{"id":6206,"date":"2024-01-28T10:07:24","date_gmt":"2024-01-28T01:07:24","guid":{"rendered":"https:\/\/now0930.pe.kr\/wordpress\/?p=6206"},"modified":"2026-10-04T08:49:34","modified_gmt":"2026-10-03T23:49:34","slug":"root-locus-design","status":"publish","type":"post","link":"https:\/\/now0930.pe.kr\/wordpress\/root-locus-design\/","title":{"rendered":"lag compensator \uc124\uacc4 root locus design"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Root Locus\ub85c damping ration\uac00 \uc815\ud574\uc84c\uc744 \uacbd\uc6b0, \ubaa9\ud45c\uc810\uc744 \uad6c\ud558\uae30<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Control Systems Engineering \uc608\uc81c<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"662\" height=\"733\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-55.png\" alt=\"\" class=\"wp-image-6211\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"934\" height=\"1051\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-56.png\" alt=\"\" class=\"wp-image-6214\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-56.png 934w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-56-768x864.png 768w\" sizes=\"auto, (max-width: 934px) 100vw, 934px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-57.png\" alt=\"\" class=\"wp-image-6215\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-57.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-57-768x1050.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"934\" height=\"658\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-58.png\" alt=\"\" class=\"wp-image-6216\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-58.png 934w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-58-768x541.png 768w\" sizes=\"auto, (max-width: 934px) 100vw, 934px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code><iframe src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/KCOW_lag_compensator.html\" width=600 height = 800 align=\"middle\"><\/iframe><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/electronics.stackexchange.com\/questions\/333310\/how-to-find-the-intersection-point-in-rootlocus-diagram\">https:\/\/electronics.stackexchange.com\/questions\/333310\/how-to-find-the-intersection-point-in-rootlocus-diagram<\/a><\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Control Systems (EBB 320): Solving for an exact point on a Root locus, by hand.\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/ZYY8IcCFg34?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"How To Find a Point  where Damping Line Crosses(intersects)Root Locus Mathematically :Control System\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/L77qdagoj_g?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n&#8220;`html\n<div class=\"chapter19-wide\">\n\n  <h1>Root Locus Design<\/h1>\n\n  <div class=\"subtitle\">\n    Root Locus \u00b7 Damping Ratio \u00b7 Integral Compensator \u00b7 Pole-Zero Compensation\n  <\/div>\n\n  <!-- ================================================= -->\n  <h2>1. Root Locus Design<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      G(s)\n      =\n      K\n      \/\n      [(s+1)(s+2)(s+10)]\n    <\/div>\n\n    <pre>\n                  +                     1\n    R(s) ------->(\u03a3)---->[ K ]---->[ ----------- ]-----> C(s)\n                  - ^              (s+1)(s+2)(s+10)       |\n                    |                                      |\n                    +--------------------------------------+\n    <\/pre>\n\n    <div class=\"formula\">\n      \u03b6 = 0.174\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>2. \uac10\uc1e0\ube44\uc640 \ubaa9\ud45c Pole<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      s\n      =\n      -\u03c3\n      \u00b1\n      j\u03c9<sub>d<\/sub>\n    <\/div>\n\n    <div class=\"formula\">\n      \u03b6\n      =\n      \u03c3 \/ \u03c9<sub>n<\/sub>\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9<sub>n<\/sub>\n      =\n      \u221a(\u03c3<sup>2<\/sup> + \u03c9<sub>d<\/sub><sup>2<\/sup>)\n    <\/div>\n\n    <div class=\"formula\">\n      \u03b6 = cos \u03b8\n    <\/div>\n\n    <pre>\n                Im\n                \u2191\n                |\n                |          \u25cf  -\u03c3 + j\u03c9d\n                |         \/|\n                |        \/ |\n                |       \/  | \u03c9d\n                |      \/\u03b8  |\n    ------------+-----+--------------------\u2192 Re\n                     -\u03c3\n    <\/pre>\n\n    <div class=\"formula\">\n      s\n      \u2248\n      -0.69\n      \u00b1\n      j3.92\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>3. Root Locus Angle Condition<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      \u03b8<sub>p1<\/sub>\n      +\n      \u03b8<sub>p2<\/sub>\n      +\n      \u03b8<sub>p3<\/sub>\n      =\n      180\u00b0\n    <\/div>\n\n    <div class=\"formula\">\n      \u03b8<sub>p1<\/sub>\n      =\n      tan<sup>-1<\/sup>\n      [\n      \u03c9<sub>d<\/sub>\/(10-\u03c3)\n      ]\n    <\/div>\n\n    <div class=\"formula\">\n      \u03b8<sub>p2<\/sub>\n      =\n      tan<sup>-1<\/sup>\n      [\n      \u03c9<sub>d<\/sub>\/(2-\u03c3)\n      ]\n    <\/div>\n\n    <div class=\"formula\">\n      \u03b8<sub>p3<\/sub>\n      =\n      tan<sup>-1<\/sup>\n      [\n      \u03c9<sub>d<\/sub>\/(1-\u03c3)\n      ]\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>4. Magnitude Condition<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      |KG(s)| = 1\n    <\/div>\n\n    <div class=\"formula\">\n      K\n      =\n      |\n      (s+10)(s+2)(s+1)\n      |\n    <\/div>\n\n    <div class=\"formula\">\n      K \u2248 164\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>5. Integral Compensator<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      G<sub>c<\/sub>(s)\n      =\n      K\n      (s+0.1)\n      \/\n      s\n    <\/div>\n\n    <div class=\"formula\">\n      G<sub>OL<\/sub>(s)\n      =\n      K\n      (s+0.1)\n      \/\n      [\n      s(s+1)(s+2)(s+10)\n      ]\n    <\/div>\n\n    <pre>\n                  +       K(s+0.1)          1\n    R(s) ------->(\u03a3)---->[ ------- ]---->[ ----------- ]-----> C(s)\n                  - ^         s          (s+1)(s+2)(s+10)       |\n                    |                                             |\n                    +---------------------------------------------+\n    <\/pre>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>6. Pole-Zero \ubc30\uce58<\/h2>\n\n  <div class=\"card\">\n\n    <pre>\n      Re axis\n\n    \u00d7----------------\u00d7------\u00d7------\u25cb----\u00d7--------------\u2192\n   -10              -2     -1    -0.1   0\n\n    \u00d7 : Pole\n    \u25cb : Zero\n    <\/pre>\n\n    <div class=\"formula\">\n      Pole:\n      s = 0\n    <\/div>\n\n    <div class=\"formula\">\n      Zero:\n      s = -0.1\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>7. \ubcf4\uc0c1 \ud6c4 Gain<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      K\n      =\n      |\n      s(s+1)(s+2)(s+10)\n      \/\n      (s+0.1)\n      |\n    <\/div>\n\n    <div class=\"formula\">\n      K \u2248 163.6\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        \ubcf4\uc0c1 \uc804 K \u2248 164\n        <br><br>\n        \ubcf4\uc0c1 \ud6c4 K \u2248 163.6\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <div class=\"keywords\">\n    Root Locus, Damping Ratio, Integral Compensator,\n    Pole-Zero Compensation, Angle Condition, Magnitude Condition\n  <\/div>\n\n<\/div>\n&#8220;`\n","protected":false},"excerpt":{"rendered":"<p>Root Locus\ub85c damping ration\uac00 \uc815\ud574\uc84c\uc744 \uacbd\uc6b0, \ubaa9\ud45c\uc810\uc744 \uad6c\ud558\uae30 Control Systems Engineering \uc608\uc81c https:\/\/electronics.stackexchange.com\/questions\/333310\/how-to-find-the-intersection-point-in-rootlocus-diagram &#8220;`html Root Locus Design Root Locus \u00b7 Damping Ratio \u00b7 Integral Compensator \u00b7 Pole-Zero Compensation 1. Root Locus Design G(s) = K \/ [(s+1)(s+2)(s+10)] + 1 R(s) &#8212;&#8212;->(\u03a3)&#8212;->[ K ]&#8212;->[ &#8212;&#8212;&#8212;&#8211; ]&#8212;&#8211;> C(s) &#8211; ^ (s+1)(s+2)(s+10) | | | +&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;+ \u03b6 = [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1185],"tags":[1237,1238],"class_list":["post-6206","post","type-post","status-publish","format-standard","hentry","category-1185","tag-lag-compansator","tag-pi-controller"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/comments?post=6206"}],"version-history":[{"count":12,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6206\/revisions"}],"predecessor-version":[{"id":9557,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6206\/revisions\/9557"}],"wp:attachment":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/media?parent=6206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/categories?post=6206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/tags?post=6206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}