Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del...

8
1 0,1,67(5,2’((’8&$&,21 8 81 1, ,9 9( (5 56 6, ,$ $1 1$ $& &, ,2 21 1$ $/ /( ( 6 6$ $1 1 - -8 8$ $1 1 ) )$ $& &8 8/ /7 7$ $( ( , ,1 1* *( (1 1, ,( (5 5, ,$ $ 5 5V VU US Sd d_ _T TU U\ \Q QW Wb bU UW WQ QT T_ _T TU U_ _\ \_ _c ci i S SU Ub b_ _c cQ Q\ \Q Qc c6 6e e^ ^S SY Y_ _^ ^U Uc cT TU U D Db bQ Q^ ^c cV VU Ub bU U^ ^S SY YQ Q 1 1e ed d_ _b b* * 4 4b b 9 9^ ^W W : :_ _c c} }6 6 @ @? ?C CD D9 97 7? ? 3 3v vd dU UT Tb bQ Q* * 3 3_ _^ ^d db b_ _\ \9 9 3 3Q Qbb bbU Ub bQ Q* * 9 9^ ^W WU U^ ^Y YU Ub bQ QQ Q5 5\ \U US Sd db bV V^ ^Y YS SQ Q 4 4U UQ Qb bd dQ Q] ]U U^ ^d d_ _T TU U5 5\ \U US Sd db bV V^ ^Y YS SQ Q 1 1e ed d_ _] ]v vd dY YS SQ Qi i2 2Y Y_ _Y Y^ ^W WU U^ ^Y YU Ub bQ QQ Q 1 1U U_ _" " # #

Transcript of Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del...

Page 1: Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del agregado de polos y ceros a las Funciones de Transferencia de Lazo Abierto y de Lazo

1

0,1,67(5,2���'(���('8&$&,218811,,99((5566,,''$$'�'� 11$$&&,,2211$$/��/��''(�(� 66$$1�1�--88$$11))$$&&88//77$$'�'� ''(�(� ,,11**((11,,((55,,$$55VVUUSSdd_�_�TTUU\�\�QQWWbbUUWWQQTT_�_�TTU�U�`̀__\\__c�c�iiSSUUbb__c�c�Q�Q�\\QQc�c�66ee^̂SSYY__^̂UUc�c�TTUUDDbbQQ^̂ccVVUUbbUU^̂SSYYQQ

11eedd__bb*�*� 44bb����99^̂WW����::__cc}�}�66����@@??CCDD9977??33vvddUUTTbbQQ** 33__^̂ddbb__\�\�9933QQbbbbUUbbQQ*�*� 99^̂WWUU^̂YYUUbb��Q�Q�55\\UUSSddbb��^̂YYSSQQ44UU`̀QQbbddQQ]]UU^̂dd_�_�TTU�U�55\\UUSSddbb��^̂YYSSQQ��11eedd__]]vvddYYSSQ�Q�i�i�22YY__YY^̂WWUU^̂YYUUbb��QQ

����11��_�_�"" #�#���

Page 2: Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del agregado de polos y ceros a las Funciones de Transferencia de Lazo Abierto y de Lazo

2

55VVUUSSdd_�_�TTUU\�\�QQWWbbUUWWQQTT_�_�TTU�U�`̀__\\__c�c�i�i�SSUUbb__c�c�Q�Q�\\QQc�c�66ee^̂SSYY__^̂UUc�c�TTUUDDbbQQ^̂ccVVUUbbUU^̂SSYYQ�Q�TTU�U�<<QQjj_�_�11RRYYUUbbdd_�_�i�i�TTU�U�<<QQjj_�_�33UUbbbbQQTT__5^�\Q�`bvSdYSQ��U\�TYcU�_�UhYd_c_�TU�e^�cYcdU]Q�TU�S_^db_\�^_�`eUTU�TU`U^TUb�c_\Q]U^dU�TU�\Q�cU\USSY�^TU� \_c� `Qbv]Udb_c� TU\� cYcdU]Q�� TU� dQ\� V_b]Q� TU� S_\_SQb� Q`b_`YQTQ]U^dU� \Qc� bQ�SUc� TU� \Q� USeQSY�^SQbQSdUb�cdYSQ��CU�]_cdbQbv�aeU�QQ��^�^�SSeeQQ^̂TT_�_�\\QQc�c�bbQQ��SSUUc�c�TTU�U�\\Q�Q�UUSSeeQQSSYY��^�^�SSQQbbQQSSddUUbb��ccddYYSSQQ����aaeeU�U�cc__^�^�\\__c�c�`̀__\\__ccTTU�U�\\Q�Q�VVee^̂SSYY��^�^�TTU�U�ddbbQQ^̂ccVVUUbbUU^̂SSYYQ�Q�TTU�U�\\QQjj_�_�SSUUbbbbQQTT__����QQVVUUSSddQQ^�^�\\Q�Q�bbUUcc`̀eeUUccddQ�Q�ddbbQQ^̂ccYYdd__bbYYQ�Q�TTU�U�ccYYccddUU]]QQc�c�TTU�U�SS__^̂ddbb__\\\Y\Y^̂UUQQ\\UUc�c�YY^̂ffQQbbYYQQ^̂ddUUc�c�SS__^�^�UU\�\�ddYYUU]]`̀__����`̀QQbbddYYSSee\\QQbb]]UU^̂ddU�U�\\Q�Q�UUccddQQRRY\Y\YYTTQQT�T�TTU�U�\\__c�c�]]YYcc]]__����\\__c�c�SSUUbb__c�c�TTU�U�\\Q�Q�VVee^̂SSYY��^̂TTU�U�ddbbQQ^̂ccVVUUbbUU^̂SSYYQ�Q���ccY�Y�UUhhYYccddUU^̂������cc__^�^�ddQQ]]RRYY}}^�^�YY]]`̀__bbddQQ^̂ddUUcc�� 5c�`_b�U\\_�aeU��\Q�QTYSY�^�TU�`_\_c�i�SUb_c�i�_SQ^SU\QSY�^�TU�`_\_c� Y^TUcUQR\Uc�i�SUb_c�TU� \Q�Ve^SY�^�TU�dbQ^cVUbU^SYQ��Q�]U^eT_�^_�c_^�^USUcQbY_c`QbQ�Q\SQ^jQb�cQdYcVQSd_bYQ]U^dU�U\�TUcU]`U�_�TUcUQT_�U^�U\�T_]Y^Y_�TU\�dYU]`_�TU�\_c�cYcdU]Qc�TUS_^db_\��1� S_^dY^eQSY�^� cU�]eUcdbQ� aeU� \Q� QTYSY�^� TU� `_\_c� i� SUb_c� Q� \Q� 6D<1� i� 6D<3� dYU^U� UVUSd_cfQbYQ^dUc�U^�\Q�bUc`eUcdQ�dbQ^cYd_bYQ�TU\�cYcdU]Q�U^�\Qj_�SUbbQT_�!!�� 11TTYYSSYY��^�^�TTU�U�ee^�^� `̀__\\_�_�UU^�^� \\Q�Q�66ee^̂SSYY��^�^�TTU�U�ddbbQQ^̂ccVVUUbbUU^̂SSYYQ�Q�TTU�U� \\Q�Q�ddbbQQiiUUSSdd__bbYYQ�Q�TTYYbbUUSSddQ�Q� ��66DD<<11��**CCYYccddUU]]QQc�c�SS__^�^�bbUUQQ\Y\Y]]UU^̂ddQQSSYY��^�^�ee^̂YYddQQbbYYQQ

Page 3: Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del agregado de polos y ceros a las Funciones de Transferencia de Lazo Abierto y de Lazo

3

=YU^dbQc�U\�fQ\_b�TU�D` cU�Y^SbU]U^dQ��U\�`_\_�eRYSQT_�U^�°!�D` cU�Q`b_hY]Q�Q\�_bYWU^�TU\�`\Q^_�²c³��i�U\]vhY]_� c_RbUY]`e\c_� _� c_RbU`Qc_� Qe]U^dQ�� 5cdQc� bUc`eUcdQc� dQ]RY}^� ]eUcdbQ^� aeU� UU\�\� `̀__\\__QQTTYYSSYY__^̂QQTT_�_� YY^̂SSbbUU]]UU^̂ddQ�Q�UU\�\�ddYYUU]]`̀_�_�TTU�U�SSbbUUSSYY]]YYUU^̂dd_�_�TTU�U� \\Q�Q� bbUUcc`̀eeUUccddQ�QQ� Q\�\� UUccSSQQ\\��^�^�TTUU\�\�ccYYccddUU]]QQ�� 5cd_� ^_� Ucc_b`bU^TU^dU�� `eUcd_� aeU� UU\�\� `̀__\\_�_� QQTTYYSSYY__^̂QQ\�\� ddYYUU^̂U� UU� U\�\� UUVVUUSSdd_�_� TTU�U� bbUUTTeeSSYYb�b� UU\�\� QQ^̂SSXX_�_� TTU�U� RRQQ^̂TTQ�Q� ��1122���� TTUU\\ccYYccddUU]]Q�Q� �Ucd_� cU� fUbv� S_^�]vc� `b_Ve^TYTQT� SeQ^T_�cU� dbQdU� U\� Q^v\YcYc� VbUSeU^SYQ\� TU� cYcdU]Qc� TUS_^db_\�\Y^UQ\Uc�Qed�^_]_c���5\�UVUSd_�TU�bUTeSYb�U\�1122�� XQSU�aeU�cU�bUS_bdU^�\_c�S_]`_^U^dUc�TU�Q\dQVbUSeU^SYQ�TU�\Q�cU�Q\�dbQ^c]YdYTQ�Q�dbQf}c�TU\�cYcdU]Q�<Qc�]Yc]Qc�S_^S\ecY_^Uc�Q^dUbY_bUc�cU�`eUTU^�_RdU^Ub�Q�`QbdYb�TU�\Qc�bUc`eUcdQc�Q\�UcSQ\�^�e^YdQbY_TU�\Q�6YW��'�#!��aeU�VeUb_^�_RdU^YTQc�S_^� .0.1667.0,2.0,0,25.0,1 \7\ SQ === GZ 5^�UcdU�SQc_SeQ^T_� D` Uc�]Qi_b� Q� �&&'�� \Q� Q]`\YdeT� TU� \Q� bUc`eUcdQ� Q\� UcSQ\�^� e^YdQbY_� cU� Y^SbU]U^dQ� S_^� U\dYU]`_��i�U\�cYcdU]Q�Uc�YY^̂UUccddQQRR\\UU��

""�� 11TTYYSSYY��^�^�TTU�U�ee^�^�`̀__\\_�_�UU^�^�\\Q�Q�VVee^̂SSYY��^�^�TTU�U�ddbbQQ^̂ccVVUUbbUU^̂SSYYQ�Q�TTU�U�\\QQjj_�_�SSUUbbbbQQTT_�_���66DD<<33��

Page 4: Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del agregado de polos y ceros a las Funciones de Transferencia de Lazo Abierto y de Lazo

4

##�� 11TTYYSSYY��^�^�TTU�U�ee^�^�SSUUbb_�_�UU^�^�\\Q�Q�VVee^̂SSYY��^�^�TTU�U�ddbbQQ^̂ccVVUUbbUU^̂SSYYQ�Q�TTU�U�\\QQjj_�_�SSUUbbbbQQTT_�_���66DD<<33��

Page 5: Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del agregado de polos y ceros a las Funciones de Transferencia de Lazo Abierto y de Lazo

5

Page 6: Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del agregado de polos y ceros a las Funciones de Transferencia de Lazo Abierto y de Lazo

6

$$�� 11TTYYSSYY��^�^� TTU�U� ee^�^� SSUUbb_�_� UU^�^� \\Q�Q� VVee^̂SSYY��^�^� TTU�U� ddbbQQ^̂ccVVUUbbUU^̂SSYYQ�Q� TTU�U� ddbbQQiiUUSSdd_�_� TTYYbbUUSSdd_�_� ��66DD<<11��**CCYYccddUU]]QQc�c�SS__^�^�bbUUQQ\Y\Y]]UU^̂ddQQSSYY��^�^�ee^̂YYddQQbbYYQQ

Page 7: Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del agregado de polos y ceros a las Funciones de Transferencia de Lazo Abierto y de Lazo

7

%%�� @@__\\__c�c�TT__]]YY^̂QQ^̂ddUUc�c�TTU�U�\\Q�Q�VVee^̂SSYY__^̂UUc�c�TTU�U�ddbbQQ^̂ccVVUUbbUU^̂SSYYQQ

Page 8: Qc 6e^SY ^Uc TU DbQ^cVUbU^SYQ - UNSJdea.unsj.edu.ar/control1b/agregado polos y ceros.pdfEfecto del agregado de polos y ceros a las Funciones de Transferencia de Lazo Abierto y de Lazo

8