{"id":332,"date":"2016-07-19T08:57:15","date_gmt":"2016-07-19T11:57:15","guid":{"rendered":"http:\/\/apcmode.com\/?page_id=332"},"modified":"2020-07-04T15:48:30","modified_gmt":"2020-07-04T18:48:30","slug":"funcao-de-transferencia","status":"publish","type":"page","link":"https:\/\/apcmode.com\/?page_id=332","title":{"rendered":"Fun\u00e7\u00e3o de Transfer\u00eancia"},"content":{"rendered":"<table style=\"width: 100%;\" border=\"1\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/apcmode.com\/?page_id=326\">Retorna para t\u00f3pico anterior<\/a><\/td>\n<td>Conte\u00fado deste t\u00f3pico<br \/>\n&#8211; <a href=\"#definicao\">Defini\u00e7\u00e3o<\/a><br \/>\n&#8211; <a href=\"#polos\">P\u00f3los, Zeros e o mapa S<\/a><br \/>\n&#8211; <a href=\"#resposta_impulsiva\">A resposta impulsiva<\/a><br \/>\n&#8211; <a href=\"#mapas\">Mapa S e a resposta impulsiva<\/a><br \/>\n&#8211; <a href=\"#resposta_degrau\">A fun\u00e7\u00e3o resposta ao degrau<\/a><br \/>\n&#8211; <a href=\"#convolucao\">Resposta usando convolu\u00e7\u00e3o<\/a><\/td>\n<td><a href=\"https:\/\/apcmode.com\/?page_id=328\">Avan\u00e7a para pr\u00f3ximo t\u00f3pico<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 id=\"definicao\"><span style=\"color: #993300;\">Defini\u00e7\u00e3o<\/span><\/h3>\n<p>Fun\u00e7\u00e3o de transfer\u00eancia \u00e9 a rela\u00e7\u00e3o entre as transformadas de Laplace do sinal de sa\u00edda (fun\u00e7\u00e3o resposta) e do sinal de entrada (fun\u00e7\u00e3o excita\u00e7\u00e3o). Aplic\u00e1vel a sistemas din\u00e2micos lineares SISO, em&nbsp;condi\u00e7\u00f5es iniciais nulas.<\/p>\n<p>Lembrando que um sistema \u00e9 a &#8220;rela\u00e7\u00e3o causa-efeito entre sinais&#8221; ent\u00e3o uma&nbsp;Fun\u00e7\u00e3o de Transfer\u00eancia \u00e9 a&nbsp;representa\u00e7\u00e3o matem\u00e1tica de um sistema.<\/p>\n<p>Exemplo 1:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-839\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-3.png\" alt=\"Sem t\u00edtulo\" width=\"745\" height=\"328\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-3.png 745w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-3-300x132.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-3-100x44.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-3-150x66.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-3-200x88.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-3-450x198.png 450w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-3-600x264.png 600w\" sizes=\"auto, (max-width: 745px) 100vw, 745px\" \/><\/p>\n<p>Exemplo 2:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-497\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a.png\" alt=\"fig32a\" width=\"800\" height=\"327\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a.png 800w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a-300x123.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a-768x314.png 768w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a-100x41.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a-150x61.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a-200x82.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a-450x184.png 450w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32a-600x245.png 600w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<ul>\n<li>A fun\u00e7\u00e3o de transfer\u00eancia, ou F.T., \u00e9 tipicamente&nbsp;designada como G(s);<\/li>\n<li>A fun\u00e7\u00e3o de transfer\u00eancia equivale a transformada de Laplace da resposta impulsiva de um sistema.<\/li>\n<\/ul>\n<hr>\n<h3 id=\"polos\"><span style=\"color: #993300;\">P\u00f3los, Zeros e o mapa S<\/span><\/h3>\n<p>J\u00e1 sabemos que uma fun\u00e7\u00e3o de transfer\u00eancia G(s) \u00e9 uma raz\u00e3o entre polin\u00f4mios em &#8220;s&#8221;. Mas suas principais propriedades s\u00e3o&nbsp;endere\u00e7ada por meio de <span style=\"color: #3366ff;\"><strong>p\u00f3los<\/strong><\/span>, <strong><span style=\"color: #3366ff;\">zeros<\/span> <\/strong>e o <strong><span style=\"color: #3366ff;\">mapa S<\/span><\/strong>.<\/p>\n<ul>\n<li><strong><span style=\"color: #3366ff;\">p\u00f3los<\/span> <\/strong>s\u00e3o as ra\u00edzes do polin\u00f4mio do <em>denominador<\/em>, ou seja, valores de &#8220;s&#8221; que, no limite, levam G(s)-&gt;inf<\/li>\n<li><span style=\"color: #3366ff;\"><strong>zeros<\/strong> <\/span>s\u00e3o as ra\u00edzes do polin\u00f4mio do <em>numerador<\/em>, ou seja, valores de &#8220;s&#8221; que tornam&nbsp;G(s)=0<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-836\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-2.png\" alt=\"Sem t\u00edtulo\" width=\"596\" height=\"296\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-2.png 596w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-2-300x149.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-2-100x50.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-2-150x74.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-2-200x99.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/Sem-t\u00edtulo-2-450x223.png 450w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/p>\n<p>O mapa &#8220;S&#8221; \u00e9 um representa\u00e7\u00e3o gr\u00e1fica para indicar com &#8220;X&#8221; a posi\u00e7\u00e3o de cada p\u00f3lo e com um &#8220;o&#8221; (c\u00edrculo) a posi\u00e7\u00e3o de cada zero. Como a vari\u00e1vel &#8220;S&#8221; \u00e9 complexa, ent\u00e3o se utiliza um plano cartesiano onde a abscissa representa&nbsp;a parte real e a ordenada representa a parte imagin\u00e1ria.<\/p>\n<p>O mapa S do exemplo anterior seria:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-507\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32e.png\" alt=\"fig32e\" width=\"501\" height=\"295\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32e.png 501w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32e-300x177.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32e-100x59.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32e-150x88.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32e-200x118.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32e-450x265.png 450w\" sizes=\"auto, (max-width: 501px) 100vw, 501px\" \/><\/p>\n<hr>\n<h3 id=\"resposta_impulsiva\"><span style=\"color: #993300;\">A resposta impulsiva<\/span><\/h3>\n<p>\u00c9 a resposta de um sistema a uma entrada do tipo impulso. Sendo chamada aqui de h(t), esta fun\u00e7\u00e3o se notabiliza por ser uma resposta do tipo &#8220;transit\u00f3rio puro&#8221;, ou seja, revela apenas&nbsp;a parte din\u00e2mica da resposta.<\/p>\n<p>Visto no dom\u00ednio &#8220;s&#8221;, a transformada de Laplace da resposta impulsiva H(s) equivale a fun\u00e7\u00e3o de transfer\u00eancia do sistema G(s). Em outras palavras, a resposta impulsiva h(t) \u00e9 a transformada inversa de Laplace da fun\u00e7\u00e3o de transfer\u00eancia do sistema.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-518\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g.png\" alt=\"fig32g\" width=\"921\" height=\"397\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g.png 921w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g-300x129.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g-768x331.png 768w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g-100x43.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g-150x65.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g-200x86.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g-450x194.png 450w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g-600x259.png 600w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32g-900x388.png 900w\" sizes=\"auto, (max-width: 921px) 100vw, 921px\" \/><\/p>\n<p>Exemplo num\u00e9rico:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-519\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32h.png\" alt=\"fig32h\" width=\"663\" height=\"428\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32h.png 663w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32h-300x194.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32h-100x65.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32h-150x97.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32h-200x129.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32h-450x290.png 450w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32h-600x387.png 600w\" sizes=\"auto, (max-width: 663px) 100vw, 663px\" \/><\/p>\n<hr>\n<h3 id=\"mapas\"><span style=\"color: #993300;\">Mapa S e a resposta impulsiva<\/span><\/h3>\n<p>A posi\u00e7\u00e3o dos p\u00f3los no mapa &#8220;S&#8221;&nbsp;determina o formato da curva de resposta impulsiva de um sistema.&nbsp;Veja exemplos abaixo.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-504\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c.png\" alt=\"fig32c\" width=\"880\" height=\"536\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c.png 880w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c-300x183.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c-768x468.png 768w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c-100x61.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c-150x91.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c-200x122.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c-450x274.png 450w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32c-600x365.png 600w\" sizes=\"auto, (max-width: 880px) 100vw, 880px\" \/><\/p>\n<p>&nbsp;<\/p>\n<hr>\n<h3 id=\"resposta_degrau\"><span style=\"color: #993300;\">A fun\u00e7\u00e3o resposta ao degrau<\/span><\/h3>\n<p>\u00c9 a resposta de um sistema a uma entrada do tipo degrau. Esta fun\u00e7\u00e3o \u00e9 muito utilizada para caracterizar a resposta din\u00e2micas de sistemas a partir de testes emp\u00edricos, visto que o sinal degrau \u00e9 o mais simples de&nbsp;ser aplicado&nbsp;em um sistema em opera\u00e7\u00e3o.<\/p>\n<p>Apesar de geralmente ser obtida por meios emp\u00edricos, a fun\u00e7\u00e3o resposta ao degrau pode ser extra\u00edda diretamente da Fun\u00e7\u00e3o de Transfer\u00eancia, fazendo-se X(s)=1\/s. Veja o exemplo:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-522\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32i.png\" alt=\"fig32i\" width=\"646\" height=\"313\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32i.png 646w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32i-300x145.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32i-100x48.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32i-150x73.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32i-200x97.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32i-450x218.png 450w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32i-600x291.png 600w\" sizes=\"auto, (max-width: 646px) 100vw, 646px\" \/><\/p>\n<p>&nbsp;<\/p>\n<hr>\n<h3 id=\"convolucao\"><span style=\"color: #993300;\">Resposta de um sistema din\u00e2mico para uma entrada gen\u00e9rica usando convolu\u00e7\u00e3o<\/span><\/h3>\n<p>J\u00e1 foi mostrado como obter a resposta de um sistema para entradas do tipo <em>impulso<\/em> e <em>degrau <\/em> a partir da fun\u00e7\u00e3o de transfer\u00eancia.&nbsp;Nesta se\u00e7\u00e3o ser\u00e1 demostrado que, conhecida a fun\u00e7\u00e3o resposta impulsiva de um sistema, \u00e9 poss\u00edvel obter sua resposta para qualquer tipo de entrada. Para facilitar, ser\u00e1 utilizado sinais discretos no tempo.<\/p>\n<p>A figura abaixo mostra um sinal cont\u00ednuo x(t) e sua vers\u00e3o amostrada x[k]. Considere que a mesma opera\u00e7\u00e3o foi feita na fun\u00e7\u00e3o resposta o degrau, resultado em h[k].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-525\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32j.png\" alt=\"fig32j\" width=\"699\" height=\"348\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32j.png 699w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32j-300x149.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32j-100x50.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32j-150x75.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32j-200x100.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32j-450x224.png 450w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32j-600x299.png 600w\" sizes=\"auto, (max-width: 699px) 100vw, 699px\" \/><\/p>\n<p>A opera\u00e7\u00e3o de convolu\u00e7\u00e3o pode ser entendida como sendo a resposta do sistema para uma entrada composta por uma sequencia de impulsos igualmente espa\u00e7ados, mas de diferentes amplitudes, tal como o sinal x[k]. A sa\u00edda, neste caso, \u00e9 a fun\u00e7\u00e3o resposta impulsiva h[k]. E, da mesmo forma como o sinal de entrada pode ser reconstitu\u00eddo como a soma desses&nbsp;impulsos defasados, a resposta pode ser obtida como o somat\u00f3rio das resposta impulsivas de cada um dos impulsos de entrada.<\/p>\n<p>No exemplo a seguir, para simplificar,&nbsp;foi usado como entrada um sinal tipo degrau unit\u00e1rio e, neste caso, a entrada \u00e9&nbsp;uma sequ\u00eancia se impulsos unit\u00e1rios. A figura mostra como a sa\u00edda \u00e9 obtida a partir da combina\u00e7\u00e3o da resposta do sistema a cada impulso de entrada.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-501\" src=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b.png\" alt=\"fig32b\" width=\"912\" height=\"824\" srcset=\"https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b.png 912w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b-300x271.png 300w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b-768x694.png 768w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b-100x90.png 100w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b-150x136.png 150w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b-200x181.png 200w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b-450x407.png 450w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b-600x542.png 600w, https:\/\/apcmode.com\/wp-content\/uploads\/2016\/07\/fig32b-900x813.png 900w\" sizes=\"auto, (max-width: 912px) 100vw, 912px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Retorna para t\u00f3pico anterior Conte\u00fado deste t\u00f3pico &#8211; Defini\u00e7\u00e3o &#8211; P\u00f3los, Zeros e o mapa S &#8211; A resposta impulsiva &#8211; Mapa S e a resposta impulsiva &#8211; A fun\u00e7\u00e3o resposta ao degrau &#8211; Resposta usando convolu\u00e7\u00e3o Avan\u00e7a para pr\u00f3ximo &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/apcmode.com\/?page_id=332\"> <span class=\"screen-reader-text\">Fun\u00e7\u00e3o de Transfer\u00eancia<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":320,"menu_order":32,"comment_status":"closed","ping_status":"closed","template":"full-width-page.php","meta":{"footnotes":""},"class_list":["post-332","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/apcmode.com\/index.php?rest_route=\/wp\/v2\/pages\/332","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/apcmode.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/apcmode.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/apcmode.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/apcmode.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=332"}],"version-history":[{"count":2,"href":"https:\/\/apcmode.com\/index.php?rest_route=\/wp\/v2\/pages\/332\/revisions"}],"predecessor-version":[{"id":1212,"href":"https:\/\/apcmode.com\/index.php?rest_route=\/wp\/v2\/pages\/332\/revisions\/1212"}],"up":[{"embeddable":true,"href":"https:\/\/apcmode.com\/index.php?rest_route=\/wp\/v2\/pages\/320"}],"wp:attachment":[{"href":"https:\/\/apcmode.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}