In the derivation of expression for peak percent overshoot, Mp = exp \u2013 \u03c0\u03be \u221a1-52 \u00d7100% Which one %3D of the following conditions is NOT required? (a) System is linear and time invariant (b) The system transfer function has a pair of complex conjugate poles and no zeroes. (c) There is no transportation delay in the system. (d) The system has zero initial conditions<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is (d) The system has zero initial conditions.<\/strong><\/p>\n\n\n\n The derivation of the expression for peak percent overshoot in a second-order system primarily depends on the system’s transfer function and its dynamic characteristics. To understand why option (d) is not required, let\u2019s break down the conditions:<\/p>\n\n\n\n Thus, the only condition that is not essential for the derivation of peak percent overshoot is (d)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" In the derivation of expression for peak percent overshoot, Mp = exp \u2013 \u03c0\u03be \u221a1-52 \u00d7100% Which one %3D of the following conditions is NOT required? (a) System is linear and time invariant (b) The system transfer function has a pair of complex conjugate poles and no zeroes. (c) There is no transportation delay in […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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-5)","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-5)","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-5)","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":[25],"tags":[],"class_list":["post-189573","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189573","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=189573"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189573\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189573"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189573"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
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This condition is necessary because the analysis for overshoot applies to linear time-invariant (LTI) systems. The peak percent overshoot and other transient characteristics are derived assuming the system follows the principles of linearity and time-invariance. Nonlinear systems or systems that change over time (time-varying systems) would have different transient behaviors, making the usual expressions for overshoot invalid.<\/li>\n\n\n\n
This is a critical condition for a second-order system to exhibit oscillatory behavior, which is a key characteristic for the peak percent overshoot. If the system has complex conjugate poles, the response is oscillatory (underdamped), leading to overshoot in response to a step input. Zeroes do not impact the presence of overshoot in the standard second-order system, but complex poles are directly related to the overshoot.<\/li>\n\n\n\n
This is also a necessary condition because transportation delay (also known as time delay) causes a phase shift in the system\u2019s response. This delay can significantly affect the overshoot and transient response. Without delay, the system\u2019s overshoot can be analyzed with standard second-order approximations. A system with a delay would need additional considerations for accurate overshoot estimation.<\/li>\n\n\n\n
This condition is not strictly required for the derivation of peak percent overshoot. The derivation of overshoot generally assumes that the system is responding to a step input and starts from rest, which implicitly means zero initial conditions. However, systems with non-zero initial conditions can also exhibit a peak overshoot, but the formula for overshoot typically assumes zero initial conditions. If initial conditions are non-zero, the transient response would be influenced by these conditions, but they do not affect the derivation of the peak overshoot formula for a typical second-order system.<\/li>\n<\/ol>\n\n\n\n