−8−6−4−202468−6−4−20246diagramma di Nyquist
6
0
0
Testo completo
(2) !"#$ % &')( +*,* -/.10,0 & 3254678 -97 #$ %:;7< =?>. @ ABDCE ; @GFHIKJ,L+H M5N F8BOJE. PRQ6STVUQ6WXQ6YXZ6UV[6U!Z]\+Q^WXQ6S_+`a+`+b,WXUWX`WdceUfce_+UVWXZhgigkj;lmUVTonkgkTV`YXQ5gkWXWXQ6Sa1g8ce`pQ^WXUYXUVWXq`a+j1gigkTVTVQrj+`smgka+j+Qkt u t vUwgxj1g8ce`iUVTWXQ6S_+Q6aceQWXUVWdceQ6smgUVaYXQyceYX`gk[6UV`a+Qkz }m~ 7~%X ~%X ~ l 6~" ~%X {| { { h~Dk u t g QyceQ6YXspUVa1gkYXQ5qQ6Y7_1gkTVUonkgkTV`YXUj+Q6Tq1gkYegkspQyceYX`iUVTWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`Q^ Wdc]gk+UVTVQkt u t `Wdce` k b,j+QyceQ6YXspUVa1gkYXQ3T Q6YXYX`YXQgpYXQ6SUVspQ 7~O j+Q6T WXUVWdceQ6smgpYXQyceYX`gk[6UV`a1g8ce`pUVaYXUVWXq`Wdc]gpgkU WXQ6S_+Q6aceU WXQ6Sa1gkTVUWXUUVa+SYXQ6WXWX`+z g ~%X b ~%X b Z ~%X t u t Z 3 YegkZ6Z6UwgkYXQ7_1gkTVUfc]g8ceUfnkgkspQ6aceQUVT 1¡e¢7¡i£7¤y%V¤r¥X¦£k§¨y§+j+Q6TVTwg^©-_+a+[6UV`a+Q }m~ gkT,nkgkYXUwgkYXQRj+Q6Toq1gkYegkspQyceYX` ªt YegkZ6Z6UwgkYXQmUVT TV_+`S`j+Q6TVTVQmYegkj+UVZ6U«WXUwg;qQ6Y¬ Z]\+QqQ6Yx¯® t±°²gkTVZ6`TwgkYXQpQ6Weg8cXc]gkspQ6aceQ TVQiUVaceQ6YXWXQ6[6UV`a+U³j+Q6T TV_+`S`Gj+Q6TVTVQYegkj+UVZ6UZ6`aT gkWXWXQiUVspsmgkSUVa1gkYXUV`+t QyceQ6YXspUVa1gkYXQxTwgq`WXUV[6UV`a+Qj+Q6U q+_+aceU!j+Uj+UVYegksmgk[6UV`a+QWX`TV`iUVasp`j+`´d7_1gkTVUfc]g8ceUfn`µ+t u t j `Wdce`¶· k bceYegkZ6Z6UwgkYXQ57_1gkTVUfc]g8ceUfnkgkspQ6aceQrUVT ¨]¡8¸1¹º¡8¥»¸o¡¶£7¤y%V¤^¥X¦£k§¨y§j+Q6TWXUVWdceQ6smgiYXQyceYX`gk[6UV`a1g8ce` gkTnkgkYXUwgkYXQrj+Q6Tq1gkYegkspQyceYX`plm¬ t°²gkTVZ6`TwgkYXQrQ6Weg8cXc]gkspQ6aceQkz g Twgxq`WXUV[6UV`a+Q5j+Q6STVUgkWXUVace`kceU¼ UVTspUVa+UVsp`3ceQ6spq`ij+U!gkWXWXQ6Wdc]gkspQ6ace`i½¿ ¾ j+Q6TWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`+¼ Z UVTonkgkTV`YXQ5l ¾ j+UlmZ6`YXYXUVWXq`a+j+Q6aceQ3gkTspUVa+UVsp`3ceQ6spq`ij+U!gkWXWXQ6Wdc]gkspQ6ace`i½ ¿ ¾ ¼ j qQ6Y7_1gkTVUonkgkTV`YXUoj+U!lmUVToWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`GQ5 Wdc]gk+UVTVQk¼ vU© gkZ6Z6UwgxYXUf©-Q6YXUVspQ6ace`\1gkUWXQ6S_+Q6aceU j+UwgkSYegkspspU,j+U!PÀ7_+UVWdcRQ^j+U!PRUVZ]\+`TVWj+Q6TVTwg©-_+a+[6UV`a+Q }xÁ6~ z diagramma di Nyquist. diagramma di Nichols. 6. 20 0.33 0.39. 10. 0.47 0.56. 4 db. 0.68. }xÁh~  7 +~~« u u . 0.82. 0. 1 1.2. 2. 1.5. −10 1.8 2.2. 0 1 0.82. −20. 1.5. 2.7 3.3. 0.68. −30 0.56. −2. 3.9 4.7 5.6. 0.47. −40. 6.8 8.2. 0.39. −4. 10. −50. 12. 0.33. 15. °`a;UVToSYegkj+`ij+Uq+YXQ6Z6UVWXUV`a+Q5Z6`a+WXQ6aceUfce`pj1gkUj+_+Q^j+UwgkSYegkspspUb7j+QyceQ6YXspUVa1gkYXQ5UWXQ6S_+Q6aceU!q1gkYegkspQyceYXUz g j+UVWXQ6Sa1gkYXQ^UVToj+UwgkSYegkspsmgq`TwgkYXQG´dZ6`spq+TVQyce`µ ~ Z]\+UV_+j+Q6YXQ^UVTj+UwgkSYegkspsmgxgkTVT UVaÃ1a+Ufce` ¼ j+UVYXQ5WXQ3UVaG1gkWXQ3gkTZ6YXUfceQ6YXUV`j+U!PÀ7_+UVWdcRUVTWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`GQ5 Wdc]gk+UVTVQkz a+`mļ WXU ļ Z UVTosmgkYXSUVa+Qrj+U© gkWXQ^j+Q6TWXUVWdceQ6smgz«ÅÇÆÈ ÂhÂh j UVTsmgkYXSUVa+Qrj+U!gkspq+UVQ6[6[hgj+Q6TWXUVWdceQ6smgz«ÅÇÉ; ÂhÂh Q j+QyceQ6YXspUVa1gkYXQ¶qQ6Y7_1gkTVU«nkgkTV`YXU«j+U«ÊËUVT«TV_+`S`Èj+Q6TVTVQ¶Yegkj+UVZ6Uj+Q6TVTwg;©-_+a+[6UV`a+Q }xÁ6~ UVaceQ6YXWXQ6Zhg±T gkWXWXQ UVspsmgkSUVa1gkYXUV`+zoÊ Á ÂhÂhÂ6ÂhÂh bÊ ÂhÂhÂ6ÂhÂh © j+QyceQ6YXspUVa1gkYXQqQ6Y7_1gkTVU!nkgkTV`YXUj+UÌUVT!WXUVWdceQ6smgm }xÁ6~ q`Wdce`¶UVaYXQyceYX`gk[6UV`a+Q_+a+Ufc]gkYXUwgGQ Wdc]gk+UVTVQkz ÂhÂhÂ6ÂhÂhÂ6ÂhÂhÂ6ÂhÂh S ©-`YXa+UVYXQ5_+a1gWdceUVsmgxj+Q6TVTwgxTwgkYXS\+Q6[6[hgij+U1gka+j1gij+Q6TWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`+z ÊÍ]β ÂhÂh vUwgxj1g8ce`iUVTWXQ6S_+Q6aceQWXUVWdceQ6smgz } ~ l 8Ï kÐ QyceQ6YXspUVa1gkYXQrqQ6Y7_1gkTVUonkgkTV`YXUoj+U!¬ UVToZ6`YXYXUVWXq`a+j+Q6aceQ3WXUVWdceQ6smgxYXQyceYX`gk[6UV`a1g8ce`GQ^ Wdc]gk+UVTVQkt 18. −6 −8. −60 −200. −6. −4. −2. 0. Ñ. 2. 4. 6. 8. 22. −190. −180. −170. −160. −150. −140. −130 gradi. −120.
(3) .
(4) ;`j+Q6a1g u gkSSUV` k u UVWXq`WdceQ u t g Q67_1gk[6UV`a+Q^ZhgkYeg8cXceQ6YXUVWdceUVZhgxj+Q6TWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`GQ5 TwgWXQ6S_+Q6aceQ 6~" ~k 1 ~ l X²" Klx u ~ ~l D k gZ6_+UZ6`YXYXUVWXq`a+j+Q^TwgxWXQ6S_+Q6aceQ3c]gkQ6TVTwgj+U `_ce\ ~ R l u k Kl ¬
(5) k ~kR 6~ R l l¬ u ~kR ~ R l Kl Kl ¬ _+UVa+j+UbUVTWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`YXUVWX_+Tfc]gxWdc]gk+UVTVQrWXQkz ~u ¬ l u l k ¾ ºaOZ6`YXYXUVWXq`a+j+Q6a+[hgªj+Q6TnkgkTV`YXQÈ ±¾6bUVTWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`q+YXQ6WXQ6ac]g/_+a1gªZ6`q+q+Uwgj+Uq`TVU Z6`spq+TVQ6WXWXUZ6`a+UV_+Sg8ceUWX_+TVT gkWXWXQ^UVspsmgkSUVa1gkYXUV`^ZhgkYeg8cXceQ6YXUV[6[hg8ceUj1gkTVTwgxq+_+TVWegk[6UV`a+Qkz Ê ¾
(6) l u k u t x Q6Y· k UVTWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`¶Qr Wdc]gk+UVTVQkt vUVZ6Z6`spQUVTWXUVWdceQ6smgmQr j+UceUVq` bq+YXQ6WXQ6ac]gi_+aQ6YXYX`YXQ gmYXQ6SUVspQ3a7_+TVTV`¶qQ6YUVa+SYXQ6WXWX`GgmSYegkj+UVa+`¶QxqQ6YUVa+SYXQ6WXWX`GgmYegkspq1gt5PRQ6T$ZhgkWX`j+U$UVa+SYXQ6WXWX`¶q1gkYegk`TVUVZ6`+b T Q6YXYX`YXQ^gYXQ6SUVspQQ5 Z6`Wdc]gkaceQ3Q5nkgkTVQkz ¿ Î l u l ¿ u t Z gka+j1gkspQ6ace`R7_1gkTVUfc]g8ceUfn`j+Q6T7TV_+`S`Rj+Q6TVTVQ Yegkj+UVZ6Uj+Q6TVTwg²©-_+a+[6UV`a+Q }m~ qQ6Y$l Q¬ Q« YXUVq`Ydc]g8ce` UV a $UVS+t u t ºToTV_+`S`j+Q6TVTVQRYegkj+UVZ6UqQ6Y²l Qr® Qr YXUVq`Ydc]g8ce`3UV a $UVS+t QrUVaceQ6YXWXQ6[6UV`a+UZ6`aT gkWXWXQ luogo delle radici 80. 60. 40. 20. 0. −20. −40. −60. −80 −160. −140. −120. −100. −80. −60. −40. −20. 0. Ñ UVspsmgkSUVa1gkYXUV`^WXU\1gka+a+`pUVaGZ6`YXYXUVWXq`a+j+Q6a+[hgij+Q6UnkgkTV`YXUoj+U!±¾Q^j+Uoʾ²ceYX`nkg8ceUgkTq+_+ace` u t g t u t j x `Wdce`m· k b+T Q67_1gk[6UV`a+Q^ZhgkYeg8cXceQ6YXUVWdceUVZhgxj+Q6TWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce`j+UfnQ6ac]gz 6~" u k1~ ~l D k vQ^WXUQ6WXq+TVUVZ6Ufc]gxUVToq1gkYegkspQyceYX`plmWXU`kcXceUVQ6a+Qkz u l h8~Dkk1~«D"k 7~ " u l 7~hk 1~" u k !#"$&% #')( "*#!#*,+.-0/ / -$&%#+.2134+.-0/ /2%657"890 *#8-;:=<?>A@CBD-0$FE,GHJI-;KMLIN. O. .
(7) luogo delle radici 40. 30. 20. 10. 0. −10. −20. −30. −40 −70. −60. −50. −40. −30. −20. −10. 0. 10. 20. !#"$&% O.')( "*#!#*,+.-0/ / -$&%#+.2134+.-0/ /2%657"890 *#8-;:=<?>A@CBD-0$FE,GHJI-;K. IN. luogo delle radici 40. 30. 20. 10. 0. −10. −20. −30. −40 −80. −70. −60. −50. −40. −30. −20. −10. !#"$&% ' *#8 *#$ 8*,+.-0/ / - $&%#+.213?N. . 0. 10. 20.
(8) ºTrWXUVWdceQ6smgª\1g q`TVUzÇ_+a+` a+Q6TVT `YXUVSUVa+Q;Q±STVUrgkTfceYXURj+_+Q)UVa 8Á k k t gka+j1gkspQ6ace` 7_1gkTVUfc]g8ceUfn`xj+Q6TUVTZ6`ace`YXa+`pj+Q6TVTVQrYegkj+UVZ6UYXUVq`Ydc]g8ce`UVa $UVS+t+t g ºTZ6`ace`YXa+`i\1g gkWXUVace`kceUonQ6YdceUVZhgkTVUUVTZ6_+UZ6Q6aceYX`Q u ~ k kR" u gGZ6`a+j+UV[6UV`a+Qpj+U spUVa+UVsp`mceQ6spq`j+U«gkWXWXQ6Wdc]gkspQ6ace`ÈWXU \1g;7_1gka+j+`ÈTVQp;Yegkj+UVZ6U³j+Q6T«WXUVWdceQ6smgGWX`a+` gkTVTVUVa+Qhg8ceQkbZ6UV`+Q5 7_1gka+j+` ~ UVaG1gkWXQ3gkTceQ6`YXQ6smgj+Q6T1gkYXUVZ6Q6aceYX` z ¿ ¿ ºTceQ6spq`j+U!gkWXWXQ6Wdc]gkspQ6ace`pnkgkTVQ57_+UVa+j+U ½ ¿
(9) ¿ Z ºTonkgkTV`YXQ5j+U!l7¾WXUZhgkTVZ6`Twgxa+Q6Tsp`j+`WXQ6S_+Q6aceQkz l ¾ }mu~ u Â Ð Ï j nkgkTV`YXUj+Ul5qQ6Y$Z6_+UUVT7WXUVWdceQ6smgRYXQyceYX`gk[6UV`a1g8ce`Q Wdc]gk+UVTVQ WXUj+QyceQ6YXspUVa1gka+`YXUVWX`TfnQ6a+j+`TwgRj+UVWXQ67_1gk[6UV`a+Q ~ u YXUVWXqQycXce`pgkj;lmj+`q`pghnQ6YRq`Wdce`p· k z k ¬ u k R l l ® lm® u k l ¾ ,gkZ6Q6a+j+`iYXUf©-Q6YXUVspQ6ace`igkUj+_+Q3j+UwgkSYegkspspU,WXU`kcXceUVQ6a+Q^Z]\+Qkz g UVTj+UwgkSYegkspsmg«q`TwgkYXQ3´dZ6`spq+TVQyce`µWXUZ]\+UV_+j+Q«gkTVT UVaÃ1a+Ufce`UVa+WXQ6YXQ6a+j+`_+a1gWXQ6spUVZ6UVYXZ6`a©-Q6YXQ6a+[hgqQ6YXZ6`YXWeg UVaGWXQ6a+WX`p`YegkYXUV`Z]\+Q3q1gkYdceQ^j1gkTVT gkTfce`Q5ceQ6YXspUVa1gxUVaG1gkWXWX`+¼ UVaG1gkWXQ3gkTZ6YXUfceQ6YXUV`j+U!PÀ7_+UVWdcRUVTWXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce ` ± 4y $ - ¼ Z UVTosmgkYXSUVa+Qrj+U© gkWXQ^j+Q6TWXUVWdceQ6smgQ ÅÇ Æ u ¼ j UVTsmgkYXSUVa+Qrj+U!gkspq+UVQ6[6[hgj+Q6TWXUVWdceQ6smgQ3 ÅÇÉ u  u j+¼ Q UVTTV_+`S`j+Q6TVTVQxYegkj+UVZ6Uj+Q6TVTwgm©-_+a+[6UV`a+Q }xÁ6~ UVaceQ6YXWXQ6ZhgGT gkWXWXQiUVspsmgkSUVa1gkYXUV`iUVa)Z6`YXYXUVWXq`a+j+Q6a+[hgj+Q6U q+_+aceUz$Ê Á u  bÊ ¼ © UnkgkTV`YXUoj+U! qQ6YZ6_+UUVTWXUVWdceQ6smgi }xÁ6~ q`Wdce`pUVaYXQyceYX`gk[6UV`a+Q5_+a+Ufc]gkYXUwg¶Q^ Wdc]gk+UVTVQrWX`a+`+z ® ® u  u ¬ u  5j+ S _+a1giWdceUVsmgxj+Q6TVTwgxTwgkYXS\+Q6[6[hgj+U1gka+j1gj+Q6T!WXUVWdceQ6smgxYXQyceYX`gk[6UV`a1g8ce`GQ ÊÍ]Î u t ºT!WXUVWdceQ6smg } ~ Q3 _+aWXUVWdceQ6smgiZ6`spq`Wdce`mj1gp_+aYXUfc]gkYXj+`Ã1a+Ufce`mUVa;ZhgkWXZhg8c]gmgkj_+aUVaceQ6SYeg8ce`YXQkt gkTVQ WXUVWdceQ6smgQ^ Wdc]gk+UVTVQrqQ6Y . ® l ®"! Î #! ® ®$! l Twgxq+YXUVsmgxUVaceQ6YXWXQ6[6UV`a+Q^Z6`a;UVToWXQ6spUwgkWXWXQ^a+Q6Sg8ceUfn`iWXU!\1gUVaGZ6`YXYXUVWXq`a+j+Q6a+[hgij+Q6TVTwgxq+_+TVWegk[6UV`a+Q Ê/% !. H. .
(10) @;ABDCE 52 461È4h8 %h . @GFHIKJ,L+H
(11) ;`j+Q6a1g u gkSSUV` k u M5N F8BOJE `smgka+j+Q Q6`YXUVZ]\+Q Q6Y5Z6UwgkWXZ6_+a+`j+Q6UWXQ6S_+Q6aceU$ceQ6Wdc^WXQ6Sa1gkYXQZ6`a±_+a1g¶Z6YX`Z6QycXc]g¶TVQgoQ6YXsmgk[6UV`a+U!Z]\+QWXUYXUfceQ6a+S`a+`¶SUV_+WdceQktT Z6_+a+U«ceQ6WdcWX`a+`ÈWXQ6S_+UfceUj1gq+Ue_ goQ6YXsmgk[6UV`a+U SUV_+WdceQmQ¶WXU«Z6`a+WXUVj+Q6Yegka+`±WX_+qQ6Yeg8ceU7_1gka+j+`È7_+Q6WdceQ¶nQ6a+S`a+` Z6`aceYegkWXWXQ6Sa1g8ceQ^ce_cXceQkt u t YXQ6SUVspQkb+_+a;WXUVWdceQ6smgj+U´ ceUVq` µiq`Wdce`pUVaGYXQyceYX`gk[6UV`a+Q5_+a+Ufc]gkYXUwg¶Q5 UVaGSYegkj+`ij+UUVa+WXQ6S_+UVYXQ _+a;YXUf©-Q6YXUVspQ6ace`q1gkYegk`TVUVZ6`xZ6`a;_+a;Q6YXYX`YXQ^j+UUVa+WXQ6S_+UVspQ6ace`ia7_+TVTV`+¼. _+a;YXUf©-Q6YXUVspQ6ace`q1gkYegk`TVUVZ6`xZ6`a;_+a;Q6YXYX`YXQ^j+UUVa+WXQ6S_+UVspQ6ace`Ã1a+Ufce`+¼. _+a;YXUf©-Q6YXUVspQ6ace`igYegkspq1gZ6`aG_+a;Q6YXYX`YXQ^j+UUVa+WXQ6S_+UVspQ6ace`ia7_+TVTV`+¼ _+a;YXUf©-Q6YXUVspQ6ace`igYegkspq1gZ6`aG_+a;Q6YXYX`YXQ^j+UUVa+WXQ6S_+UVspQ6ace`Ã1a+Ufce`+¼ t³PRQ6T7ZhgkWX`j+U7WXUVWdceQ6spUgYXQyceYX`gk[6UV`a+Q«a+`a3_+a+Ufc]gkYXUwgbqQ6Y UVTZhgkTVZ6`TV`j+Q6TVT Q6YXYX`YXQ«gYXQ6SUVspQ 7~%X ~%X
(12) ~%X Q q`WXWXUV+UVTVQ3_ceUVTVUV[6[hgkYXQ^TVQ3WdceQ6WXWXQ©-`YXsx_+TVQ5ceYX`nkg8ceQqQ6YrUVT!ZhgkWX`gmYXQyceYX`gk[6UV`a+Q_+a+Ufc]gkYXUwgiWXQxWXU _ceUVTVUV[6[hgpgkT q`Wdce`ij+U }m~ Twgx©-_+a+[6UV`a+Q } h~ Á Ð Ð Ð Ï } h~ Á Ð Á ÐÏ Ð . } h~ Á Ð Ð Ð Ï } h~ Á Ð Ð Ð Ï Á t vUwg u }m~ T Q67_1gk[6UV`a+QxZhgkYeg8cXceQ6YXUVWdceUVZhgpj+U$_+a±WXUVWdceQ6smgmYXQyceYX`gk[6UV`a1g8ce`gkT!nkgkYXUwgkYXQj+U ¬ t Q¶Yegkj+UVZ6Uj+`q+q+UVQ ~ gka+Z]\+QG7_+Q6TVTVQ¶Z6`spq+TVQ6WXWXQ j+Q6TZ6`YXYXUVWXq`a+j+Q6aceQTV_+`S`Èj+Q6TVTVQmYegkj+UVZ6U²gkT«nkgkYXUwgkYXQmj+Q6T q1gkYegkspQyceYX`iWX`a+`ice_cXceQ5Q^WX`TVQ^TVQ5WX`TV_+[6UV`a+U j+Q6TVT Q67_1gk[6UV`a+QÐ Ð . j+Q6T!WXUVWdceQ6smgxj+UQ67_1gk[6UV`a+Uz u }m~ bÐ Ð j+Q6T!WXUVWdceQ6smgxj+UQ67_1gk[6UV`a+Uz u }m~ bÐ Ð b Ð Ð t vUwg } Î ~ UVT1WXUVWdceQ6smggkjgka+Q6TVTV`^Z]\+UV_+WX`xZ6`YXYXUVWXq`a+j+Q6aceQrgkT,WXUVWdceQ6smg3TVUVa+QhgkYXQ }m~ q`Wdce`UVamYXQyceYX`gk[6UV`a+Q _+a+Ufc]gkYXUwga+Q6Sg8ceUfnkgt «TV_+`S\+UgkjP Z6`Wdc]gkaceQ3WX`a+`iUq+_+aceU!j+Q6Tq+Uwgka+`Z6`spq+TVQ6WXWX`pj+`nQ Q^ Z6`Wdc]gkaceQ3UVTsp`j+_+TV`xj+U }m~ Ê Q^ Z6`Wdc]gkaceQ3UVTsp`j+_+TV`xj+U } Î ~ Ê Q^ Z6`Wdc]gkaceQ3Twg© gkWXQ^j+U }m~ Ê . Q^ Z6`Wdc]gkaceQ3Twg© gkWXQ^j+U } Î ~ Ê t ºTTV_+`S`j+Q6TVTVQrYegkj+UVZ6Uq+YXQ6WXQ6ac]gmgkTVspQ6a+`_+agkWXUVace`kce`nQ6YdceUVZhgkTVQ ~ "! $# ¬ Q^ UVToSYegkj+`iYXQ6Twg8ceUfn` . 7_1gka+j+` Q3 Á Q5 q`WXUfceUfnkg 7_1gka+j+` Q3 Á Q5 a+Q6Sg8ceUfnkg 7_1gka+j+` Q3 Á Q5 q`WXUfceUfnkg. 7_1gka+j+` Q3 Á Q5 a+Q6Sg8ceUfnkg t&%Ra;WXUVWdceQ6smgxZ6`a;YXUfc]gkYXj+` }m~ ')Ð (+* q`Wdce`iUVaGYXQyceYX`gk[6UV`a+Q5Z6`a;_+a;S_1gkj1gkSa+`p. Q^ _+a;WXUVWdceQ6smgTVUVa+QhgkYXQ. q+YXQ6WXQ6ac]gp_+a;Q6YXYX`YXQ3ga7_+TVTV`iqQ6YUVa+SYXQ6WXWX`mgSYegkj+UVa+`_+a+Ufc]gkYXUV` Q^ _+a;WXUVWdceQ6smgigx© gkWXQ^spUVa+UVsmg. UVTWX_+`pj+UwgkSYegkspsmg3j+U!PÀ7_+UVWdcRceQ6a+j+Q3gkTVT `YXUVSUVa+QRQ6j;\1giUVaÃ1a+UfceQrUVaceQ6YXWXQ6[6UV`a+UZ6`a;T gkWXWXQ5YXQhgkTVQ Q^ Wdc]gk+UVTVQ5qQ6Y`Sa+UnkgkTV`YXQrj+U! ,.
(13) t º a;Z6`YXYXUVWXq`a+j+Q6a+[hgj+U_+a1giYegkj+UVZ6Q5sx_+TfceUVq+Twgj+U`YXj+UVa+Q UVTTV_+`S`j+Q6TVTVQ5Yegkj+UVZ6U q+YXQ6WXQ6ac]g YegkspUQ6aceYegkaceU. q+YXQ6WXQ6ac]g YegkspUQ6aceYegkaceUQ YegkspUo_+WXZ6Q6aceU. UYegkspUQ6aceYegkaceUWXU!gkTfceQ6YXa1gka+`pg7_+Q6TVTVU_+WXZ6Q6aceU. TVQrc]gka+SQ6aceU!gkUYegkspUoQ6aceYegkaceU!Q6j;_+WXZ6Q6aceU!j+UfnUVj+`a+`iUVToq+Uwgka+`iUVaGWXQycXce`YXUj+U!gkspq+UVQ6[6[hg t ºTceQ6`YXQ6smgxj+Q6T!1gkYXUVZ6Q6aceYX`ij+Q6TTV_+`S`j+Q6TVTVQ5Yegkj+UVZ6UWXU!gkq+q+TVUVZhg WX`TV`pgx©-_+a+[6UV`a+U }m~ Z6`a;SYegkj+`iYXQ6Twg8ceUfn` u. WX`TV`pgx©-_+a+[6UV`a+U }m~ Z6`a;SYegkj+`iYXQ6Twg8ceUfn` WX`TV`pgx©-_+a+[6UV`a+U }m~ Z6`a;SYegkj+`iYXQ6Twg8ceUfn` t³WXPRUQ6© TVgTwgmT WXUVqQ6Z6`k`cea+Q6WXj1Uog¶Z]\+©-`Q3YXsxUVT_+WXUVTwWdgkce[6Q6UVsm`a+gQ3b+j+`Q6TfceT³YXQ5Z6YXgiUfceQ6qYX`kUV`mceQ6j+YU³ghnPQ6ÀYX7Q3_+_+UVWda;chbq7`_+TV`Q6TVWXTwQ6gmspnkq+gkTVTVUVUVZ6j1Q5gm`igka+j+Z]`\+q+Qiq+UVq`iQ6Yra+Q6WXTVUVTWd ce`Q6YXspUVSU^UVa+´dQkUVb a+Wdc]gk+UVTVUVµ+b WXUwgig© gkWXQ5spUVa+UVsmg gk++Uwgq`TVUoWXQ6spq+TVUVZ6UWX_+TVT gkWXWXQ5UVspsmgkSUVa1gkYXUV`. a+`agk++Uwgq`TVUoWX_+TVT gkWXWXQ^UVspsmgkSUVa1gkYXUV` a+`a;WXU© gka+a+`iUVq`kceQ6WXU!gkSSUV_+aceUfnQ u t g8ce`_+aWXUVWdceQ6smg }m~ bqQ6YZhgkTVZ6`TwgkYXQ«UVTS_1gkj1gkSa+`rWdc]g8ceUVZ6`rj+Q6T+WXUVWdceQ6smgYXQyceYX`gk[6UV`a1g8ce` } Î ~ Á Ð Ð _ceUVTVUV[6[hgka+j+`xUTV_+`S\+Ugkj Z6`Wdc]gkaceQ3WXUj+QynQ3TVQ6SSQ6YXQ5UVTonkgkTV`YXQ^Å j+Q6TVTwgxq+Ue_ q+UVZ6Z6`TwgZ6UVYXZ6`a©-Q6YXQ6a+[hgiQ6WdceQ6YXa1giQ5c]gka+SQ6aceQ3gkTj+UwgkSYegkspsmg3q`TwgkYXQrZ6`spq+TVQyce` }m~ Ê j+Q6TVTwgxq+Ue_ SYegka+j+Q^Z6UVYXZ6`a©-Q6YXQ6a+[hgiUVaceQ6YXa1gQ5c]gka+SQ6aceQgkTj+UwgkSYegkspsmg3q`TwgkYXQ5Z6`spq+TVQyce` }m~ Ê . j+Q6TVTwgxZ6UVYXZ6`a©-Q6YXQ6a+[hgiZ]\+Q3q1gkWXWegiqQ6YUVTq+_+ace` }m~ j+Q6TVTwgxZ6UVYXZ6`a©-Q6YXQ6a+[hgiZ]\+Q3q1gkWXWegiqQ6YUVTq+_+ace` }m~ uu t _1gka+j+`;Q5 q`WXWXUV+UVTVQr_ceUVTVUV[6[hgkYXTV`+b7UVTspQyce`j+`ij+Q6TZ6`ace`YXa+`pj+Q6TVTVQrYegkj+UVZ6UWXU!gkq+q+TVUVZhg gkUWX`TVUWXUVWdceQ6spUTVUVa+QhgkYXUoZ6`a;YXQyceYX`gk[6UV`a+Q5_+a+Ufc]gkYXUwg gkUWX`TVUWXUVWdceQ6spUTVUVa+QhgkYXUoZ6`a;YXQyceYX`gk[6UV`a+Q^gkTVSQ6+YXUVZhg. gkUWXUVWdceQ6spUTVUVa+QhgkYXUoZ6`a;YXQyceYX`gk[6UV`a+Q57_1gkTV_+a+7_+Q u t ºTZ6`ace`YXa+`xj+Q6TVTVQYegkj+UVZ6U,Wdce_+j+UwgbWX_+Toq+Uwgka+`Z6`spq+TVQ6WXWX`+bTVQRZ6_+YdnQ5j+Q6WXZ6YXUfcXceQrj1gkTVTVQYegkj+UVZ6Uj+Q6TVT Q67_1gk[6UV`a+Q ZhgkYeg8cXceQ6YXUVWdceUVZhggkTonkgkYXUwgkYXQ5j+U_+a;q1gkYegkspQyceYX`+t gkTVQ5q1gkYegkspQyceYX` q+_ `p Q6WXWXQ6YXQ_+aGq1gkYegkspQyceYX`i7_1gkTV_+a+7_+Q^j+Q6TVT Q67_1gk[6UV`a+Q5ZhgkYeg8cXceQ6YXUVWdceUVZhg. j+QynQQ6WXWXQ6YXQ3_+a;q1gkYegkspQyceYX`Z]\+Q3Q6aceYegiTVUVa+QhgkYXspQ6aceQ5a+Q6TVT Q67_1gk[6UV`a+QrZhgkYeg8cXceQ6YXUVWdceUVZhg j+QynQQ6WXWXQ6YXQ3_+a1giZ6`Wdc]gkaceQ^j+UceQ6spq`iYXQ6Twg8ceUfnkgxgkj;_+a;q`TV``pgkj;_+a+`i[6Q6YX`pj+Q6TWXUVWdceQ6smg u t Q6Y3Wdce_+j+UwgkYXQpUVaÇsp`j+` ´dQ6Weg8cXce`µ;TwgGWdc]gk+UVTVUfc8g¶ j+U _+aWXUVWdceQ6smg;g;YXUfc]gkYXj+`Ã1a+Ufce`;UVaÇYXQyceYX`gk[6UV`a+QpWXU q+_ ` _ceUVTVUV[6[hgkYXQ UVTZ6YXUfceQ6YXUV`j+U `_ce\. UVTZ6YXUfceQ6YXUV`j+U!PÀ7_+UVWdc UVTTV_+`S`j+Q6TVTVQ5Yegkj+UVZ6U u t³vUwgka+`/ÅÇÎ }m~ Q6jÅ Á Ìsmg }m~ Ê bYXUVWXqQycXceUfnkgkspQ6aceQkbUVTS_1gkj1gkSa+`ªWdc]g8ceUVZ6` Q±UVTnkgkTV`YXQ smgkWXWXUVsp`±j+Q6Tsp`j+_+TV`±j+Q6TVTwgÈ©-_+a+[6UV`a+QGj+UYXUVWXq`Wdc]g)gkYXsp`a+UVZhg±j+Q6TWXUVWdceQ6smg)TVUVa+QhgkYXQ¶Wdc]gk+UVTVQ }m~ t ºT q+UVZ6Z6`ij+UYXUVWX`a1gka+[hgp Å
(14) ±j+Q6TWXUVWdceQ6smg }m~ Q^ j+QyÃ1a+Ufce`iZ6`spQ5WXQ6S_+Q Å
(15) ; Å Á. Å
(16) ; Å
(17) ; Å Á ÅÇÎ. Å
(18) ; Å Á /ÅÇÎ ~ WXQÅÇÎb,Å Á Q6jÈ Å
(19) ÈWX`a+`pQ6WXq+YXQ6WXWXU UVaGj+ . .
(20)
Documenti correlati
[r]
ereditate
Se si verifica
Nel caso in cui invece A sia invertibile, si calcoli la matrice inversa A
- se valgono convessità delle preferenze e ottimo interno, la tangenza è necessaria e sufficiente per ottimo, - se vale solo convessità potremmo avere un ottimo di frontiera
[r]
Trovare il valore ottimale della costante C j per ciascuna variabile
equivalente alla densità di probabilità della