798;:.<=8?>@8BACA8;:EDGFH<JILK;:AMINAODGFQPR8TS#I1:.FE8VUF
WRXZY\[^]`_baMcedf_hgMijYlkM[m]`_b])nceiogqpN_r[^cCgdscutGY\[mvkM[^w _bY\[^cxaE_yn`dzg^]vzcedf_rijce[OnY|{~}f`g
vkM[^w _bY\[^caE_ydf_b] Y])n%ggdijY\[_btCgaMcep!]`_b])nceiogupN_r[^cCgdscc{~}M`
W M MpN_bte_hgMijY_r[_r[^\dscG]]YgMp]`_b])nceiogpN_r[^cCgdsckM[]cG\[gMp,clJ}xtGY\[] cnn`dsY
}M`Yx] cnn`dsYR}MLaMcep'pg df_b] Y])n%g¡¢}L]`_!Ynn _bce[^c£tGY\ijc¤
R}M¦¥§{~}M
}M
WR¨¦pN_!] cnn`df_!aE_BgMi _bcGwwOg£covg^]c£aMcep'pg df_b] Y])n%g¡¢}9df_b]kMp©n%gM[^YuªBk_r[^aE_«¤
¬
|}M
¬b®
¥ ¬
{~}M
¬b®¯°¬
}M
¬b®
±
|}M¥
±
{~}M
¯ ±
}M
WlY] cnn`dsY|}MaMcep'pgdf_b] Y])n%g²caBkM[^ªBk^c³kM[g´ ceds]`_bY\[^cµgMp©ncedzgOn%ga!gMp'pg
vkM[^w _bY\[^caE_;df_b] Y])n%gxgdijY\[_btCg~{~}M µZaMcep'p,Y] cnn`dsY
}M¶aMcep.]cG\[gMp,c·aE_
_r[^\dscG]]YB¹¸y_!aE_btGcte^c_rp!]`_b])nceiogpN_r[^cCgdsc»º½¼#¾f¿0À _rpÁ]cG\[gMp,caE_@_r[^\dscG]]YB
Wlc·aE_,ÂQcedsce[^wc~[^cep'p,Y] cnn`dsY~cGªBk_ôegMp,Y\[^Y|gxaE_,ÂQcedsce[^wc~[^cep'pgdf_b] Y])n%gncei Y Ä
dzgMp,cÅ«p;]`_b])nceiogÆpN_r[^cCgdscÇdf_rk^]t_rdg|gl_r[^]cG\k_rdsccG]gOnn%gMijce[OncÈprÉ'gM[^a!gMijce[OnYÆaMcep
]cG\[gMp,c£aE_@_r[^\dscG]]YEµ.Y´C´ cedsYx¡¢}¥§ÊËJ}»ÌÊ ÍÏÎÐ µB]c£c£]Y\p,Yu]c¤
¬
{~}M
¬
¥ÑÊ Ò ±
{~}M¥ÏÎ
WlcuaE_,ÂQcedsce[^wcn`dzgÈpg|df_b] Y])n%gm¡¢}Óc_rpy]cG\[gMp,cxaE_Ô_r[^\dscG]]YÈJ}9]Y\[^Yqn%gM[OnY
iog^(_bYMdf_(ªBkgM[OnYq _«k
¬
{~}M
¬;Õ
¥ÑÊ c ±
{~}M
Õ
¥ÏÎ\
WlÖEced;ijY\p©n _^]`_b])ncei_pN_r[^cCgdf_ cG]`_b])nc]Y\p,YkM[_r[Onced+´egMp'p,YoaE_Á MkMp,]g^w _bY\[_C? ced¢_rp^ªBkgMp,c
´egMp,c·pgudscepg^w _bY\[^c
¬
{~}M
¬!×
Ê c ±
{~}M
×
Î\¹Øjk^cG])nY~_r[Onced+´egMp'p,YaE_M´egMp,YMdf_
aE_MÙ]`_(te_hgMiogqÚ`ÀMÛ¢Ü(ÀÝyÀÞ`ÞOÀMÛZ¾ß
WlÖEced(tGY\[O´ ce[^w _bY\[^c9pg9àgM[^a!gj g^]]gM[Onc¶Ì[^cep'pgÓiog^(_bYMdV gd+nc¹aMc_tCg^]`_aE_ _r[OncedscG]]c
dzgOn _btGYÁжc£a!gOn%ga!g_Á´egMp,YMdf_(aE_Má ced_(ªBkgMpN_
¬
{~}M
¬b®â
Ê ãä
®
Wå_r _btCgMijce[Oncpg|àgM[^a!gÇ g^]]gM[Onc~c a!gOn%g~a!gRkM[R_r[Onced+´egMp'p,YÈaE_V´egMp,YMdf_QaMcep@n _r Y
æçèéçèê?tGY\[æ~cjê?aMcnncjÝ¢ë.¼ìÞOÀeíGîïÛVîÜMî½¾ÀðÁ¼«îï
Wq¸y_b])nceiog£aE_!n _r YÝyÀÞ`ÞOÀÇÚ`ÀÞ`ÞCï ÔgM[^a!g g^]]gM[Onc£ÎxçÙÑçÙ ê
w j dB
G ( ) |
| w
20 dB K
-20 dB
K-3 db
banda passante
Passa basso
w H
3 dB
w j dB
G ( ) |
| w
20 dB K
-20 dB
K-3 db
banda passante
Passa basso
w H
3 dB
Wq¸y_b])nceiog£aE_!n _r YÝyÀÞ`ÞOÀRÀÁ¼#¾ï ÔgM[^a!g g^]]gM[Oncj æ çèéçá
w j dB
G ( ) |
| w
20 dB
K
-20 dB
K-3 db
banda passante Passa alto
w L
3 dB
w j dB
G ( ) |
| w
20 dB
K
-20 dB
K-3 db
banda passante Passa alto
w L
3 dB
Wq¸y_b])nceiog£aE_!n _r YÝyÀÞ`ÞOÀÇÚ`ÀMÛ¢Ü(À ÔgM[^a!g g^]]gM[OncÓ æ çÙÑçÙ ê
w j dB
G ( ) |
| w
20 dB
K
-20 dB
K-3 db
banda passante
Passa banda
w L w
H
3 dB
w j dB
G ( ) |
| w
20 dB
K
-20 dB
K-3 db
banda passante
Passa banda
w L w
H
3 dB
Wq¸y_b])nceiog£aE_!n _r YÆßC¼«î î3Û¢ÀRÚ`ÀMÛ¢Ü(À
ÔgM[^a!gx g^]]gM[OncÎuçèéçè
æ
cj
ê
çÙÑç á
w j dB
G ( ) |
| w
20 dB K
-20 dB
K-3 db
banda passante
Elimina banda
banda passante
w L w
H
3 dB 3 dB
w j dB
G ( ) |
| w
20 dB K
-20 dB
K-3 db
banda passante
Elimina banda
banda passante
w L w
H
3 dB 3 dB
WRXZY\[^]`_baMcedf_hgMijYkM[]`_b])nceiogaMcep@ df_rijYuYMdsaE_r[^ctGY\[·\kg^a!g^\[^Y ])n%gOn _btGYkM[_Ãn%gdf_bYB¤
{~}f¥
¯
WlÅe]`_b])ncei_OaMcepÁ df_rijYoYMdsaE_r[^c¶]Y\[^Y£aE_Cn _r Y g^]]g£àg^]]Yoc pgp,YMdsYàgM[^a!g g^]]gM[Onc
cÎxçèéçÙê tGY\[!¤
ê ¥
W M MpN_bte_hgMijYÆ_r[È_r[^\dscG]]YRgMpy]`_b])nceiog{~}fkM[|_ri MkMp,]Yldscnn%gM[^Y\pgdscxJ}9aE_
aBkMdzgOn%gÈcÈgMi _bcGwwOg
̪Bk_r[^aE_JgdscCg kM[_Ãn%gdf_hgeÐ`²¸y_hgÇg^acG]cei _bYÇ¥
Î\¤
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
Segnale
Impulso rettangolare
Wlg£n`dzg^]vzYMdiogOn%gaE_QgM Mpg^tGc
}fLaMcep!]cG\[gMp,c£aE_@_r[^\dscG]]YxJ}»df_b]kMp©n%g!¤
}f¦¥
V
ãTÒ
WlYu] cnn`dsY
}MLaMcep!]cG\[gMp,c£aE_y_r[^\dscG]]YuJ}»df_b]kMp©n%gªBk_r[^aE_«¤
}M¦¥
ÁM
ã?Ò
WlYu] cnn`dsY
}MLaMcep!]cG\[gMp,c£aE_y_r[^\dscG]]YuJ}»df_b]kMp©n%g!¤
}M¦¥
ÁM
ã?Ò
WlÖEcedÔL¥
Î~p,Yu] cnn`dsY
}M9df_b]kMp©n%g!¤
10 0 10 1 10 2
−40
−35
−30
−25
−20
−15
−10
−5 0 5
ω
|F( ω )| [dB]
Spettro delle Ampiezze
YÆ] cnn`dsYÆ]`_ gM[M[MkMp'pg ced½ ¥ £
tGY\[q
¥
³ÖEcedL Í äC
p,Y
] cnn`dsYmaMcep'p,cgMi _bcGwwcaMcepB]cG\[gMp,cucm_r[Cvzcedf_bYMdscug
Îqdf_b] cnnYgMp'p,Y~] cnn`dsY
gMp'p,càg^]]c MkMp,]g^w _bY\[_«
Wq¸y_hgo ê ¥ÏäeÎ¥ÏäC Yx] cnn`dsYR}M½aMcep'pgxdf_b] Y])n%g¡¢}9df_b]kMp©n%g!¤
10 0 10 1 10 2
−40
−35
−30
−25
−20
−15
−10
−5 0 5
ω
|X( ω )|(c), |G(j ω )|(r), |Y( ω )|(b) [dB]
Spettro delle Ampiezze
Wl(É'gM[^a!gMijce[OnYncei YMdzgMp,coaMcep'pgxdf_b] Y])n%g [^cepMncei Ydf_b]kMp©n%g!¤
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
Segnale
Risposta(r) all’impulso(b)
WlcÇ df_r[^t_r gMpN_ÔtGY\i Y\[^ce[On _=] cnn`dzgMpN_JÌ cedL `Ðu g^]]gM[^Y dzgOn _btCgMijce[Onc
_r[O´egdf_hgOnc·gMp'prÉk^]t_Ãn%gaMcepE]`_b])nceiogmpN_r[^cCgdscÅ«[O´ cGtGcmp,ctGY\i Y\[^ce[On _.] cnn`dzgMpN_Q ced
ͧ
ê
]Y\[^YqgOnnce[MkgOnc·a!gMpB]`_b])nceiogaMcep¢ df_rijY~YMdsaE_r[^cØjk_r[^aE_;pgdf_b] Y])n%g
¡¢}[^Y\[ MkÁY£cG]]cedsc ´ cep,Y!tGc½tGY\ijc9_rpC]cG\[gMp,caE__r[^\dscG]]YoJ} µ\iog]`_MiogM[On _bce[^c
kM[g àMk^Y\[g·]`_ri_rpN_Ãn`k^aE_r[^covdzgu_(aBk^c]cG\[gMpN_«
Wq¸y_hgo ê ¥
Î¥? ¶Yu] cnn`dsYu|}M½aMcep'pg df_b] Y])n%g¡¢}9df_b]kMp©n%g!¤
10 0 10 1 10 2
−40
−35
−30
−25
−20
−15
−10
−5 0 5
ω
|X( ω )|(c), |G(j ω )|(r), |Y( ω )|(b) [dB]
Spettro delle Ampiezze
Wl(É'gM[^a!gMijce[OnYncei YMdzgMp,coaMcep'pgxdf_b] Y])n%g [^cepMncei Ydf_b]kMp©n%g!¤
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
Segnale
Risposta(r) all’impulso(b)
WÔ_b] cnnYÇgMpZtCg^]Y dscGtGcGaMce[OncgM[^te^c|kM[gl gd+ncmaMcep'p,c| df_r[^t_r gMpN_;tGY\i Y\[^ce[On _
] cnn`dzgMpN_(Ì cedy ? ÐLc gOnnce[MkgOn%gja!gMp]`_b])nceiogÓaMcep\ df_rijYYMdsaE_r[^cÅ«[
|}M¦]`_E cedsaMcàMk^Y\[g gd+ncjaMceptGY\[Once[MkOnYm_r[gMp©n%gjvdscGªBk^ce[^wOg£aMcep]cG\[gMp,cÓaE_
_r[^\dscG]]YuªBk_r[^aE_Qpgxdf_b] Y])n%g¡¢}c _rkOnnY])nYqp,ce[On%g!
Wq¸y_hgo ê ¥¥?
¶Yu] cnn`dsYuR}MLaMcep'pg df_b] Y])n%g¡¢}9df_b]kMp©n%g!¤
10 0 10 1 10 2
−40
−35
−30
−25
−20
−15
−10
−5 0 5
ω
|X( ω )|(c), |G(j ω )|(r), |Y( ω )|(b) [dB]
Spettro delle Ampiezze
Wl(É'gM[^a!gMijce[OnYncei YMdzgMp,coaMcep'pgxdf_b] Y])n%g [^cepMncei Ydf_b]kMp©n%g!¤
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
Segnale
Risposta(r) all’impulso(b)
WlÅ«[oªBk^cG])nY·tCg^]YgM[^te^cp,cÓtGY\i Y\[^ce[On _M] cnn`dzgMpN_Mgàg^]]gjvdscGªBk^ce[^wOg£]Y\[^YugOnnc`Ä
[MkgOncoa!gMpM]`_b])nceiog£aMcep. df_rijYYMdsaE_r[^c£c ªBk^cep'p,c_r[·gMp©n%g£vdscGªBk^ce[^wOg]Y\[^Yu]Y])n%gM[GÄ
w _hgMp'ijce[Onc¶]tGY\i gds]c½gdf_b] Y])n%g ¡¢}¹cijY\p©nYxp,ce[On%gjc[^Y\[df_bcG]tGcjgj]cG\k_rdsc
ced¦[MkMp'pg prÉ«_r[^\dscG]]YxJ}`
W M MpN_bte_hgMijY_r[ _r[^\dscG]]Y gMp ]`_b])nceiogl{~}f kM[ _ri MkMp,]Yln`df_hgM[^Y\pgdscÈJ}aE_
aBkMdzgOn%g
¶cgMi _bcGwwOg
oÌgdscCg kM[_Ãn%gdf_hgeÐ`¹¸y_hgg^a cG]cei _bYL¥
Î\
Wq¸y_hgoê³¥ÏäeÎ\Yx] cnn`dsYR}MLaMcep'pg df_b] Y])n%g¡¢}9df_b]kMp©n%g!¤
10 0 10 1 10 2
−40
−35
−30
−25
−20
−15
−10
−5 0 5
ω
|X( ω )|(c), |G(j ω )|(r), |Y( ω )|(b) [dB]
Spettro delle Ampiezze
Wl(É'gM[^a!gMijce[OnYncei YMdzgMp,coaMcep'pgxdf_b] Y])n%g [^cepMncei Ydf_b]kMp©n%g!¤
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
Segnale
Risposta(r) all’impulso(b) triangolare
WlY£] cnn`dsYoaMcep'p,c9gMi _bcGwwc½aE_R}Mc»]Y])n%gM[^w _hgMp'ijce[Onc9_baMce[On _btGYgMp'p,Y£] cnn`dsY
aE_
}MgtGY]gc£aMY´ÁkOnY~gMp'p,YMdzgx_rp@df_Ãn%gdsaMYuaE_(¡¢}9df_b] cnnY gJ}
! ""#%$'&()&+* "*,"$'&+-.*0/,*,%&132#* 4%54 6
WlYu] cnn`dsYuaMcep'p,covg^]`_!aMcep'pg df_b] Y])n%g¡¢}»df_b]kMp©n%g!¤
10 0 10 1 10 2
−250
−200
−150
−100
−50 0 50 100 150 200
ω
arg X( ω )(c), G(j ω )(r), Y( ω )(b) [deg]
Spettro delle Fasi
W·ce[On`dscp,Y·] cnn`dsYaMcep'p,c gMi _bcGwwc»aE_M|}MLcj]Y])n%gM[^w _hgMp'ijce[Onco_baMce[On _btGYgMp'p,Y
] cnn`dsYqaE_
}M µ_QaBk^cx] cnn`df_VaMcep'p,cuvg^]`_VaE_,ÂQcedf_b]tGY\[^YqvdzgRp,YMdsYEµ gM[^te^cq ced
MkMp,]g^w _bY\[_EdscepgOn _ôegMijce[Onc£ _btGtGY\p,cÅ«[ gd+n _btGY\pgdscp,Y] cnn`dsYaE_vg^]cÓaE_M|}M
dscG]ce[On%ggM[^Y\pN_yi_r[^YMdf_ df_b] cnnY gMp'p,Yu] cnn`dsYaE_(vg^]coaE_
}M`
Wq¸y_ gdpg9_r[½ªBk^cG])nY9tCg^]Y»aE_ÞOÀÞOÀ ßOÛZ¾ïî3Û ¿îf¾ÀM¿0Ü\ï Y9aE_¿îf¾ÀM¿0Ü\ïÈÜMîOÀÞCß aMcep'pg
vg^]coaMcep!]cG\[gMp,c£aE_Vk^]t_Ãn%gxdf_b] cnnY gªBk^cep'pg·aMcep!]cG\[gMp,c£aE_y_r[^\dscG]]YB
WÈØjkgMpN_Ãn%gOn _ôegMijce[Onc»kM[df_Ãn%gdsaMY aE_Cvg^]c9_r[On`dsY!aMYnnYoa!g£kM[»]`_b])nceiog pN_r[^cCgdscÓ_r[^aBk^tGc
kM[ df_Ãn%gdsaMYuvdzgx_rpÁ]cG\[gMp,c£aE_y_r[^\dscG]]Yuc_rp!]cG\[gMp,c£aE_Vk^]t_Ãn%g!
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
Segnale
Risposta(r) all’impulso(b) triangolare
Wq¸y_!tGY\[^]`_baMcedf_Bg^a cG]cei _bY_rpÁ]`_b])nceioggvg^]c[^Y\[mi_r[_riog!¤
{G}f¦¥
ã?
¯
gO´ ce[Onc|ijY!aBkMp,Y kM[_Ãn%gdf_bYlgn`kOnnc|p,c| MkMp,]g^w _bY\[_̪Bk_r[^aE_àgM[^a!gl_r[V[_Ãn%geÐ µ½iog
te^c_r[On`dsY!aBk^tGcukM[mdf_Ãn%gdsaMYuaE_!vg^]c a!gxg£Ä
Î
WR¨¦pN_ ] cnn`df_ aMcep'p,c gMi _bcGwwclaE_
}M~c aE_LR}M~]Y\[^YÙ_baMce[On _bt_LcG]]ce[^aMY
¬
{G}M
¬ ¥
ced¢ ÆYR] cnn`dsY|aMcep'p,c vg^]`_ Ì ced ¥
ÎÐ aMcep'pgÇdf_b] Y])n%g
¡¢}»df_b]kMp©n%g!¤
10 0 10 1 10 2
−350
−300
−250
−200
−150
−100
−50 0 50 100 150 200
ω arg X( ω )(c), G r (j ω )(r), Y( ω )(b) [deg]
Spettro delle Fasi
WlÅ«pVdf_Ãn%gdsaMYxaE_!vg^]c _r[On`dsY!aMYnnY~a!gMpE]`_b])nceiogu{G}f]`_(n`dzg^aBk^tGcx_r[kM[df_Ãn%gdsaMYmaMcep
]cG\[gMp,c¡¢} df_b] cnnY»gLJ} µ^Y\p©n`dsc g^a£kM[gM[^a!gMijce[OnYj_r[ ïÛZ¾f¿ ï OÀÞCß _r[L]cG\k_ÃnY
g_!tCgMià_!aE_(aMcedf_ôegOn%gaMcep!]cG\[gMp,c£aE_@_r[^\dscG]]YB¤
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Segnale
Risposta(r) all’impulso(b) triangolare
798;:.<=8?>@8BACA8;:EDGFH<;FyI AMINAODGFQPHILUFÁDU;8@I :y8EDeI
WRXZY\[^]`_baMcedf_hgMijYkM[]`_b])nceiogudscn`dsYMg^w _bY\[gOnYutGY\[mdscn`dsYMg^w _bY\[^ckM[_Ãn%gdf_hg!¤
C(s) G(s) Y(s)
R(s) X(s)
C(s) G(s) Y(s)
R(s) X(s)
Å«p\kg^a!g^\[^YaE_LgM[^cep'p,Y²aMcep¦]`_b])nceiog {}fxcpgHvkM[^w _bY\[^cHaE_n`dzg^]vzcedf_rijce[OnY
_r[^\dscG]]Y Äk^]t_Ãn%gu{ }f9df_b]kMp©n%gM[^YB¤
{
}f¦¥~}f%{~}f {
}f¥
|}f
}f
¥
~}f%{~}f
¯
~}f%{~}f
¥ { }f
¯
{ }f
Wlgpgds\^cGwwOgaE_.àgM[^a!gaMcepM]`_b])nceiog·dscn`dsYMg^w _bY\[gOnY { }f¶ MkÁYcG]]cedscj])n _riogOn%g
tGY\[^Y]tGce[^aMYq_rp!\kg^a!g^\[^Y a.É'gM[^cep'p,Y{ }f`
WlÖEced¦p,c MkMp,]g^w _bY\[_M n%gMpN_!te^c
¬ { }M
¬
µ\´egMp,cprÉ'gM M dsY]]`_riog^w _bY\[^c¤
¬ { }M
¬ ¥ ¬{ }M
¬
¬ ¯
{ }M
¬ ×
ijce[On`dsc· ced¦p,c MkMp,]g^w _bY\[_Á?n%gMpN_(te^c
¬
{ }M
¬Bâ
Î(µ.]`_@g!¤
¬{ O}M
¬ ¥ ¬
{ }M
¬
¬ ¯ { }M
¬ × ¬
{ }M
¬ ¬ { C}M
¬Bâ
Î
Å«[^aE_btCgOn _ôegMijce[Onc9aBkM[^ªBk^c·p,c MkMp,]g^w _bY\[_MaE_n%g^\pN_bYte^cjaMcepN_ri_Ãn%gM[^Y pgàgM[^a!g£aMcep
]`_b])nceiogdscn`dsYMg^w _bY\[gOnY{ C}f]Y\[^Y³_r[OnYMd[^YgMp'p,c MkMp,]g^w _bY\[_ ced·p,c|ªBkgMpN_
¬ { }M
¬!×
WlgàgM[^a!g g^]]gM[OncaE_¢kM[u]`_b])nceiog _r[dscn`dsYMg^w _bY\[^cmkM[_Ãn%gdf_hgtGYMddf_b] Y\[^aMcm_r[^aE_©Ä
tCgOn _ôegMijce[Onc»gMp'p,c£ MkMp,]g^w _bY\[_ è ced p,c9ªBkgMpN_(_rp!ijY!aBkMp,YaMcepe\kg^a!g^\[^YaE_MgM[^cep'p,Y
¬ { }M
¬
cuiog^(_bYMdsc£aE_
W cepetCg^]Yte^c[^Y\[ot_]`_hgM[^Y MkMp,]g^w _bY\[_ Ï ced p,c9ªBkgMpN_(_rp\ijY!aBkMp,YaMcep\kg^a!g^\[^Y
aE_=gM[^cep'p,YÇ]`_hg
¬{ }M
¬ Í
µLpglàgM[^a!gqaMcep¢]`_b])nceiog|_r[ldscn`dsYMg^w _bY\[^cRkM[_Ãn%gdf_hg
tGY(_r[^t_baMctGY\[ªBk^cep'pg·aMcep!\kg^a!g^\[^Y aE_EgM[^cep'p,YB
W[^te^cx ced¹_rp(]`_b])nceiog dscn`dsYMg^w _bY\[gOnY{ }fL´egMp,Y\[^Y|p,c])ncG]]ctGY\[^]`_baMcedzg^w _bY\[_
te^cp,cGMgM[^Ypgx dsY\[OncGwwOgaMcepÁ]`_b])nceioggMp'pg]kgxpgds\^cGwwOgaE_yàgM[^a!g!¶ÖEced+n%gM[OnY
cedJiog^]]`_ri_bwwOgdsc£pgo´ cep,Y!t_Ãn`gaE_.df_b] Y])n%gY!tGtGYMddscgMp'pgdsMgdsc_rpB _«k Y]]`_rà_rp,c·pg
àgM[^a!gaMcep!]`_b])nceiogudscn`dsYMg^w _bY\[gOnY~{ }f`
W¦gOnYxte^c_rp(\kg^a!g^\[^Y~aE_BgM[^cep'p,Y{ }f ¥ ~}f%{~}fLtGY\[On _bce[^ctGY\ijc£vgOnnYMdsc
pg vkM[^w _bY\[^cmaE_yn`dzg^]vzcedf_rijce[OnYqaMcepVtGY\[On`dsY\p'p,YMdsc ~}f£c c´M_baMce[Oncxte^cxce[^cedzgMpÄ
ijce[OnctGY\[O´M_bce[^cÌtGY\i gOn _rà_rp'ijce[Onc·tGY\[Èpgu])n%gMà_rpN_Ãn`guaMcep.]`_b])nceiogctGY\[mgMp©n`dsc
] cGt_\te^caE_EtGY\[On`dsY\p'p,YÁÐ dsYcnn%gdscu_rp(tGY\[On`dsY\p'p,YMdsc ~}f½tGY\[\kg^a!g^\[^YRiog^ Ä
(_bYMdsc Y]]`_rà_rp,c~Å«[mªBk^cG])nYlijY!aMY]`_QgMp'pgdsMgÈpgÈàgM[^a!g|ÌcªBk_r[^aE_¢gMkMijce[On%gqpg
dsY\[OncGwwOgeÐLaMcep!]`_b])nceiogudscn`dsYMg^w _bY\[gOnYB
W ÓÖÔdsYcnn%gM[^aMY _r[ÆijY!aMY|Y\ M YMd+n`kM[^Y _rpQtGY\[On`dsY\p'p,YMdsc ~}f
cÆce[^cedzgMp'ijce[Onc Y]]`_rà_rp,cµ£ijcGaE_hgM[OncÇtGY\[On`dsY\p'p,YT_r[dscn`dsYMg^w _bY\[^cµÓgMp'pgdsMgdscHg
_hg^tGcedscpg àgM[^a!g·aE_ykM[·]`_b])nceiog·{~}f`
Å«p dsY\àMp,ceiog£ dzgOn _btGYcte^c prÉ'gMp'pgdsMgMijce[OnYjaE_MàgM[^a!g9aE_ÁkM[»]`_b])nceiog p,ce[OnY·_ri MpN_©Ä
tCgprÉ'gM M MpN_btCg^w _bY\[^c aE_M]cG\[gMpN_MaE_E_r[^\dscG]]YaE_Mcep,c´egOn%ggMi _bcGwwOgjte^c· Yn`dsceàMàcedsY
[^Y\[ df_bce[On`dzgdsc[^cep'p,co] cGt_\te^coaMcepÁ]`_b])nceiog£tGY\[On`dsY\p'pgOnYÌcG]cei _«¤J]gOn`kMdzg^w _bY\[_ìµ
pN_ri_Ãn _.ijcGtGtCgM[_bt_!Y \]`_bt_ìµZpN_ri_Ãn _!ce[^cedscn _bt_ìµ+##'Ð`
W !"$# %$&('%$)+*,-#-)/.0."&(,)1%2!"!3.")546&78&7 9., %%$&(,)
{~}f:746;8<)5,)59.")= +%$)>8)5)5!"!"?.
&@A 9., %%$8B
WRXZY\[^]`_baMcedf_hgMijY g^a cG]cei _bY~_rp!]cG\k^ce[Onc£]`_b])nceiogudscn`dsYMg^w _bY\[gOnYB¤
K Y(s)
R(s) X(s)
G(s)
K Y(s)
R(s) X(s)
G(s)
{~}f¦¥ ê
¯ ê
Å«p\\kg^a!g^\[^Y~aE_.gM[^cep'p,Yq{ }fcxpg·vkM[^w _bY\[^caE_\n`dzg^]vzcedf_rijce[OnY_r[^\dscG]]Y Äk^]t_Ãn%g
{ O}f9df_b]kMp©n%gM[^YB¤
{ }f¥ Ê {~}f¥
Ê ê
¯
ê
{ C}f¥
|}f
}f
¥ Ê {~}f
¯ Ê {~}f
¥ Ê ê
¯ }fÊ
¯
ê
W(]cei _bYaE_MgMp'pgdsMgMijce[OnYaMcep'pgàgM[^a!gÓn`dzgMi_Ãncodscn`dsYMg^w _bY\[^c ced=kM[o\kg^a!g^\[^Y
aE_EgM[^cep'p,YuaE_!n _r Y g^]]gGÄàg^]]YB
w 20 dB
-20 dB
w H
banda passante guadagno d’anello
j dB
G ( ) |
| 0 w
banda passante sistema retroazionato
w H0
0 dB
dB a j
G ( ) |
| w
w 20 dB
-20 dB
w H
banda passante guadagno d’anello
j dB
G ( ) |
| 0 w
banda passante sistema retroazionato
w H0
0 dB
dB a j
G ( ) |
| w
W(]cei _bYaE_MgMp'pgdsMgMijce[OnYaMcep'pgàgM[^a!gÓn`dzgMi_Ãncodscn`dsYMg^w _bY\[^c ced=kM[o\kg^a!g^\[^Y
aE_EgM[^cep'p,YuaE_!n _r Y g^]]gGÄàgM[^a!g!
w
dB a j
G ( ) |
| w
20 dB w
L
banda passante sistema retroazionato
j dB
G ( ) |
| 0 w
w H
w L0 w
H0
banda passante guadagno d’anello
0 dB w
dB a j
G ( ) |
| w
20 dB w
L
banda passante sistema retroazionato
j dB
G ( ) |
| 0 w
w H
w L0 w
H0
banda passante guadagno d’anello
0 dB
WlgvkM[^w _bY\[^caE_Án`dzg^]vzcedf_rijce[OnYaMcep(]`_b])nceiogudscn`dsYMg^w _bY\[gOnYmcgM[^tGYMdzgaMcepy df_rijY
YMdsaE_r[^c
{ }f¥
|}f
}f
¥ Ê {~}f
¯ Ê {~}f
¥ Ê ê
¯ }fÊ
¯
ê
ªBk_r[^aE_V Y\[^ce[^aMY
Ê ¥ ê
ê
ã
pgxpgds\^cGwwOgaE_yàgM[^a!g·aMcep!]`_b])nceiogdscn`dsYMg^w _bY\[gOnY g^]]ga!g£ ê go ê
WRXZY\[Æê ¥
ÎcÈê ¥
ÎeÎ_aE_hg^\dzgMii_JaMcep'p,clgMi _bcGwwcRaE_½{ }Mxc
{ }MÓdf_b]kMp©n%gM[^YB¤
10 0 10 1 10 2 10 3
−20
−15
−10
−5 0 5 10 15 20
ω
|G a (j ω )| (b−−), |G 0 (j ω )| (r) [dB]
Diagramma delle Ampiezze con ω H =10 e K=9
WRXZY\[Æ ê ¥
ÎcÈ ê ¥
ÎeÎ_aE_hg^\dzgMii_JaMcep'p,clgMi _bcGwwcRaE_½{ }Mxc
{ O}MÓdf_b]kMp©n%gM[^YB¤
10 0 10 1 10 2 10 3
−20
−15
−10
−5 0 5 10 15 20
ω
|G a (j ω )| (b−−), |G 0 (j ω )| (r) [dB]
Diagramma delle Ampiezze con ω H =10 e K=9
WRXZY\[Æê ¥ äeÎcÈê ¥
ÎeÎ_aE_hg^\dzgMii_JaMcep'p,clgMi _bcGwwcRaE_½{ }Mxc
{ O}MÓdf_b]kMp©n%gM[^YB¤
10 0 10 1 10 2 10 3
−20
−15
−10
−5 0 5 10 15 20
ω
|G a (j ω )| (b−−), |G 0 (j ω )| (r) [dB]
Diagramma delle Ampiezze con ω H =30 e K=2.33
WRXZY\[j ê ¥
Îc» ê ¥
ÎeÎup,cdf_b] Y])nc gMp'prÉ«_ri MkMp,]Ymdscnn%gM[^Y\pgdscÓaMcep]`_b])nceiog
{~}f c£aMcep!]`_b])nceiogudscn`dsYMg^w _bY\[gOnY~{
}f»df_b]kMp©n%gM[^YB¤
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
anello aperto(r−−), retroazione e comp.(g)
Confronto risposte all’impulso(b)
WRXZY\[jê³¥ÏäeÎc»ê ½¥
ÎeÎup,cdf_b] Y])nc gMp'prÉ«_ri MkMp,]Ymdscnn%gM[^Y\pgdscÓaMcep]`_b])nceiog
{~}f c£aMcep!]`_b])nceiogudscn`dsYMg^w _bY\[gOnY~{ }f»df_b]kMp©n%gM[^YB¤
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
anello aperto(r−−), retroazione e comp.(g)
Confronto risposte all’impulso(b)
WRXZY\[Æ ê ¥
Îc| ê ¥
ÎeÎ\pN__r[^\dscG]]`_ gMpJ]`_b])nceiog {~}fucHgMpJ]`_b])nceiog
dscn`dsYMg^w _bY\[gOnYm{ C}f9df_b]kMp©n%gM[^YB¤
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−15
−10
−5 0 5 10 15
Tempo [s]
anello aperto(r−−), retroazione e comp.(g)
Confronto segnali di controllo
WRXZY\[Æê ¥ äeÎc|ê ¥
ÎeÎ\pN__r[^\dscG]]`_ gMpJ]`_b])nceiog {~}fucHgMpJ]`_b])nceiog
dscn`dsYMg^w _bY\[gOnYm{ }f9df_b]kMp©n%gM[^YÌgOnnce[^w _bY\[^cgMp'pg]tCgMpg£´ ced+n _btCgMp,c«Ð`¤
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−4
−3
−2
−1 0 1 2 3 4 5 6
Tempo [s]
anello aperto(r−−), retroazione e comp.(g)
Confronto segnali di controllo
WRXZY\[u ê ¥
Îmc ê ¥
ÎeÎ|p,cdf_b] Y])ncxgMp'prÉ«_ri MkMp,]YÇdscnn%gM[^Y\pgdscaMcepy]`_b])nc`Ä
iogm{~}f¶caMcep.]`_b])nceiog~dscn`dsYMg^w _bY\[gOnY|{
}f»tGY\[xc]ce[^wOg ¸\Qå V Å
]kMp'prÉ«_r[^\dscG]]YB¤
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
Sistema con (−) e senza(−−) saturazione
Confronto risposte all’impulso(b)
WRXZY\[uꧥ äeÎmcê £¥
ÎeÎ|p,cdf_b] Y])ncxgMp'prÉ«_ri MkMp,]YÇdscnn%gM[^Y\pgdscaMcepy]`_b])nc`Ä
iogm{~}f¶caMcep.]`_b])nceiog~dscn`dsYMg^w _bY\[gOnY|{ }f»tGY\[xc]ce[^wOg ¸\Qå V Å
]kMp'prÉ«_r[^\dscG]]YB¤
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Tempo [s]
Sistema con (−) e senza(−−) saturazione
Confronto risposte all’impulso(b)
! ""#%$'&()&+* "*,"$'&+-.*0/,*,%&132#* 4%54
798;:.<=8T>@8BACA8;:EDGF F@FVSyI÷D8<JILUINA!> QAODC8
Wlg pgds\^cGwwOgaE_VàgM[^a!gaE_VkM[·]`_b])nceiogc_r[mdscepg^w _bY\[^ctGY\[ _!ncei _(aE_Bg^]]cG])n%gGÄ
ijce[OnYc£aE_(]gMpN_Ãn%gte^c_baMce[On _\tCgM[^Yqpg´ cep,Y!t_Ãn`gaE_ydf_b] Y])n%g!
WlÖEced£kM[Ç]`_b])nceiogÈaMcep¹ df_rijY YMdsaE_r[^cHÌcH ced9cG])nce[^]`_bY\[^cl ced£_ ]`_b])ncei_=tGY\[ kM[
Y\p,YÇaMY\i_r[gM[Onc^Ð_rpVncei YRaE_Ôg^]]cG])n%gMijce[OnY|c|pgÆpgds\^cGwwOgaE_JàgM[^a!gq]Y\[^Y
_r[O´ ceds]gMijce[Onc· dsY\ YMdsw _bY\[gMpN_«¤
{~}f¥
ê
¯
ê
¶¥
ä
ê
WlÖEced»kM[]`_b])nceiog aMcepV]cGtGY\[^aMYRYMdsaE_r[^cmtGY\[Ç Y\pN_ZtGY\i Mp,cG]]`_QcxtGY\[_rk^MgOn _ ÌcÈ ced
cG])nce[^]`_bY\[^c cedL_.]`_b])ncei_\tGY\[q Y\pN_.tGY\i Mp,cG]]`_BctGY\[_rk^MgOn _@aMY\i_r[gM[On _÷Ð µ¢g gdf_
tGY!ct_bce[Onc~aE_Ô]ijYMdswOgMijce[OnYEµ _rpZncei YÇaE_ g^]]cG])n%gMijce[OnY|cÇpglpgds\^cGwwOgqaE_
àgM[^a!g]Y\[^Y_r[O´ ceds]gMijce[Onc dsY\ YMdsw _bY\[gMpN_«¤
{~}f¥
¯
¯ ê × ¥ ä
WÈØjkgMpN_Ãn%gOn _ôegMijce[Onc_rpncei YaE_!]gMpN_Ãn%g
aE_@kM[]`_b])nceiog£aE_Mn _r Y g^]]guàg^]]Y c
_r[O´ ceds]gMijce[Onc· dsY\ YMdsw _bY\[gMp,c·gMp'pgxàgM[^a!gm g^]]gM[Onc
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
−1.5
−1
−0.5 0 0.5 1 1.5
diagramma di Nyquist
0.47 0.56
0.68 0.82
1 1.2 1.5 2.2
0.15 0.18 0.22 0.27 0.33 0.39 0.47
0.56 0.68 1
0 10 20 30 40 50 60
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
risposta nel tempo
secondi
Øjk^cep'pN_df_r YMd+n%gOn _½_r[ \\kMdzg ]Y\[^YT_¦aE_hg^\dzgMii_ aE_ ªBk_b])nmaMc_¦]cG\k^ce[On _¦aBk^c
]`_b])ncei_«¤
{ 6 }f¦¥
Î
(}f
¯ }f
¯
Î
{ }f¦¥
(}f
¯ }f
¯
Î
BgM[^tGYEµ;]Y\[^Yldf_r YMd+n%gOn _@\pN_QgM[^a!gMijce[On _Encei YMdzgMpN_.aMcep'pgÈdf_b] Y])n%g gMp.\dzg^aE_r[^Y
aMc_¹tGYMddf_b] Y\[^aMce[On _L]`_b])ncei_½_r[³dscn`dsYMg^w _bY\[^c²kM[_Ãn%gdf_hg! XZY\ijcl]`_¶ MkÁY²´ cGaMcedsc
a!g_J\dzg\t_ìµ [^c_aBk^cÇtCg^]`_L_rp ncei Y aE_]gMpN_Ãn%gÌ
6 ×
c ×
]0Ðmc
t_rdstCg x_r[O´ ceds]gMijce[Onco dsY\ YMdsw _bY\[gMp,cogMp'pgpgds\^cGwwOg aE_\àgM[^a!goaMc_aBk^cÓ]`_b])ncei_
dscn`dzg^w _bY\[gOn _LÌ3 ê 6 × Î
cÈ ê × Î
Ðt_bYÁcHgMp'p,c MkMp,]g^w _bY\[_ ê aE_
_r[Onceds]cGw _bY\[^c£aMc_(aE_hg^\dzgMii_ÁaE_ ªBk_b])ntGY\[ _rp!tGcedste_bYkM[_Ãn%gdf_bYB