−2000−1800−1600−1400−1200−1000−800−600−400−2000−200−150−100−50050100150200diagramma di Nyquist
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Testo completo
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(6) " #!$% &'(*)#)+-,.!$ /10 2. 3546 74 8:9. >< = ? = @ =. ;4 89. A=. B CEDF4 7!GHCJI!9LKMCCJNGHCJGPOP9Q8:RSKH9LOPKH4 RUTQCV4 7WRUOP4XKYCVZ 4KHOHRUOP4R [R7!DF4\^]!RDF9Q7!I4'KMCJ_`9LKMCa89Q7 OP4bRNJNV9:_dc!7TQCV4 7WC#egfPh i = KYCVZ 4KHOHRUOP9I!CjGP9L6 c!CVOP4k*GMCjGP4 GHOHCVOHc!CJGHDLRbRImlnCJN*oURNV4Up KM9#RGHGP9L6 7!RUOP4q9jGMCKMCJGPZ 4 7!IWR5RNaNV9#GP9L6 c9Q7(OHCrI4 8:R7!I9\. { hvu =. szt. hvu =. y hvu = s w. sx. | hvu =. egfPh i = s. s. e~}Qh i =* h L< i *h i+ ? i+J<>= A h = ih i+ <Ll( = = e h i =# ? h i5 irh i? m= h l iq= . = eh i =* h i1i } h = i5h i <L? i= ? = < R = 4 GPOP4 w < kDLRNJDF4 NJRUKH9'N 9LKHKM4KH9bR.KH9L6 CJ89 fPh" = Z9LKXCJ76KH9QGMGP4.R.6KMRI!CJ7!4 { hvu =@ hvu = \BCcOHCJNJCVTLTQCNJR KH9QNaRUTQCV4 79 fPh" =* { h" = | fh" = I4>o9 | fPh" =9g DLRt NJDF4 NJRUOP4RUZ!ZNJCJDLR7!I4CJNWDF4 8:R7WI4OPKM9QGPZW ~RNJNJR¡_vc!7!TQCV4 79¢£h i =# }¬ ¤:¤¥ ¥ ¦"§©¦d¨«§©ª ¨«ª!® t h i = \5BC o9LKMCV[DM¯!C°DY¯9¡6 NaC°GPOP9QGHGHC°KYCJGHc!NVOHRUOHC GHC Z 4 GHGH4 744OPOP9Q79LKH9±cOHCJNJCVTLTQR7WI4NJR~_`4KY8c!NaR h" =* }¬ ²¤³ ´ \ t } h" =* µ ¬ ¶µ P· h " =*¡¸ hdCJN°GMCJGPOP9Q8:R 9¡ Ca7!GPOHRU¹WCJNJ9 = h" =*º t t t < ¹ = 3RNJDF4 NJRUKH9»N"9LKHKH4KH9»RKM9L6 CJ89 fHh" = Z9LKCa76KH9QGHGP4:R~KYR8ZWR { hvu =# uY\jBC°cOHCJNJCVTLTQC NJR~_v4KM8±c!NJR h" =* ¤½²³¼ \ t t } h" =* h " =*¡¸ hdCJN°GMCJGPOP9Q8:R 9¡ Ca7!GPOHRU¹WCJNJ9 = h" =*º t t t < D = 3RNJDF4 NJRUKH9»N"9LKHKH4KH9»RKM9L6 CJ89 fHh" = Z 9LKCa76KH9QGHGP4RZRUKMRU¹ 4 NJR { hvu = u \5BC°cOHCaNJCVTLTQC NJR~_v4KM8cWNJR h" =# ¤² ³¾ \ t t } h" =* h" =* } ¿ h" =*¡¸ hdCJN°GMCJGPOP9Q8:R 9¡ Ca7!GPOHRU¹WCJNJ9 = t R CaGP9L6 7!RUKH9»Árc!RNJCVOHRUOHCJoÂR89Q7(OP9»CJN°I!CaRU6KMt R8:8:R~Z 4 NJRUKH9:ÃYÄUÅÆÇVÈQÉ"ÄXI9QNJNV9g_dc!7TQCV4 7!CEt ef«h i R~ZWRUKHOHCVKM9gIWRNEI!CJRU6KMR8S8:R ? =À = I!C°;ÊÁ(c!CaGPO+4OPOP9Q7(c!OP4cOHCJNaCVTLTQR7!I4DF4 7^CJN°DF4 8SR7!I4Ë_vKH9QGPZW \ diagramma di Nyquist. diagramma di Nyquist. diagramma di Nyquist 250. 500. 200. 200. 400. 150. 150. 300. 100. 200. 50. 100. 100. 50. 0. 0. −50. −100. −100. −200. 0. −50. −100 −150. −300. −200. −400. −150. ? ¹ =+À 9LOP9LKY8:CJ7!RUKH9GP9k!CJ7£¹WRGP9RNEDFKMCVOP9LKMCJ4:I!C°;ÊÁrc!CJGPOLkCJN°GHCaGPOP9Q8:R~KH9LOPKH4 RUTQCJ4 7!RUOP4£e f h i =9 GPOHRU¹CJNV9gZ 9LK w Ì< \ e»¶} h i =q9¡ GHOHRU¹WCJNV9Í 7!4Î±Ï GHCÎ ÐÏ e h i =9¡ GPOHRU¹WCJNJ9±Í 74Î ÐSÏ GHCÎ±Ï eP h i =q9¡ GPOHRU¹CJNV9Í 74Î~Ï GHCÎ ÐÏ ? D =~À 9LOP9LKM8SCJ7!RUKH9k5GHc!NI!CJRU6KMR8S8:R'I!C;ÊÁ(cWCJGPOLk#CJN8:RUKM6 CJ79I!C5_vRGH9£ÑÒ fq9£CaN58SRUKH6 CJ79I!CR8ZWCJ9LTLTQRÑ.ÓfqI!9QNJNJR _dc!7TQCV4 7!9egf«h i = \*Ô9LKMCV[DLRUKH9¡C KMCaGHc!NVOHRUOHC4OPOP9Q7rcOHCEOPKMR8SCVOP9¡N 4Z!TQCJ4 79 @ I9QNEDF4 8:R7WI4Ë_vKH9QGPZW \ ÑÒ} -?@rJ<<LÕ Ñ.Ò <QÖ<UJ<LÕ ÑÒ° Ø×UÖrÙ Õ ÑÓE} 74 7^I9LOP9LKM8SCJ7!RU¹WCJNJ9 Ñ.Ó 74 7^I!9LOP9LKM8:CJ7!RU¹CJNV9 ÑÓ Ú<Q?r A Ö @ =:Û OHCJNaCVTLTQR7!I4nCJNDFKMCVOP9LKMCV4nIWCÜ4 cOH¯ÝhdcOHCJNJCJTLTQRUKH9^CJNDF4 8:R7WI4ÞKH4 c!OH¯! = k+I9LOP9LKM8:CJ7WRUKH9^Z 9LKSÁrc!RNJCoURNV4KMCI!C w CJN GHCaGPOP9Q8:RKH9LOPKM4 RUTQCV4 7!RUOP4 9¡ GHOHRU¹WCJNV9\ ß A ÖU @:à w à ÙU ×à w àá ~à w àÞ<Q?r A Ö −250 −50. 0. 50. 100. 150. 200. 250. −500 −80. −60. −40. −20. 0. 20. 40. −200 −2000. −1800. −1600. −1400. −1200. −1000. −800. −600. −400. −200. 0.
(7) A R =5â KYRDLDLCJRUKH9CJNNJc464I9QNJNV9KMRI!CJDLCÁrc!RNJCVOHRUOHCVo4~I9QNJNaR¡_dc!7TQCV4 7!9gegfPh i = Z L9 K ä w ã \ Û OHCJNJCVTLTQRUKH9gCJNDF4 8:R7!I4KH4r4OHNJ \ luogo delle radici. luogo delle radici. luogo delle radici. 100. 10. 10. 80. 8. 8. 60. 6. 6. 40. 4. 4. 20. 2. 2. 0. 0. 0. −20. −2. −2. −40. −4. −4. −60. −6. −6. −80. −8. −8. A ¹ =â KMRDLDLCJRUKH9CJN°NJc464:I9QNaNV9gKMRI!CJDLC°I9QNaNJR±_vc!7!TQCV4 79¡egfPh i = Z9LK w àá \jåZ!ZNJCJDLRUKH9KH4r4OHNJ :RNJNaR~_vc!7!TQCV4 79~qegfh i = \ −100. −200. −150. −100. −50. −10 −5. 0. −4. −3. −2. −1. luogo delle radici. 0. 1. 2. 3. 4. 5. −8. −6. −4. −2. 0. 2. luogo delle radici. luogo delle radici. 5. −10 −10. 20. 8. 15. 6. 10. 4. 5. 2. 0. 0. −5. −2. −10. −4. −15. −6. 4. 3. 2. 1. 0. −1. −2. −3. −4. A D = Ü9QNaRUOHCVoÂR8:9Q7 OP9^RN+NJc!464'I!9QNJNV9XKMRI!CJDLC5Z 9LK w ã kI9LOP9LKM8SCJ7!RUKH9X6 NJCRGHCJ7(OP4OHC kjC5ZWcW7 OHCI!CI!CVKYR8:RUTQCV4 79 y f k#C DF4KHKMCJGHZ4 7WI9Q7 OHCoÂRNV4KYC wSæ f kNV9bCJ7(OP9LKMGP9LTQCJ4 7!C+çfgDF4 7ºN ßRGMGP9bCJ8S8:RU6 CJ7!RUKMCJ49bCDF4KMKMCJGPZ 4 7!I9Q7(OHC+oURNV4KMC wè fShdc!GHRUKH9 N 4Z!TQCV4 7!9 @ I9QN°DF4 8:R7!I!4ËKH4r4OHNJ = Í 79QGHGHc!7RGMCJ7 OP4OP4 < RGHCJ7(OP4OP4GMc!N°GP9Q8:CJRGMGP9»79L6 RUOHCVo4 < RGMCJ7 OP4OP4XGHc!N°GP9Q8SCJRGHGP9»79L6 RUOHCJo4 y } <QÙÖré wSæ } -@Ùr A ? y} < y } -@Ùr A ? wæ } -@Ù?@ wæ } - y 7!4 y 74 y A Ù A wSæ Ø?rß ?é wæ 74 wæ 74 ç#} 7!4 çj} 74 ç#} A Ù@< w:è } Ú<Q?r A Ö wè } 74 w:è } 7!4 A I =â KMRGP_v4KM8:RUKH9»N"9QÁ(c!RUTQCJ4 79¡DLRUKMRUOPOP9LKMCaGPOHCJDLRZ 9LK+4OPOP9Q79LKH9±CJN°DF4 7(OP4KM74I!9QNJNV9gKMRI!CJDLC RN°oURUKMCJRUKM9»I9QN°ZWRUKMR8:9LOPKH4Sl\ 74 7OPKYRGP_`4KY8:RU¹WCJNV9 < } §V¨ ¬ ¶ë} ª §©µ ¨ §V¬¨ µ } ¬P ª ¬¨ ¬¨Hꧩ¨ ª µ ¬ ¨ ¬ê ª - < } Fí ¨ µ §V¨ ¬ } §VP¨ µYª ì ¬ · ¨ ¨P¬ §V¨ Pµ · ì ª ¨ ¬ P· ª©î º A 9 =+ 4 GPOP4 w Ì< k!OPKMRDLDLCJRUKH9CJN°DF4 7 OP4KY74SI9QNJNJ9qKYRI!CJDLC°I9QNEGMCJGPOP9Q8:RSef«h i = RN°oURUKMCJRUKH9»I9QNEZWRUKMR89LOPKH4l ã \ −5 −5. −4. −3. −2. −1. 0. 1. 2. 3. −20 −2. −1.5. −1. −0.5. 0. 0.5. 1. 1.5. 2. −8 −1. 0. 1. 2. 3. 4. 5. 6. luogo delle radici. luogo delle radici. 8. 30. 6. 20. 4. 10. 2. 0. 0. −2. −10. −4 −20. 7 4 7^I!CJGHZ4 7WCV¹WCJNV9 A _ =À 9LOP9LKM8:CJ7WRUKH9»Z 9LKÁ(cWRNJC oÂRNJ4KMC°I9QN°ZWRUKYR89LOPKH4SlXCJN°GHCJGHOP9Q8:R~KH9LOPKH4 RUTQCV4 7WRUOP4 9¡ RGHCa7 OP4OHCJDLR8:9Q7 OP9±GPOHRU¹WCJNV9\ <<UÙ à l à 74 7^I!CJGHZ4 7WCV¹WCJNV9 ~à l àï@Ù Ù A 6 =+À 9LOP9LKM8:Ca7!RUKH9»Z 9LKÁrc!RNV9oURNV4KH9»I!C°l£GHC°¯!RCaN°8:CJ7!CJ8:4OP9Q8Z 4SIWC°RGHGP9QGPOHR89Q7(OP4I!9QNEGHCJGPOP9Q8SR~KH9LOPKH4 RUTQCV4 7!RUOP4\ l A é ×(érð ñ çò -?rß @é 74 7^I!CJGHZ4 7WCV¹WCJNV9 l Ú<QérÙ<Uð ñ çò ºó×r<Q@< −6. −30. −16. −14. −12. −10. −8. −6. −4. −2. 0. 2. −8 −20. −15. −10. −5. 0. 5.
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