi)

Jpωp = −Csinc sgn(4ω)− bp ωp

Jsωs = Csinc sgn(4ω)− bs ωs

4ω = ωp − ωs

Csinc = Fsinc(xi,∆ω)K4sinc sgn(4ω)

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P-Ai

E08<D

P =

[

Psx

Pdx

]

-Ai =

[

Ainn + Abic1+ sgn(Xi)

2−(

Ainn + Abic1− sgn(Xi)

2

) ]

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P

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ATi

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xi

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ωp

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?

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¾ -

FsincK4sinc

6

6

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- ¾

6xi

- ¾

1

Jss+bs

?

?

ωs¾ -

Cs

ωs

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ATi =

[

Ainn + Abic1+ sgn(Xi)

2−(Ainn + Abic

1− sgn(Xi)2

)]

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−15 −10 −5 0 5 10 15

−400

−300

−200

−100

0

100

200

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400

Spostamento [mm]

For

za [N

]

Reazione vincolare A−BSgancio marcia

voO1e<4@?92|¾7bǽ<½Cy é 4@?m:52jR�8<S>O1[0O18<D@-G]ÂXY8<?>[i2°?>-0S>O1Sm69-0DH69-�25/�A�85698@b

0 200 400 600 800 1000 1200 1400 1600 18000

10

20

30

40

50

60

Corrente [mA]

Pre

ssio

ne [b

ar]

Risposta della valvola di innesto

voO1e<4@?92|¾Cbǽ5¾7y é 4@?m:52jE08<?>?>-0DH69-G]±R@?>-0S>S>O18<D@-uR�-0?�/`_ -0/1-=6>69?>8;:525/^:H8</12�B@O�O1D@D@-0Sm698@b

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Pout = Pin

(

Iv − IoffImax − Ioff

)

B@8a:<-5yPout

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Ioff/k2°E08<?>?>-0DH69-uB@O�85Å¡S>-=6iz

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

10

20

30

40P

re

ssio

ne

[b

ar]

PEc1

PEc1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

500

1000

1500

Tempo [s]

Co

rre

nte

[m

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Ë »

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

−10

−5

0

5

10

Po

siz

ion

e [m

m]

Pos. in. a.Pos. in. e.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

4500

5000

5500

6000

6500

7000

Tempo [s]

[giri/m

in]

Giri prim. a.Giri prim. e.Giri sec. a. Giri sec. a.

voO1e<4@?92�'Cb &7y K\D@BV25A�-0DH698Ä[email protected]/1E04@D@O®RV25?925A�-=69?>O®Ei25?92h6>69-0?>O1Sm69O1E0O®B@4@?925DH69-�4@DV2Ei25A|p@Ok2h6I2�R�-0?�B@4@-tSm69?92h69-0e<O1-MB@O�E08<DH69?>8</1/18@b