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e e e K K 0 0 0 G(s) G(s) - - - t t t s s s r r e e x x y y c c

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(2)      !"# $&%  '(' $ )()+* ,-.#. /103254 07698:8<;=076987> /103?A@B0 > ;M?ONKCEPQA?ARTSU07V"P&N W RX?A6YP&>. CEDF/G/. HIDKJL/. Z\[K]U^_Za`ZAbdce^gfhjiLkmliLn\bdi=hj^ghbdiLo1Ze^gnqpjirbdpjc\ZtsL^gcmnituv^gf`^_ZtkmpdZto o1Z=`^xwzyU{l^ghb `iLfgf_Z=|}lnsL^gcmniM~1€ ‚+[ i ƒ pj^g„ cmpb†ZAbdc‡niLfgf_Z‰ˆkmlpdZFhjctbjbdcmhb†Ztn\bditŠ(‹#Z‡|}lnsL^gcmniŒ~1TB[ncmn=ŽZK„ cmfg^5ZK„ZtpbdipjiZtfgi„ cmhj^bd^‘tZOŠ r. e. x. K. e. y. -t0 s. c. G(s). diagramma di Nyquist. 0.5. 0. 1. 1.2. 1.8. 0.82 0.68. −0.5 0.56 −1 0.47. −1.5 0.39. −2 0.33 −2.5 −3. −2.5. −2. −1.5. −1. −0.5. 0. 0.5. 1. w,iL^5fg^go ^bd^`iLfgf_Z‡„pjiL’L^ghj^gcmni’LcmnhjiLn\bd^b†ZF`Ztf5kmpdZAˆ’Lc“ ZOŠ”B[‰• cmhbdc—–™˜š”Gi›œ˜ža^gn`^g’Ztpji1^gfo1Ztpjkm^gni1`^(|XZthji=Ÿ— YiG^gfo1Ztpjkm^gni1`^+Zto „^giLsLsZIŸ—¡9`iLf hj^ghbdiLo1ZKpjirbdpjc\ZtsL^gcmnZAbdcŠ ¢ o1Ztpjkm^gni`^5Zto „^giLsLsZO“(£MX¤OŠ \£‡`¥[+„ iLp+‚¦˜E”ŒpdZt`§AhjiL’ ¢ o1Ztpjkm^gni`^3|XZthjit“£U”mŠ ¨m©KkmpdZt`^vXOŠ ¨\ªt¨KpdZt`[„ iLp+‚¦˜«O¬ ¤m©\£A­KpdZt`§AhjiL’ OZ Š®£m[• cmhbdc:–¯˜°” `irbdiLpjo ^gnZtpjiK„ iLp{lZtfg^±‘tZtfgcmpj^&`^&›œF²³G^gf&hj^ghbdiLo1ZGpjirbdpjc\ZtsL^gcmnZAbdcIi ƒ Zthj^gn\bdctbd^g’Z ¢ o iLn\bdihb†Zt¥^gfgitŠ ´ n`^g’Ztn`c’Lcmn=‚±œf_Z „lfghdZtsL^gcmni‰Ztfgf_ZF{lZtfgi‰^gf#`^_ZtkmpdZto o1ZK`^±wzyU{l^ghb`^&~1TB[x^gn\bdiLpjhjiL’Zf_Z ’L^gpj’Lcmn ¢ |}iLpjiLnsZMln^b†Ztpj^_ZOu3^gf±o1Zthjhj^go cGpj^b†Ztpj`chj^ ’Ztfg’Lcmf_Z1’Lcmo i= ´ f&o1Ztpjkm^gni‡`^±|XZthjiF`ir‘mi iLhjhjiLpji iLhj„pjiLhjhjc:^gn pdZt`^_Ztn\bd^µ[¶“ ‚±œ·¸œ,¹ºŸ— a»¼O¬ ¤m©\£A­ ›œz¹½O¬ ¨\ªt¨Œ»¾›œ¹½O¬®¿A­ªv ‹#ZKhjiLkmliLn\bdiˆkmlpdZFo cmhbdpdZK^gf3`^_ZtkmpdZto o1Z‰`^5wzyU{l^ghb`^#~1TB[i`^#~1TB[ÀAÁÂÄÃÆÅ’LcmnM›œx˜ºO¬®¿A­ª&hLŠ. Ç.

(3) diagramma di Nyquist. 0.5. 1. 0.82 0. 1.8. 1. 0.68. 1.2 1.2 1.5 2.2. 0.82. 0.56. 0.68. −0.5 0.56. 0.47 −1 0.47. 0.39 −1.5 0.39. 0.33. −2. 0.33. −2.5 −3. −2.5. −2. −1.5. −1. −0.5. 0. 0.5. 1. OZ Š ¨\[7• cmhbdc–Șɣ+`irbdiLpjo ^gnZtpjiv„ iLp#{lZtfg^m‘tZtfgcmpj^m`^m›œ²½z^gfmhj^ghbdiLo1Zzpjirbdpjc\ZtsL^gcmnZAbdci(ƒ Zthj^gn\bdctbd^g’Zto iLn\bdi hb†Zt¥^gfgitŠ Ê hjhjiLn`cFŸ—¡=˜É£UuUZtn’†Ži’Lcmn ›œx˜ºŒ^gfhj^ghbdiLo1Zpjirbdpjc\ZtsL^gcmnZAbdcncmn:iƒ Zthj^gn\bdctbd^g’Zto iLn\bdizhb†Zt¥^gfgiz„ iLpj’†Ži Ë ^gf3`^_ZtkmpdZto o1Z‰`^#wzyU{l^ghb,`^ £ ~1TB[(^gn\bdiLpjhjiL’Z ^gf3„ln\bdc1’Lpj^bd^g’Lc ¢ ”mŠ ¥[K]U^_Z‡`ZAbdcF^gf7hjiLkmliLn\bdi‰hj^ghbdiLo1ZK^gnGpjirbdpjc\ZtsL^gcmni’Lcmn:–šÌYKiŒÍ7ÎÌYOŠ r. e. C(s). x. N.L.. y. G(s). y. c Y1 -1. 1. 2. 3. x. ” Ï TB[ ˜ – -Y1 1 ~ T  B  [ ˜  Tн”B[Ñ ¥7Š”B[xÒ+Ztfg’Lcmf_Ztpjif_ZKpjirbjb†ZK`^5’Ztpj^g’LcF^gnG|}lnsL^gcmni`^5ÓUŠ Ê hjhjiLn`c Ï X\[ ˜ÉÔÕf_Z‡pjirbjb†ZF`^5’Ztpj^g’LcMiƒ cmpj^gsLsLcmn\b†Ztfgiipj^ghjlfb†ZO“&ÖK˜ Ó ˜ºÓ ~1X\[ ¥7Š®£m[+• cmhbdc ӌ˜ºF`irbdiLpjo ^gnZtpji^gf7„ln\bdc `^5f_Z‘mcmpjc:µ×œ¸ØdÖtœ¶[¶Š Ù ZAbdcK’†ŽiŒf_Z‡pjirbjb†ZF`^5’Ztpj^g’LcMiƒ ÖF˜ºÓ˜«K^gf7„ln\bdc `^7f_Z‘mcmpjcFpj^ghjlfb†ZMµ×œ¸ØdÖtœ¶[v˜Ú”m؆\[¶Š ¥7Š ¨\[• cmhbdc:Ó=˜ÛMiÍ7ΘۣM`^ghjiLkmnZtpji {lZtfg^b†ZAbd^‘tZto iLn\bdiKf_Z|}lnsL^gcmni `iLhj’Lpj^bjbd^‘tZ=Ü1µ×3[`iLf(¥fgcU’L’Lc ncmnMfg^gniZtpjiwŒŠ ‹ Š ‹#Z‡|}lnsL^gcmni`iLhj’Lpj^bjbd^‘tZGiƒ {liLfgf_ZK`^7lnZFhdZAbdlpdZtsL^gcmni{l^gn`^T“. Ý.

(4) funzione descrittiva. 2.5. 2. 1.5. 1. 0.5. 0. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ¥7Š ­[,• cmhbdcGÓF˜ÚOu7Í7Îx˜Þ£Uu7–ߘޣ pj^g’Z‘tZtpjiG}{lZtn`cG„ cmhjhj^g¥^gfgi^gnao cU`cZtnZtfg^bd^g’Lc[xZto „^giLsLsZFàIâ á i „lfghdZtsL^gcmni‚ â á `iLkmfg^ ir‘miLn\bdlZtfg^±’L^g’Lfg^#fg^go ^bdi„pjiLhjiLn\bd^&niLf±hj^ghbdiLo1Z hj„ iL’L^ˆ’Ztn`cGhji‡iLhjhj^±hjcmncGhb†Zt¥^gfg^5c ^gnhb†Zt¥^gfg^TŠ ã pdZto ^bdiF^gf ’Lpj^bdiLpj^gc=`^(äzcmlObdŽhj^vpj^g’Z‘tZ=’†Ži1^gfv`^_ZtkmpdZto o1Z`^(n\yU{l^ghb‡`^ Ï €t‚+[~1€t‚+[^gn\bdiLpjhjiL’Z:^gf hjiLo ^_ZthjhjipjiZtfginiLk\ZAbd^‘mce^gn ¢ ”„ iLp‰‚á ˜š”mŠ—å„„fg^g’Ztn`ca^gf(o irbdcU`ce`iLfgf_Z=|}lnsL^gcmni`iLhj’Lpj^bjbd^‘tZahj^ pj^g’Z‘tZK’†ŽiiLhj^ghbdiln=’L^g’LfgcFfg^go ^bdi,hb†Zt¥^gfgi`^#Zto „^giLsLsZ‡àIᘫ£U¬ ­ªm¿UŠ diagrammi polari di gb e di −1/F(X). 0.5. 1.2. 0. 1.5. 2.2. 1. 0.82. −0.5 0.68. −1. 0.56. −1.5. −2 0.47. −2.5 −3. −2.5. −2. −1.5. −1. −0.5. 0. 0.5. 1. ¥7Š®¿m[,• cmhbdcGÓK˜æ1i‡–¾˜”mu pj^g’Z‘tZtpjiG}hji‡iLhj^ghbdcmnc[z„ iLp{lZtfg^#‘tZtfgcmpj^#`^±Í7ÎÌɝ1^gf#„ln\bdcG`^ f_Z‘mcmpjcai ƒ kmfgcm¥Ztfgo iLn\bdiZthj^gn\bdctbd^g’Zto iLn\bdihb†Zt¥^gfgitŠvç^glhbd^ˆ’Ztpjif_Z‡pj^ghj„ cmhb†ZOŠ • iLp–Șæ”,^gf`^_ZtkmpdZto o1Z`^ wzyU{l^ghb`^ Ï €t‚+[~1€t‚+[±^gn\bdiLpjhjiL’ZŒ^gfhjiLo ^_Zthjhji,pjiZtfgizniLk\ZAbd^‘mcŒ^gn=茔Bém£UŠ ‹#Z‡„ iLn`iLnsZK`iLf7„pj^go cŒbdpdZAbjbdcK`iLfgf_ZŒncmnMfg^gniZtpj^bAZF ƒ iƒ Í7ÎjéU”i{l^gn`^3^gf kmpdZAˆ’LcK`^&茔BétÜ1µ×3[(„Ztpbdi`Z 茔BéOÍ7ζŠ å,ê n’†Ži1Ë ncmnI‘U^ hj^_ZtncM’L^g’Lfg^&fg^go ^bdi‰iF^gf „ln\bdc=`^ f_Z‘mcmpjc=hj^_ZGkmfgcm¥Ztfgo iLn\bdiKZthj^gn\bdctbd^g’Zto iLn\bdi hb†Zt¥^gfgituie ƒ niL’LiLhjhdZtpj^gc뒆Ži¦èŒ”BétÜ1µ×3[1hj^_Z’Lcmo „fgirb†Zto iLn\bdieZtf`^|}lcmpj^`iLfgf_Z<pjiLkm^gcmniepdZt’L’†Ž^glhdZq`Ztf `^_ZtkmpdZto o1ZŒ`^#wzyU{l^ghb,`^ Ï €t‚+[~1€t‚+[¶ŠvìliLhbdc1Z‘‘U^giLni„ iLp,Í7Î+íY£UŠ ¥7Š ¤\[ • cmhbdc‰–Șæ”muÍ7Îv˜æ”zi,Ó˜«O¬®¿hbdl`^_Ztpjizf_Zhb†Zt¥^gfg^bAZƒ `iLf„ln\bdc‰`^f_Z‘mcmpjclObd^gfg^gsLsZtn`c^gf’Lpj^bdiLpj^gc `iLf’LiLpj’†Ž^gcŠ Ù ^ghjiLkmnZtpjie^gf’LiLpj’†Ž^gc¦’Lpj^bd^g’LcŠîXw,ctb†ZO“¦^gf`^_ZtkmpdZto o1Z<`^wzyU{l^ghb=`^ Ï €&‚+[~1€&‚+[ „pjiLhjiLn\b†Z ln:Zthj^gn\bdctbdc‡‘miLpbd^g’Ztfgi„ iLpxïð,˜æè£m[¶Š ´ f’LiLpj’†Ž^gc¦’Lpj^bd^g’Lcq`iLkmiLniLpdZëniLfhjiLo ^g„^_Ztnc¦Zqhj^gn^ghbdpdZq`iLfgf_Zpjirbjb†Z‘miLpbd^g’Ztfgie„ZthjhdZtn\bdi—„ iLp ¢ ”mŠ ´ f `^_ZtkmpdZto o1Z<`^wzyU{l^ghb:`^ Ï €&‚+[~1€&‚+[^gn\bdiLpjhjiL’Zë„ iLpb†Ztn\bdcë^gf’LiLpj’†Ž^gcë’Lpj^bd^g’Lc¦i—{l^gn`^ncmn«hj^ „ cmhjhjcmncFbdpdZtpjpji’Lcmn’Lfglhj^gcmn^7hjlfgf_Z‡hb†Zt¥^gfg^bAZ‰ƒ `iLf5„ln\bdc `^5f_Z‘mcmpjcŠ ñ.

(5) ’¸[K]U^_Z‡`ZAbdcK^gf3hj^ghbdiLo1ZKfg^gniZtpji~1TB[¶u^7`^_ZtkmpdZto o ^`^5òcU`i`iLfgf_Z‰|}lnsL^gcmni~1€ ‚+[(hjcmncFpj^g„ cmpb†ZAbd^3niLfgf_Z ˆkmlpdZKhjctbjbdcmhb†Ztn\bditŠ ’tŠ”B[ ´ n`^g’Ztpji^gf7kmlZt`ZtkmncFhb†ZAbd^g’Lc ~1X\[`iLf5hj^ghbdiLo1ZF~1TB[¶Š ~1X\[ ˜æ”¸mŒ˜½­\t`ò ’tŠ®£m[,äz^g„ cmpb†ZtpjiŒf_ZF¥Ztn`Z„ZthjhdZtn\bdi‡`iLf±hj^ghbdiLo1Z1~1TB[zhj„ iL’L^ˆ’Ztn`cG`^ ’†Ži‡bd^g„ c `^±hj^ghbdiLo1Z hj^ bdpdZAbjb†Z ^gnMpjiLf_ZtsL^gcmniZtf7’Lcmn’Lirbjbdc1`^7¥Ztn`ZF„ZthjhdZtn\bditŠ ´ f5hj^ghbdiLo1ZGiƒ bd^7bd^g„ cK„ZthjhdZF¥Zthjhjc1if_ZKhjlZF¥Ztn`ZK„ZthjhdZtn\bdi1iƒ óژÞô Ú”LõTŠ ’tŠ ¨\[x]bd^go1Ztpji^gf3bdiLo „ cF`^#ZthjhjiLhb†Zto iLn\bdcFö3ð`iLf5hj^ghbdiLo1ZF~1TB[¶Š(ç^glhbd^ˆ’Ztpjif_Z‡pj^ghj„ cmhb†ZOŠ ´ f hj^ghbdiLo1Z ŽZ1lna„ cmfgc1`cmo ^gnZtn\bdiŒ„ iLpz‚Y˜³”‡„ iLpb†Ztn\bdc^gf5bdiLo „ c1`^±ZthjhjiLhb†Zto iLn\bdcGpj^ghjlfb†Z ^gn`^g’ZAbd^ ¢ ‘tZto iLn\bdiö3ð,÷ɨthLŠ ’tŠ ­[x]bd^go1Ztpjif_ZK¥Ztn`ZF„ZthjhdZtn\bdiŒ`iLf5hj^ghbdiLo1ZKpjirbdpjc\ZtsL^gcmnZAbdc“ ~1TB[ ~Œø&TB[ ˜ ”Ðë ~1TB[ ‹#Z¥Ztn`ZG„ZthjhdZtn\bdi=iF ƒ Zt„„pjcmhjhj^go1ZAbd^‘tZto iLn\bdi‰`ZAb†ZG`Zt^±‘tZtfgcmpj^ `^ ‚É„ iLp^&{lZtfg^,ù ~1€t‚+[¸ù3² ”F{l^gn`^ óژÚô É¨mAõTŠ ’tŠ®¿m[x]U’Lpj^‘miLpjiŒi^gn`^g’Ztpjihjlf#kmpdZAˆ’LcF^gf7o cU`lfgc‡if_Z‰|XZthji`^#~1€ ‚+[(„ iLp+‚¦˜«¨OŠ o cU`lfgc“&¨mOŠ®£tú=T£túOŠ ¤m¨K`¥[¶ûZtpjkmcmo iLn\bdc“ ¢ ©m©OŠ®£t¤‡kmpdZt`^( ¢ ”mŠ®¿A­”pdZt`^_Ztn\bd^µ[ ampiezza. db. 50 40 30 20 10 0 −10 −20 −30 −1 10. 0. 1. 10. 10. 10. fase. 0 gradi. 2. rad/sec. −50 −100 −150 −200 −1 10. 0. 1. 10. ü. 10. 2. rad/sec. 10.

(6) `[K]U^7|XZt’L’L^_Z‡pj^|}iLpj^go iLn\bdcFZtf7o cU`iLfgfgcK• Š®ý‡Š®çKŠ`^5ln=hj^ghbdiLo1ZKiLfgirbjbdpjc Ï Ï þð. þð     –      Î ”   ð Å  ð

(7) .   ” Î   Å  . ÿð  ‚      – ´ f7‘mirbjbdcmpji`^5hb†ZAbdcF`ZF’Lcmnhj^g`iLpdZtpjiFiƒ ^gf3hjiLkmliLn\bdit“  ˜ þ ð߂ . ¢ o iL’L’Ztn^g’LcFZthjhjiLkmnZAbdc“ ÿœ –  . – œ.  . –  . .  ÿ œ. .  . . Å. Î. . œ. ÿ œ. ‹5io1ZAbdpj^g’L^zu au"!i$#³ŽZtnnc f_Z‡hjiLkmliLn\bdi‰hbdpjlObjbdlpdZO“ %&  ð  %& è  ðÕè– %& ”  ()  ()  ()    Î Ø ۘ – è  è– Ø !ژ   Ø #ژ+* ”¯ ”, ¦˜   ' à  – è   茔 ´ f5o cU`iLfgfgc‰`^gnZto ^g’LcK`iLf5hj^ghbdiLo1ZKniLfgfgcKhj„ZtsL^gcF`iLkmfg^7hb†ZAbd^ iƒ {l^gn`^7^gf7hjiLkmliLn\bdit“ %&  ð  %& è  ð è– %& ”  ()  () %&3þ 2 ð ()  () %& þ ð () ÿ    Î ‚2 ‚ Ð   *  ð œ$, – è  è– ˜ ÿœ ÿ2œ   ' à  – è   茔 .0/ 1 - .0/ 1 .0/ 1 - .0/ 1 - .0/ 1 - .04 / 1 2. . ˜ 5. -. *  ”¯  ”6,  .0/ #. cm„„lpjitu^gnMo cU`cKiL{l^‘tZtfgiLn\bditu^gf7hjiLkmliLn\bdit“ %&3þ 2 ð () %& è 8ø9 77 è '9 :7 ': ‚2 ˜ è ;<= : : > ;<: 2ÿ œ  – – œ¯è - .0/ 1 2. -. 5. ˜ -. *  ”   ”6,  .0/ #. . . .0/ . !. 1. . (). &% Î 7 %& þ ð )( 9 ‚ Ð . è '";<: ? ÿœ  – œ 1 - 0.  / 1. 1. @.  (). *   è – œ .0/ 1 !. ÿ ð œ$, .0/ 1 4.

(8) i¸[K]U^5pj^g’Z‘U^7^gf7o cU`iLfgfgcK• Š®ý‡Š®çKŠ`iLf5hj^ghbdiLo1ZKo iL’L’Ztn^g’LcFpj^g„ cmpb†ZAbdcK^gnGˆkmlpdZOŠ ´ f hj^ghbdiLo1ZŒo iL’L’Ztn^g’Lciƒ ’Lcmhbd^bdl^bdcŒ`Z‰lnGZtfg¥ iLpjc‰`^ ^gniLpjsL^_Z u’†Ži=pjlctb†Z—Za‘miLfgcU’L^bAZ: ƒ ‚,uZI’Ll^i= ƒ Zt„„fg^g’ZAb†Zef_Ze’Lcm„„^_Z iLhbdiLpjnB Z A7Š ã pdZto ^bdiln:pjlfgfgcFiLf_Zthbd^g’Lc Z‘miLn\bdi‡pj^gkm^g`^bAZ‰ƒ bdcmp ¢ hj^gcmnZtfgi&–GÎ7i pdZtkmkm^gc+’Lcmhb†Ztn\bdi  uBDf C Ztfg¥ iLpjc+hj„^gnkmi lnZxo1ZthjhdZ Ÿ ’†Žiz’Lcmo „pj^go ilnZo cmfgf_Z,fg^gniZtpji’LcmnF’LcUirê ’L^giLn\bdiz`^Opj^ ¢ km^g`^bAZ,ƒ – Ñ Š&‹#Z,|}cmpjsZ,iLhjiLpj’L^b†ZAb†Z`Ztfgf_Zzo cmfgf_Ziƒ nlfgf_Zz{lZtn`c f_ZMo1ZthjhdZ:hj^vbdpjc¸‘tZ:niLfgf_ZM„ cmhj^gsL^gcmniF×9˜°OŠ:‹C ^gniLpjsL^_Z=i1f_Z o1ZthjhdZhjcmncŒhjcmkmkmirbjbdizZt` ZAbjbdpj^bdc‘U^ghj’LcmhjcŒ’LcmnF’LcUirê ’L^giLn\bd^`^ ZAbjbdpj^bdcKfg^gniZtpji  Î+i  Ñ pj^ghj„ irbjbd^‘tZto iLn\bditŠ. b1 K1 J R. w t M b2 x K2. ´ f5o cU`iLfgfgc‡• Š®ý‡Š®çKŠ`iLf5hj^ghbdiLo1ZKo iL’L’Ztn^g’Lc ZthjhjiLkmnZAbdc=iƒ ^gf7hjiLkmliLn\bdit“ A  . Å. ‚ ‚. . . Î.   øÎ .  . –GÎ. 

(9) FE. Î . ”. Ü Î.  . Å. . . Å . . Î.  6I. HG. Î. Ÿ Î. ø. Ü Ñ  – Ñ. . ”. . . . ×2.  Ü Ñ. KJ. Ñ. . . . Å. Î. . cm„„lpjitu^gnMo cU`cKiL{l^‘tZtfgiLn\bditu^gf7hjiLkmliLn\bdit“ A. Ü Î . . . ”. ‚. . . . . ø. Î. . ×2. ‹#ZK`iLhj’Lpj^gsL^gcmni`iLf5hj^ghbdiLo1ZKniLfgfgcKhj„ZtsL^gcF`iLkmfg^7hb†ZAbd^ %LL è  Î %LL    (NMM %LL ‚ 2 (NMM &  'Î   ) & Ü2Î ) & ” E ˜   Ÿ Î ×O  2Ü    ' I  Ñ -. .0/ . -. 1 - .0/ 1 2. 5 ˜  ‚. Ü Ñ  ˜. ”. -. *  ”¯. Q. .0/ #. . . .     ”, 1.  . i ƒ f_Z‡hjiLkmliLn\bdit“  茔  Î  (NMM L%L ‚ (NMM Î è ø  ) & Ü Î ) Ð ×2 ø è  Ñ èŒ” Ü Ñ  ”  .0/ 1 - .0/ 1 .  Ü Ñ. – Ñ .  Ð9Ÿ  Ñ. . . Ü Ñ  . –GÎ .  Î#Ð . ‚.   øÎ. %LL ” N( MM &).  P- .04A /P1 . - .0/ 1 !.

(10)

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