{"id":156189,"date":"2023-08-29T14:28:35","date_gmt":"2023-08-29T08:58:35","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156189"},"modified":"2023-08-29T14:39:59","modified_gmt":"2023-08-29T09:09:59","slug":"the-forward-path-transfer-function-ls-of-the-control-system-shown-in-figure-a-has-the-asymptotic-bode-plot-shown","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/the-forward-path-transfer-function-ls-of-the-control-system-shown-in-figure-a-has-the-asymptotic-bode-plot-shown\/","title":{"rendered":"The forward path transfer function L(s) of the control system shown in Figure (a) has the asymptotic Bode plot shown"},"content":{"rendered":"\n

Q. The forward path transfer function L<\/em>(s<\/em>) of the control system shown in Figure (a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d <\/em>(t<\/em>) is given by d<\/em>(t<\/em>) = 0.1sin(wt<\/em>) where w = 5 rad s <\/em>, the steady-state amplitude of the output y<\/em>(t<\/em>) is<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Sol:<\/p>\n\n\n\n

as r = 0 <\/p>\n\n\n\n

y = – y L(s) + d<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

From bode magnitude plot <\/p>\n\n\n\n

At \u03c9 = 5 rad\/sec, magnitude of L(s) = 40 dB <\/p>\n\n\n\n

\u21d2 magnitude of L(s) = 100 <\/p>\n\n\n\n

From Bode phase plot <\/p>\n\n\n\n

\u2220L(s) = 120\u00b0 at \u03c9 = 5 rad\/sec L(s) at 5 rad\/sec = 100 \u2220-120\u00b0<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Q. The forward path transfer function L(s) of the control system shown in Figure (a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d (t) is given by d(t) = 0.1sin(wt) where w = 5 rad s , the steady-state amplitude of the output y(t) is Sol: as r = 0 […]<\/p>\n","protected":false},"author":419,"featured_media":156193,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-156189","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156189","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=156189"}],"version-history":[{"count":3,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156189\/revisions"}],"predecessor-version":[{"id":156201,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156189\/revisions\/156201"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156193"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}