{"id":6156,"date":"2024-01-22T18:32:10","date_gmt":"2024-01-22T09:32:10","guid":{"rendered":"https:\/\/now0930.pe.kr\/wordpress\/?p=6156"},"modified":"2026-10-04T08:39:34","modified_gmt":"2026-10-03T23:39:34","slug":"nyquist-plot-time-dealy","status":"publish","type":"post","link":"https:\/\/now0930.pe.kr\/wordpress\/nyquist-plot-time-dealy\/","title":{"rendered":"Nyquist Plot Time Dealy"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Time delay\ub41c Nyquist Plot<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1312\" height=\"1000\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-35.png\" alt=\"\" class=\"wp-image-6146\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-35.png 1312w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-35-768x585.png 768w\" sizes=\"auto, (max-width: 1312px) 100vw, 1312px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/nate9389.tistory.com\/1934\">https:\/\/nate9389.tistory.com\/1934<\/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=\"Nyquist Stability Criterion \ud83c\udf1f Second-Order System with Time Delay \ud83c\udf1f Calculations &amp; MATLAB Simulation\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/5iJJvdLyR8c?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<p class=\"wp-block-paragraph\"><a href=\"https:\/\/electronics.stackexchange.com\/questions\/340566\/how-to-determine-the-critical-delay-for-a-closed-loop-system\">https:\/\/electronics.stackexchange.com\/questions\/340566\/how-to-determine-the-critical-delay-for-a-closed-loop-system<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"985\" height=\"1076\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-36.png\" alt=\"\" class=\"wp-image-6153\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-36.png 985w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-36-768x839.png 768w\" sizes=\"auto, (max-width: 985px) 100vw, 985px\" \/><\/figure>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/05\/PM_GM.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"PM_GM\uc758 \uc0bd\uc785.\"><\/object><a id=\"wp-block-file--media-14f11fc8-2419-4bfa-8c3d-55ec4eef42c4\" href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/05\/PM_GM.pdf\">PM_GM<\/a><a href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/05\/PM_GM.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-14f11fc8-2419-4bfa-8c3d-55ec4eef42c4\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1312\" height=\"1015\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-37.png\" alt=\"\" class=\"wp-image-6154\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-37.png 1312w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-37-768x594.png 768w\" sizes=\"auto, (max-width: 1312px) 100vw, 1312px\" \/><\/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\/05\/\uc81c\ubaa9-\uc5c6\uc74c.jpg\" alt=\"\" class=\"wp-image-7335\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/05\/\uc81c\ubaa9-\uc5c6\uc74c.jpg 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/05\/\uc81c\ubaa9-\uc5c6\uc74c-768x1050.jpg 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=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-38.png\" alt=\"\" class=\"wp-image-6160\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-38.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-38-768x1050.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=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-39.png\" alt=\"\" class=\"wp-image-6161\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-39.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-39-768x1050.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=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-40.png\" alt=\"\" class=\"wp-image-6162\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-40.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-40-768x1050.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=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-41.png\" alt=\"\" class=\"wp-image-6163\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-41.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-41-768x1050.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=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-42.png\" alt=\"\" class=\"wp-image-6164\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-42.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-42-768x1050.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code><iframe loading=\"lazy\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/Nyquist-Criterion-Time-Delayed.html\" width=\"600\" height=\"800\" align=\"middle\"><\/iframe><\/code><\/pre>\n\n\n\n&#8220;`html\n<div class=\"chapter19-wide\">\n\n  <h1>Nyquist Plot Time Delay<\/h1>\n\n  <div class=\"subtitle\">\n    Time Delay \u00b7 Nyquist Plot \u00b7 Gain Crossover \u00b7 Phase Crossover \u00b7 Delay Margin\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>1. \uc2dc\uac04\uc9c0\uc5f0 \uc2dc\uc2a4\ud15c<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc2dc\uac04\uc9c0\uc5f0\uc774 \ud3ec\ud568\ub41c \uc2dc\uc2a4\ud15c\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ud45c\ud604\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      L(s)\n      =\n      G(s)e<sup>-Ts<\/sup>\n    <\/div>\n\n    <p>\n      \uc2dc\uac04\uc601\uc5ed\uc5d0\uc11c\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-Ts<\/sup>F(s)\n      \u2194\n      f(t-T)\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c e<sup>-Ts<\/sup>\ub294 \uc785\ub825 \ub610\ub294 \ucd9c\ub825\uc774\n      T\ub9cc\ud07c \ub2a6\uac8c \ub098\ud0c0\ub098\ub294 \uc21c\uc218 \uc2dc\uac04\uc9c0\uc5f0\uc744 \uc758\ubbf8\ud55c\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>2. \uc8fc\ud30c\uc218\uc601\uc5ed\uc758 \uc2dc\uac04\uc9c0\uc5f0<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc8fc\ud30c\uc218\uc751\ub2f5\uc5d0\uc11c\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      s = j\u03c9\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c \uc2dc\uac04\uc9c0\uc5f0 \ud56d\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-j\u03c9T<\/sup>\n    <\/div>\n\n    <p>\n      \uac00 \ub41c\ub2e4.\n    <\/p>\n\n    <p>\n      Euler \uad00\uacc4\ub97c \uc774\uc6a9\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-j\u03c9T<\/sup>\n      =\n      cos(\u03c9T)\n      &#8211;\n      j sin(\u03c9T)\n    <\/div>\n\n    <p>\n      \ud06c\uae30\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      |e<sup>-j\u03c9T<\/sup>| = 1\n    <\/div>\n\n    <p>\n      \uc704\uc0c1\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      \u2220e<sup>-j\u03c9T<\/sup>\n      =\n      -\u03c9T\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        \uc21c\uc218 \uc2dc\uac04\uc9c0\uc5f0\uc740 Gain\uc758 \ud06c\uae30\ub294 \ubcc0\ud654\uc2dc\ud0a4\uc9c0 \uc54a\uace0\n        \uc8fc\ud30c\uc218\uc5d0 \ube44\ub840\ud558\ub294 \ucd94\uac00 \uc704\uc0c1\uc9c0\uc5f0 -\u03c9T\ub97c \ub9cc\ub4e0\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>3. Nyquist Plot\uc5d0 \ubbf8\uce58\ub294 \uc601\ud5a5<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc2dc\uac04\uc9c0\uc5f0\uc774 \uc5c6\ub294 \uc8fc\ud30c\uc218\uc751\ub2f5\uc774\n    <\/p>\n\n    <div class=\"formula\">\n      G(j\u03c9)\n    <\/div>\n\n    <p>\n      \ub77c\uba74 \uc2dc\uac04\uc9c0\uc5f0\uc774 \uc788\uc744 \ub54c\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      L(j\u03c9)\n      =\n      G(j\u03c9)e<sup>-j\u03c9T<\/sup>\n    <\/div>\n\n    <p>\n      \uac00 \ub41c\ub2e4.\n    <\/p>\n\n    <p>\n      \uc2dc\uac04\uc9c0\uc5f0 \ud56d\uc758 \ud06c\uae30\ub294 1\uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      |L(j\u03c9)|\n      =\n      |G(j\u03c9)|\n    <\/div>\n\n    <p>\n      \uc774\ub2e4.\n    <\/p>\n\n    <p>\n      \uadf8\ub7ec\ub098 \uc704\uc0c1\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      \u2220L(j\u03c9)\n      =\n      \u2220G(j\u03c9)\n      &#8211;\n      \u03c9T\n    <\/div>\n\n    <p>\n      \uac00 \ub41c\ub2e4.\n    <\/p>\n\n    <div class=\"memory\">\n      <strong>\n        \uc2dc\uac04\uc9c0\uc5f0\uc774 \uc99d\uac00\ud560\uc218\ub85d Nyquist plot\uc740\n        \ub3d9\uc77c\ud55c \ud06c\uae30\ub97c \uc720\uc9c0\ud558\uba74\uc11c \uc704\uc0c1\ubc29\ud5a5\uc73c\ub85c \ub354 \ud68c\uc804\ud55c\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>4. Gain Crossover Frequency\uc640 \uc2dc\uac04\uc9c0\uc5f0<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Gain Crossover Frequency \u03c9<sub>gc<\/sub>\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      |G(j\u03c9<sub>gc<\/sub>)| = 1\n    <\/div>\n\n    <p>\n      \uc744 \ub9cc\uc871\ud558\ub294 \uc8fc\ud30c\uc218\uc774\ub2e4.\n    <\/p>\n\n    <p>\n      \uc2dc\uac04\uc9c0\uc5f0 \uc694\uc18c\ub294 \ud06c\uae30\uac00 \ud56d\uc0c1 1\uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      |e<sup>-j\u03c9T<\/sup>| = 1\n    <\/div>\n\n    <p>\n      \uc2dc\uac04\uc9c0\uc5f0\uc744 \ucd94\uac00\ud574\ub3c4\n      Gain Crossover Frequency \uc790\uccb4\ub294 \ubcc0\ud558\uc9c0 \uc54a\ub294\ub2e4.\n    <\/p>\n\n    <div class=\"memory\">\n      <strong>\n        \uc21c\uc218 \uc2dc\uac04\uc9c0\uc5f0\uc740 Magnitude\ub97c \ubc14\uafb8\uc9c0 \uc54a\uc73c\ubbc0\ub85c\n        \u03c9<sub>gc<\/sub>\ub294 \uadf8\ub300\ub85c\uc774\uace0,\n        \uadf8 \uc704\uce58\uc5d0\uc11c Phase\ub9cc \uac10\uc18c\ud55c\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>5. Delay Margin<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Delay Margin T<sub>dm<\/sub>\uc740\n      \uc548\uc815\ud55c \uc2dc\uc2a4\ud15c\uc5d0 \uc2dc\uac04\uc9c0\uc5f0\uc744 \ucd94\uac00\ud588\uc744 \ub54c\n      \uc2dc\uc2a4\ud15c\uc774 \ubd88\uc548\uc815 \uacbd\uacc4\uc5d0 \ub3c4\ub2ec\ud558\uae30 \uc9c1\uc804\uae4c\uc9c0\n      \ud5c8\uc6a9\ud560 \uc218 \uc788\ub294 \ucd5c\ub300 \uc2dc\uac04\uc9c0\uc5f0\uc774\ub2e4.\n    <\/p>\n\n    <p>\n      \uc548\uc815 \ud55c\uacc4\uc5d0\uc11c\ub294 Nyquist plot\uc774\n      Critical Point -1\uc744 \uc9c0\ub09c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      G(j\u03c9<sub>gc<\/sub>)\n      e<sup>-j\u03c9<sub>gc<\/sub>T<sub>dm<\/sub><\/sup>\n      =\n      -1\n    <\/div>\n\n    <p>\n      \ud06c\uae30\ub294 \uc774\ubbf8\n    <\/p>\n\n    <div class=\"formula\">\n      |G(j\u03c9<sub>gc<\/sub>)| = 1\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c \uc704\uc0c1\uc870\uac74\ub9cc \uace0\ub824\ud558\uba74 \ub41c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \u2220G(j\u03c9<sub>gc<\/sub>)\n      &#8211;\n      \u03c9<sub>gc<\/sub>T<sub>dm<\/sub>\n      =\n      -\u03c0\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>6. Phase Margin\uacfc Delay Margin<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Phase Margin\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      PM\n      =\n      \u03c0\n      +\n      \u2220G(j\u03c9<sub>gc<\/sub>)\n    <\/div>\n\n    <p>\n      \uc774\ub2e4.\n    <\/p>\n\n    <p>\n      \uc548\uc815 \ud55c\uacc4\uc5d0\uc11c \ud544\uc694\ud55c \ucd94\uac00 \uc704\uc0c1\uc9c0\uc5f0\uc774\n      \ubc14\ub85c Phase Margin\uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      \u03c9<sub>gc<\/sub>T<sub>dm<\/sub>\n      =\n      PM\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      T<sub>dm<\/sub>\n      =\n      PM \/ \u03c9<sub>gc<\/sub>\n    <\/div>\n\n    <p>\n      \uc5ec\uae30\uc11c PM\uc740 rad \ub2e8\uc704\uc774\uc5b4\uc57c \ud55c\ub2e4.\n    <\/p>\n\n    <p>\n      PM\uc774 degree\ub85c \uc8fc\uc5b4\uc9c0\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      T<sub>dm<\/sub>\n      =\n      (PM \/ \u03c9<sub>gc<\/sub>)\n      \u00d7\n      (\u03c0 \/ 180\u00b0)\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        Delay Margin\uc740\n        Phase Margin\uc744 Gain Crossover Frequency\ub85c \ub098\ub208 \uac12\uc774\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>7. PDF \uc608\uc81c<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ucca8\ubd80 PDF\uc5d0\uc11c\ub294 \ub2e4\uc74c \uac12\uc744 \uc0ac\uc6a9\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      PM = 104\u00b0\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9<sub>gc<\/sub>\n      =\n      1.62 rad\/s\n    <\/div>\n\n    <p>\n      Delay Margin\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      T<sub>dm<\/sub>\n      =\n      (104\u00b0 \/ 1.62)\n      \u00d7\n      (\u03c0 \/ 180\u00b0)\n    <\/div>\n\n    <div class=\"formula\">\n      T<sub>dm<\/sub>\n      \u2248\n      1.12 s\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        PDF\uc758 MATLAB Nyquist \uacb0\uacfc\uc5d0\uc11c\ub3c4\n        Phase Margin = 104\u00b0,\n        Delay Margin = 1.12 s,\n        \u03c9<sub>gc<\/sub> = 1.62 rad\/s\ub85c \ub098\ud0c0\ub09c\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>8. \ubb38\uc81c<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ubb38\uc81c\uc758 \ud3d0\ub8e8\ud504 \uc804\ub2ec\ud568\uc218\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      L(s)\n      =\n      G(s)H(s)\n      =\n      e<sup>-Ts<\/sup>\n      \u00b7\n      [2\u221a2 \/ (s+1)<sup>3<\/sup>]\n    <\/div>\n\n    <p>\n      \uc2dc\uac04\uc9c0\uc5f0 T=0\uc77c \ub54c\ub294 \uc548\uc815\ud558\ub2e4\uace0 \uc8fc\uc5b4\uc838 \uc788\ub2e4.\n    <\/p>\n\n    <p>\n      \ub2e4\uc74c \ud56d\ubaa9\uc744 \uacc4\uc0b0\ud55c\ub2e4.\n    <\/p>\n\n    <ol>\n      <li>Gain Crossover Frequency \u03c9<sub>cg<\/sub><\/li>\n      <li>Phase Crossover Frequency \u03c9<sub>cp<\/sub><\/li>\n      <li>Gain Margin<\/li>\n      <li>Phase Margin<\/li>\n      <li>\uc2dc\uac04\uc9c0\uc5f0 \uacbd\uacc4\uac12 T<\/li>\n    <\/ol>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>9. Gain Crossover Frequency \u03c9<sub>cg<\/sub><\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc2dc\uac04\uc9c0\uc5f0\uc740 \ud06c\uae30\uc5d0 \uc601\ud5a5\uc744 \uc8fc\uc9c0 \uc54a\uc73c\ubbc0\ub85c\n      T=0\uc778 \uc804\ub2ec\ud568\uc218\uc5d0\uc11c \ud06c\uae30\uc870\uac74\uc744 \uacc4\uc0b0\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      G(s)\n      =\n      2\u221a2 \/ (s+1)<sup>3<\/sup>\n    <\/div>\n\n    <p>\n      s=j\u03c9\ub97c \ub300\uc785\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      |G(j\u03c9)|\n      =\n      2\u221a2\n      \/\n      |1+j\u03c9|<sup>3<\/sup>\n    <\/div>\n\n    <p>\n      \uadf8\ub9ac\uace0\n    <\/p>\n\n    <div class=\"formula\">\n      |1+j\u03c9|\n      =\n      \u221a(1+\u03c9<sup>2<\/sup>)\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      |G(j\u03c9)|\n      =\n      2\u221a2\n      \/\n      (1+\u03c9<sup>2<\/sup>)<sup>3\/2<\/sup>\n    <\/div>\n\n    <p>\n      Gain Crossover \uc870\uac74\n    <\/p>\n\n    <div class=\"formula\">\n      |G(j\u03c9<sub>cg<\/sub>)|\n      =\n      1\n    <\/div>\n\n    <p>\n      \uc744 \uc801\uc6a9\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      2\u221a2\n      =\n      (1+\u03c9<sub>cg<\/sub><sup>2<\/sup>)<sup>3\/2<\/sup>\n    <\/div>\n\n    <div class=\"formula\">\n      1+\u03c9<sub>cg<\/sub><sup>2<\/sup>\n      =\n      2\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9<sub>cg<\/sub>\n      =\n      1 rad\/s\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>10. Phase Crossover Frequency \u03c9<sub>cp<\/sub><\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      T=0\uc77c \ub54c \uc804\ub2ec\ud568\uc218\uc758 \uc704\uc0c1\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      \u2220G(j\u03c9)\n      =\n      -3tan<sup>-1<\/sup>(\u03c9)\n    <\/div>\n\n    <p>\n      \uc774\ub2e4.\n    <\/p>\n\n    <p>\n      Phase Crossover Frequency\uc5d0\uc11c\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      \u2220G(j\u03c9<sub>cp<\/sub>)\n      =\n      -180\u00b0\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      -3tan<sup>-1<\/sup>(\u03c9<sub>cp<\/sub>)\n      =\n      -180\u00b0\n    <\/div>\n\n    <div class=\"formula\">\n      tan<sup>-1<\/sup>(\u03c9<sub>cp<\/sub>)\n      =\n      60\u00b0\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9<sub>cp<\/sub>\n      =\n      tan60\u00b0\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9<sub>cp<\/sub>\n      =\n      \u221a3 rad\/s\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>11. Gain Margin<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Phase Crossover Frequency\n    <\/p>\n\n    <div class=\"formula\">\n      \u03c9<sub>cp<\/sub> = \u221a3\n    <\/div>\n\n    <p>\n      \uc5d0\uc11c magnitude\ub97c \uacc4\uc0b0\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      |G(j\u221a3)|\n      =\n      2\u221a2\n      \/\n      (1+3)<sup>3\/2<\/sup>\n    <\/div>\n\n    <div class=\"formula\">\n      =\n      2\u221a2 \/ 8\n    <\/div>\n\n    <div class=\"formula\">\n      =\n      \u221a2 \/ 4\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c Gain Margin\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      GM\n      =\n      1 \/ |G(j\u03c9<sub>cp<\/sub>)|\n    <\/div>\n\n    <div class=\"formula\">\n      GM\n      =\n      2\u221a2\n    <\/div>\n\n    <div class=\"formula\">\n      GM\n      \u2248\n      2.828\n    <\/div>\n\n    <p>\n      dB\ub85c \ub098\ud0c0\ub0b4\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      GM<sub>dB<\/sub>\n      =\n      20log<sub>10<\/sub>(2\u221a2)\n    <\/div>\n\n    <div class=\"formula\">\n      GM<sub>dB<\/sub>\n      \u2248\n      9.03 dB\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>12. Phase Margin<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Gain Crossover Frequency\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      \u03c9<sub>cg<\/sub>\n      =\n      1 rad\/s\n    <\/div>\n\n    <p>\n      \uc774\ub2e4.\n    <\/p>\n\n    <p>\n      \uc774\ub54c \uc704\uc0c1\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      \u2220G(j)\n      =\n      -3tan<sup>-1<\/sup>(1)\n    <\/div>\n\n    <div class=\"formula\">\n      =\n      -3 \u00d7 45\u00b0\n    <\/div>\n\n    <div class=\"formula\">\n      =\n      -135\u00b0\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      PM\n      =\n      180\u00b0 &#8211; 135\u00b0\n    <\/div>\n\n    <div class=\"formula\">\n      PM\n      =\n      45\u00b0\n    <\/div>\n\n    <p>\n      rad\ub85c \ubcc0\ud658\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      PM\n      =\n      \u03c0\/4\n      \u2248\n      0.785 rad\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>13. \ucd5c\ub300 \ud5c8\uc6a9 \uc2dc\uac04\uc9c0\uc5f0<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc548\uc815 \ud55c\uacc4\uc5d0\uc11c \uc2dc\uac04\uc9c0\uc5f0\uc774\n      \uae30\uc874 Phase Margin\uc744 \ubaa8\ub450 \uc18c\ubaa8\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      T<sub>max<\/sub>\n      =\n      PM \/ \u03c9<sub>cg<\/sub>\n    <\/div>\n\n    <p>\n      \uc55e\uc5d0\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      PM = \u03c0\/4 rad\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9<sub>cg<\/sub> = 1 rad\/s\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      T<sub>max<\/sub>\n      =\n      (\u03c0\/4) \/ 1\n    <\/div>\n\n    <div class=\"formula\">\n      T<sub>max<\/sub>\n      =\n      \u03c0\/4\n    <\/div>\n\n    <div class=\"formula\">\n      T<sub>max<\/sub>\n      \u2248\n      0.785 s\n    <\/div>\n\n    <div class=\"warning\">\n      <strong>\n        T = T<sub>max<\/sub>\uc5d0\uc11c\ub294 Nyquist plot\uc774\n        -1\uc810\uc744 \uc9c0\ub098\uba70 marginal stability \uc0c1\ud0dc\uac00 \ub41c\ub2e4.\n        T\uac00 \uc774\ubcf4\ub2e4 \ucee4\uc9c0\uba74 \uc548\uc815\uc131\uc744 \uc783\uc744 \uc218 \uc788\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>14. \ubb38\uc81c \uacb0\uacfc \uc815\ub9ac<\/h2>\n\n  <div class=\"table-wrap\">\n\n    <table>\n\n      <thead>\n        <tr>\n          <th>\ud56d\ubaa9<\/th>\n          <th>\uacb0\uacfc<\/th>\n        <\/tr>\n      <\/thead>\n\n      <tbody>\n\n        <tr>\n          <td><strong>Gain Crossover Frequency<\/strong><\/td>\n          <td>\n            \u03c9<sub>cg<\/sub> = 1 rad\/s\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Phase Crossover Frequency<\/strong><\/td>\n          <td>\n            \u03c9<sub>cp<\/sub> = \u221a3 rad\/s\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Gain Margin<\/strong><\/td>\n          <td>\n            GM = 2\u221a2 \u2248 2.828\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Gain Margin [dB]<\/strong><\/td>\n          <td>\n            \u2248 9.03 dB\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Phase Margin<\/strong><\/td>\n          <td>\n            PM = 45\u00b0 = \u03c0\/4 rad\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Maximum Time Delay<\/strong><\/td>\n          <td>\n            T<sub>max<\/sub> = \u03c0\/4 \u2248 0.785 s\n          <\/td>\n        <\/tr>\n\n      <\/tbody>\n\n    <\/table>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>15. PM, GM, Delay Margin \ube44\uad50<\/h2>\n\n  <div class=\"table-wrap\">\n\n    <table>\n\n      <thead>\n        <tr>\n          <th>\ud56d\ubaa9<\/th>\n          <th>\uc758\ubbf8<\/th>\n          <th>\uae30\uc900<\/th>\n        <\/tr>\n      <\/thead>\n\n      <tbody>\n\n        <tr>\n          <td><strong>Gain Margin<\/strong><\/td>\n          <td>\ucd94\uac00 \uac00\ub2a5\ud55c Gain<\/td>\n          <td>\u2220G = -180\u00b0<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Phase Margin<\/strong><\/td>\n          <td>\ucd94\uac00 \uac00\ub2a5\ud55c Phase Lag<\/td>\n          <td>|G| = 1<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Delay Margin<\/strong><\/td>\n          <td>\ucd94\uac00 \uac00\ub2a5\ud55c Time Delay<\/td>\n          <td>\n            T<sub>dm<\/sub>\n            =\n            PM \/ \u03c9<sub>gc<\/sub>\n          <\/td>\n        <\/tr>\n\n      <\/tbody>\n\n    <\/table>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>16. \ud575\uc2ec \uae30\uc5b5 \ubb38\uc7a5<\/h2>\n\n  <div class=\"memory\">\n\n    <ol>\n\n      <li>\n        <strong>\n          \uc2dc\uac04\uc9c0\uc5f0 T\ub294 s-domain\uc5d0\uc11c\n          e<sup>-Ts<\/sup>\ub85c \ud45c\ud604\ud55c\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          e<sup>-j\u03c9T<\/sup>\uc758 \ud06c\uae30\ub294 1\uc774\uace0\n          \uc704\uc0c1\uc740 -\u03c9T\uc774\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          \ub530\ub77c\uc11c \uc21c\uc218 \uc2dc\uac04\uc9c0\uc5f0\uc740\n          Gain Crossover Frequency\ub294 \ubc14\uafb8\uc9c0 \uc54a\uace0\n          Phase\ub9cc \uac10\uc18c\uc2dc\ud0a8\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          \uc2dc\uac04\uc9c0\uc5f0\uc774 \uc99d\uac00\ud558\uba74 Nyquist plot\uc774 \ub354 \ud68c\uc804\ud558\uc5ec\n          -1\uc810\uc5d0 \uac00\uae4c\uc6cc\uc9c4\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          Delay Margin\uc740 \uae30\uc874 Phase Margin\uc744\n          \ubaa8\ub450 \uc18c\ubaa8\ud558\ub294 \uc2dc\uac04\uc9c0\uc5f0\uc774\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          PM\uc744 rad\ub85c \ub098\ud0c0\ub0b4\uba74\n          T<sub>dm<\/sub> = PM\/\u03c9<sub>gc<\/sub>\uc774\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          \ubb38\uc81c\uc758 \uc2dc\uc2a4\ud15c\uc5d0\uc11c\ub294\n          \u03c9<sub>cg<\/sub>=1,\n          PM=45\u00b0\uc774\ubbc0\ub85c\n          T<sub>max<\/sub>\u22480.785 s\uc774\ub2e4.\n        <\/strong>\n      <\/li>\n\n    <\/ol>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <div class=\"keywords\">\n    Nyquist Plot, Time Delay, Delay Margin,\n    Phase Margin, Gain Margin,\n    Gain Crossover Frequency, Phase Crossover Frequency,\n    e^-Ts, Phase Lag, Stability Margin\n  <\/div>\n\n<\/div>\n&#8220;`\n","protected":false},"excerpt":{"rendered":"<p>Time delay\ub41c Nyquist Plot https:\/\/nate9389.tistory.com\/1934 https:\/\/electronics.stackexchange.com\/questions\/340566\/how-to-determine-the-critical-delay-for-a-closed-loop-system &#8220;`html Nyquist Plot Time Delay Time Delay \u00b7 Nyquist Plot \u00b7 Gain Crossover \u00b7 Phase Crossover \u00b7 Delay Margin 1. \uc2dc\uac04\uc9c0\uc5f0 \uc2dc\uc2a4\ud15c \uc2dc\uac04\uc9c0\uc5f0\uc774 \ud3ec\ud568\ub41c \uc2dc\uc2a4\ud15c\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ud45c\ud604\ud55c\ub2e4. L(s) = G(s)e-Ts \uc2dc\uac04\uc601\uc5ed\uc5d0\uc11c\ub294 e-TsF(s) \u2194 f(t-T) \uc774\ubbc0\ub85c e-Ts\ub294 \uc785\ub825 \ub610\ub294 \ucd9c\ub825\uc774 T\ub9cc\ud07c \ub2a6\uac8c \ub098\ud0c0\ub098\ub294 \uc21c\uc218 \uc2dc\uac04\uc9c0\uc5f0\uc744 \uc758\ubbf8\ud55c\ub2e4. 2. \uc8fc\ud30c\uc218\uc601\uc5ed\uc758 \uc2dc\uac04\uc9c0\uc5f0 [&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":[1225,1222,1223,1224],"class_list":["post-6156","post","type-post","status-publish","format-standard","hentry","category-1185","tag-delay-margin","tag-nyquist","tag-nyquistplot","tag-timedelay"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6156","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=6156"}],"version-history":[{"count":14,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6156\/revisions"}],"predecessor-version":[{"id":9550,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6156\/revisions\/9550"}],"wp:attachment":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/media?parent=6156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/categories?post=6156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/tags?post=6156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}