{"id":7238,"date":"2024-04-28T09:01:54","date_gmt":"2024-04-28T00:01:54","guid":{"rendered":"https:\/\/now0930.pe.kr\/wordpress\/?p=7238"},"modified":"2026-10-04T10:21:17","modified_gmt":"2026-10-04T01:21:17","slug":"canonical-form-transfer-function","status":"publish","type":"post","link":"https:\/\/now0930.pe.kr\/wordpress\/canonical-form-transfer-function\/","title":{"rendered":"state space \uc554\uae30 \ud56d\ubaa9"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/jeong-hyeonmin.github.io\/control%20theory\/state-stace-design\">https:\/\/jeong-hyeonmin.github.io\/control%20theory\/state-stace-design<\/a><\/p>\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\/04\/State-Space-Design-34-\uacf5\ub300\uc0dd-\uc774\uc57c\uae30.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"State-Space-Design-34-\uacf5\ub300\uc0dd-\uc774\uc57c\uae30\uc758 \uc0bd\uc785.\"><\/object><a id=\"wp-block-file--media-2e6f14fa-41a1-4fd9-a586-e4707f94ebd1\" href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/04\/State-Space-Design-34-\uacf5\ub300\uc0dd-\uc774\uc57c\uae30.pdf\">State-Space-Design-34-\uacf5\ub300\uc0dd-\uc774\uc57c\uae30<\/a><a href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/04\/State-Space-Design-34-\uacf5\ub300\uc0dd-\uc774\uc57c\uae30.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-2e6f14fa-41a1-4fd9-a586-e4707f94ebd1\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\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\/04\/NeoStudio_20240428_085806.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"NeoStudio_20240428_085806\uc758 \uc0bd\uc785.\"><\/object><a id=\"wp-block-file--media-ced1f645-c71c-4a6d-87ac-78b2c9fe46c1\" href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/04\/NeoStudio_20240428_085806.pdf\">NeoStudio_20240428_085806<\/a><a href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/04\/NeoStudio_20240428_085806.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-ced1f645-c71c-4a6d-87ac-78b2c9fe46c1\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\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\/04\/NeoStudio_20250420_232415_\uc0b0\uc5c5\uacc4\uce21\uc81c\uc5b4-\uae30\uc220\uc0ac15.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"NeoStudio_20250420_232415_\uc0b0\uc5c5\uacc4\uce21\uc81c\uc5b4 \uae30\uc220\uc0ac15\uc758 \uc0bd\uc785.\"><\/object><a id=\"wp-block-file--media-52d3a143-dd5a-4d78-82d8-0e8e5d8c768f\" href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/04\/NeoStudio_20250420_232415_\uc0b0\uc5c5\uacc4\uce21\uc81c\uc5b4-\uae30\uc220\uc0ac15.pdf\">NeoStudio_20250420_232415_\uc0b0\uc5c5\uacc4\uce21\uc81c\uc5b4 \uae30\uc220\uc0ac15<\/a><a href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/04\/NeoStudio_20250420_232415_\uc0b0\uc5c5\uacc4\uce21\uc81c\uc5b4-\uae30\uc220\uc0ac15.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-52d3a143-dd5a-4d78-82d8-0e8e5d8c768f\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\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=\"2022 05 09 \uc81c\uc5b4\uc2dc\uc2a4\ud15c\uc124\uacc4 Chap7(3)\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/1jzJ9I-hiKg?start=1680&amp;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<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\/04\/NeoStudio_20240428_121246-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"NeoStudio_20240428_121246-1\uc758 \uc0bd\uc785.\"><\/object><a id=\"wp-block-file--media-0181e96c-dedb-47fb-9554-df999d31627a\" href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/04\/NeoStudio_20240428_121246-1.pdf\">NeoStudio_20240428_121246-1<\/a><a href=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/04\/NeoStudio_20240428_121246-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-0181e96c-dedb-47fb-9554-df999d31627a\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n&#8220;`html\n<div class=\"chapter19-wide\">\n\n  <h1>Canonical Form \u00b7 Transfer Function<\/h1>\n\n  <div class=\"subtitle\">\n    State Space \u00b7 Controllable Canonical Form \u00b7 Transfer Function \u00b7 Matrix Exponential \u00b7 Controllability \u00b7 Observability\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>1. Transfer Function \u2192 Canonical Form<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uccab \ubc88\uc9f8 NeoStudio PDF\uc5d0\uc11c\ub294\n      Transfer Function\uc73c\ub85c\ubd80\ud130\n      Canonical Form\uc758 \uc0c1\ud0dc\uacf5\uac04 \ud589\ub82c\uc744 \ubc14\ub85c \uad6c\uc131\ud558\ub294 \uc608\uc81c\ub97c \uc0ac\uc6a9\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      G(s)\n      =\n      \\frac{s+2}{s^2+7s+12}\n    <\/div>\n\n    <p>\n      \ubd84\ubaa8 \uacc4\uc218\uc640 \ubd84\uc790 \uacc4\uc218\ub97c \uc774\uc6a9\ud558\uc5ec\n      \ub2e4\uc74c \uc0c1\ud0dc\uacf5\uac04 \ud589\ub82c\uc744 \uad6c\uc131\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      A =\n      \\begin{bmatrix}\n      -7 &#038; -12 \\\\\n      1 &#038; 0\n      \\end{bmatrix}\n    <\/div>\n\n    <div class=\"formula\">\n      B =\n      \\begin{bmatrix}\n      1 \\\\\n      0\n      \\end{bmatrix}\n    <\/div>\n\n    <div class=\"formula\">\n      C =\n      \\begin{bmatrix}\n      1 &#038; 2\n      \\end{bmatrix}\n    <\/div>\n\n    <div class=\"formula\">\n      D = 0\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        \ubd84\ubaa8 \uacc4\uc218\ub294 A \ud589\ub82c,\n        \uc785\ub825\uc740 B,\n        \ubd84\uc790 \uacc4\uc218\ub294 C\uc5d0 \ubc30\uce58\ud558\ub294 \ud615\ud0dc\ub85c \uae30\ub85d\ub418\uc5b4 \uc788\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>2. Canonical Form\uc758 \uae30\ubcf8 \ud615\ud0dc<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294 \ubd84\ubaa8\uacc4\uc218\ub97c A \ud589\ub82c\uc5d0 \ubc30\uce58\ud558\uace0\n      B\ub294 \uccab \ubc88\uc9f8 \uc694\uc18c\ub9cc 1,\n      \ub098\uba38\uc9c0\ub294 0\uc73c\ub85c \ub450\ub294 \ud615\ud0dc\ub97c \uc0ac\uc6a9\ud55c\ub2e4.\n    <\/p>\n\n    <pre>\n      Transfer Function\n             \u2502\n             \u25bc\n      \ubd84\ubaa8 \uacc4\uc218 \ud655\uc778\n             \u2502\n             \u25bc\n            A\n             \u2502\n      \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n      \u2502             \u2502\n      \u25bc             \u25bc\n      B             C\n    [1,0,...]\u1d40   \ubd84\uc790 \uacc4\uc218\n    <\/pre>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>3. \ucd9c\ub825\ud589\ub82c C<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ucd9c\ub825\uc740 \ub2e4\uc74c \uc0c1\ud0dc\uacf5\uac04 \uad00\uacc4\ub85c \ud45c\ud604\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      y = Cx\n    <\/div>\n\n    <div class=\"formula\">\n      y =\n      \\begin{bmatrix}\n      c_1 &#038; c_2\n      \\end{bmatrix}\n      \\begin{bmatrix}\n      x_1 \\\\\n      x_2\n      \\end{bmatrix}\n    <\/div>\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294 x1, x2\uac00\n      \uc5b4\ub5a4 \ubb3c\ub9ac\ub7c9\uc778\uc9c0\ubcf4\ub2e4\n      \uc0c1\ud0dc\ubcc0\uc218\ub97c \uc5b4\ub5bb\uac8c \uc815\uc758\ud588\ub294\uc9c0\uac00 \uc911\uc694\ud558\ub2e4\ub294 \ud750\ub984\uc73c\ub85c \uae30\ub85d\ub418\uc5b4 \uc788\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>4. \ub450 \ubc88\uc9f8 \uc608\uc81c<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      \\frac{Y(s)}{U(s)}\n      =\n      \\frac{s+3}{s^2+3s+2}\n    <\/div>\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294 \uc774 \uc804\ub2ec\ud568\uc218\ub97c\n      \ub2e4\uc74c\uacfc \uac19\uc774 \uc0c1\ud0dc\uacf5\uac04 \ud615\ud0dc\ub85c \uc62e\uae34\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      A =\n      \\begin{bmatrix}\n      -3 &#038; -2 \\\\\n      1 &#038; 0\n      \\end{bmatrix}\n    <\/div>\n\n    <div class=\"formula\">\n      B =\n      \\begin{bmatrix}\n      1 \\\\\n      0\n      \\end{bmatrix}\n    <\/div>\n\n    <div class=\"formula\">\n      C =\n      \\begin{bmatrix}\n      1 &#038; 3\n      \\end{bmatrix}\n    <\/div>\n\n    <div class=\"formula\">\n      D = 0\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>5. \ub450 \uc608\uc81c \ube44\uad50<\/h2>\n\n  <div class=\"table-wrap\">\n\n    <table>\n      <thead>\n        <tr>\n          <th>\ud56d\ubaa9<\/th>\n          <th>\uc608\uc81c 1<\/th>\n          <th>\uc608\uc81c 2<\/th>\n        <\/tr>\n      <\/thead>\n      <tbody>\n\n        <tr>\n          <td><strong>Transfer Function<\/strong><\/td>\n          <td>(s+2)\/(s\u00b2+7s+12)<\/td>\n          <td>(s+3)\/(s\u00b2+3s+2)<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>A \uccab \ud589<\/strong><\/td>\n          <td>[-7, -12]<\/td>\n          <td>[-3, -2]<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>A \ub458\uc9f8 \ud589<\/strong><\/td>\n          <td>[1, 0]<\/td>\n          <td>[1, 0]<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>B<\/strong><\/td>\n          <td>[1, 0]\u1d40<\/td>\n          <td>[1, 0]\u1d40<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>C<\/strong><\/td>\n          <td>[1, 2]<\/td>\n          <td>[1, 3]<\/td>\n        <\/tr>\n\n      <\/tbody>\n    <\/table>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>6. Controllability Matrix<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ub450 \ubc88\uc9f8 NeoStudio PDF\ub294\n      Controllability Canonical Form\uc744 \ub9cc\ub4e4\uae30 \uc704\ud55c\n      \ubcc0\ud658\ud589\ub82c T\uc758 \uc720\ub3c4\ub85c \uc774\uc5b4\uc9c4\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \\mathcal{C}\n      =\n      \\begin{bmatrix}\n      B &#038; AB &#038; A^2B &#038; \\cdots\n      \\end{bmatrix}\n    <\/div>\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294\n      Controllability Matrix\uac00\n      Full Rank\ub77c\ub294 \uc804\uc81c\uc5d0\uc11c \ubcc0\ud658\uc744 \uc9c4\ud589\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      rank(\\mathcal{C}) = n\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>7. \uc0c1\ud0dc\ubcc0\uc218 \ubcc0\ud658<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uae30\uc874 \uc0c1\ud0dc x\uc640 \uc0c8\ub85c\uc6b4 \uc0c1\ud0dc z\uc758 \uad00\uacc4\ub97c\n      \ub2e4\uc74c\uacfc \uac19\uc774 \ub454\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      x = Tz\n    <\/div>\n\n    <div class=\"formula\">\n      z = T^{-1}x\n    <\/div>\n\n    <p>\n      \uc6d0\ub798 \uc2dc\uc2a4\ud15c\n    <\/p>\n\n    <div class=\"formula\">\n      \\dot{x} = Ax + Bu\n    <\/div>\n\n    <p>\n      \uc5d0 x = Tz\ub97c \ub300\uc785\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      T\\dot{z}\n      =\n      ATz + Bu\n    <\/div>\n\n    <div class=\"formula\">\n      \\dot{z}\n      =\n      T^{-1}ATz\n      +\n      T^{-1}Bu\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>8. \ubcc0\ud658 \ud6c4 \ud589\ub82c<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      \\bar{A}\n      =\n      T^{-1}AT\n    <\/div>\n\n    <div class=\"formula\">\n      \\bar{B}\n      =\n      T^{-1}B\n    <\/div>\n\n    <p>\n      \ud544\uae30\uc758 \ubaa9\uc801\uc740\n      \\bar{A}, \\bar{B}\ub97c\n      Canonical Form\uc73c\ub85c \ub9cc\ub4dc\ub294 \uac83\uc774\ub2e4.\n    <\/p>\n\n    <div class=\"memory\">\n      <strong>\n        \uc801\uc808\ud55c T\ub97c \uc120\uc815\ud558\uc5ec\n        \uc6d0\ub798 \uc2dc\uc2a4\ud15c\uacfc \uac19\uc740 \ub3d9\ud2b9\uc131\uc744 \uac00\uc9c0\uba74\uc11c\n        \uc0c1\ud0dc\uacf5\uac04 \ud45c\ud604\ub9cc Canonical Form\uc73c\ub85c \ubcc0\ud658\ud55c\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>9. Canonical Form\uc758 B \ud589\ub82c<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      3\ucc28 \uc2dc\uc2a4\ud15c \uc608\uc81c\uc5d0\uc11c\ub294\n      \ubcc0\ud658 \ud6c4 B\ub97c \ub2e4\uc74c \ud615\ud0dc\ub85c \ub454\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \\bar{B}\n      =\n      \\begin{bmatrix}\n      0 \\\\\n      0 \\\\\n      1\n      \\end{bmatrix}\n    <\/div>\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294 T\ub97c \uad6c\uc131\ud558\ub294 \uc5f4\ubca1\ud130\ub97c\n      t1, t2, t3\ub85c \ub450\uace0 \uad00\uacc4\ub97c \uc720\ub3c4\ud55c\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>10. T\uc758 \uc5f4\ubca1\ud130 \uad00\uacc4<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ud544\uae30\uc758 \uc720\ub3c4\uc5d0\uc11c\n      T\uc758 \uc5f4\ubca1\ud130 \uc0ac\uc774\uc5d0\ub294\n      A\uc640\uc758 \uacf1\uc744 \uc774\uc6a9\ud55c \uad00\uacc4\uac00 \ub9cc\ub4e4\uc5b4\uc9c4\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      t_2^T = t_1^T A\n    <\/div>\n\n    <div class=\"formula\">\n      t_3^T = t_1^T A^2\n    <\/div>\n\n    <p>\n      \ub610\ud55c \ubcc0\ud658 \ud6c4 B \uc870\uac74\uc5d0\uc11c\n      \ub2e4\uc74c \uad00\uacc4\uac00 \ub098\uc628\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      t_1^T B = 0\n    <\/div>\n\n    <div class=\"formula\">\n      t_1^T AB = 0\n    <\/div>\n\n    <div class=\"formula\">\n      t_1^T A^2B = 1\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>11. T\uc640 Controllability Matrix<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc704 \uc870\uac74\uc744 \ud55c \ubc88\uc5d0 \uc4f0\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      t_1^T\n      \\begin{bmatrix}\n      B &#038; AB &#038; A^2B\n      \\end{bmatrix}\n      =\n      \\begin{bmatrix}\n      0 &#038; 0 &#038; 1\n      \\end{bmatrix}\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      t_1^T\n      =\n      \\begin{bmatrix}\n      0 &#038; 0 &#038; 1\n      \\end{bmatrix}\n      \\begin{bmatrix}\n      B &#038; AB &#038; A^2B\n      \\end{bmatrix}^{-1}\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        \ubcc0\ud658\ud589\ub82c T\ub97c \uad6c\ud560 \ub54c\n        Controllability Matrix\uc758 \uc5ed\ud589\ub82c\uc744 \uc774\uc6a9\ud55c\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>12. Matrix Exponential<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc138 \ubc88\uc9f8 NeoStudio PDF\ub294\n      State Space \ubcf5\uc2b5\ub0b4\uc6a9\uc73c\ub85c \uc774\uc5b4\uc9c4\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      e^{at}\n      =\n      \\sum_{k=0}^{\\infty}\n      \\frac{a^k t^k}{k!}\n    <\/div>\n\n    <p>\n      \uc774\ub97c Matrix\ub85c \ud655\uc7a5\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      e^{At}\n      =\n      I\n      +\n      At\n      +\n      \\frac{A^2t^2}{2!}\n      +\n      \\cdots\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>13. State Transition Matrix<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      \\Phi(t)\n      =\n      e^{At}\n    <\/div>\n\n    <div class=\"formula\">\n      e^{At}\n      =\n      \\mathcal{L}^{-1}\n      \\left\\{\n      (sI-A)^{-1}\n      \\right\\}\n    <\/div>\n\n    <p>\n      \ud544\uae30\uc5d0\ub294 \ub2e4\uc74c \uc131\uc9c8\uc774 \uae30\ub85d\ub418\uc5b4 \uc788\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \\Phi(-t)\n      =\n      e^{-At}\n    <\/div>\n\n    <div class=\"formula\">\n      \\Phi(0)\n      =\n      I\n    <\/div>\n\n    <div class=\"formula\">\n      \\Phi^{-1}(t)\n      =\n      \\Phi(-t)\n    <\/div>\n\n    <div class=\"formula\">\n      \\Phi(t_1+t_2)\n      =\n      \\Phi(t_1)\\Phi(t_2)\n    <\/div>\n\n    <div class=\"formula\">\n      \\Phi(nt)\n      =\n      \\Phi^n(t)\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>14. Matrix Exponential \uc608\uc81c<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      A =\n      \\begin{bmatrix}\n      0 &#038; 1 \\\\\n      -2 &#038; -3\n      \\end{bmatrix}\n    <\/div>\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294\n      \ub2e4\uc74c \uad00\uacc4\ub85c \u03a6(t)\ub97c \uad6c\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \\Phi(t)\n      =\n      \\mathcal{L}^{-1}\n      \\left\\{\n      (sI-A)^{-1}\n      \\right\\}\n    <\/div>\n\n    <p>\n      \uadf8\ub9ac\uace0\n    <\/p>\n\n    <div class=\"formula\">\n      sI-A\n      =\n      \\begin{bmatrix}\n      s &#038; -1 \\\\\n      2 &#038; s+3\n      \\end{bmatrix}\n    <\/div>\n\n    <p>\n      \ub85c \ub450\uace0 \uc5ed\ud589\ub82c\uc744 \uacc4\uc0b0\ud558\ub294 \uacfc\uc815\uc744 \uc801\uace0 \uc788\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>15. Non-homogeneous State Equation<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      \\dot{x}\n      =\n      Ax + Bu\n    <\/div>\n\n    <p>\n      \uc785\ub825\uc774 \uc874\uc7ac\ud558\ub294 \uacbd\uc6b0\uc758 \uc0c1\ud0dc\ud574\ub294\n      \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\ub9ac\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      x(t)\n      =\n      e^{At}x(0)\n      +\n      \\int_0^t\n      e^{A(t-\\tau)}\n      Bu(\\tau)d\\tau\n    <\/div>\n\n    <p>\n      State Transition Matrix\ub97c \uc0ac\uc6a9\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      x(t)\n      =\n      \\Phi(t)x(0)\n      +\n      \\int_0^t\n      \\Phi(t-\\tau)Bu(\\tau)d\\tau\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>16. Laplace Form<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      (sI-A)X\n      =\n      x(0)+BU\n    <\/div>\n\n    <div class=\"formula\">\n      X\n      =\n      (sI-A)^{-1}x(0)\n      +\n      (sI-A)^{-1}BU\n    <\/div>\n\n    <p>\n      Inverse Laplace Transform\uacfc\n      Convolution\uc744 \ud1b5\ud574\n      \uac19\uc740 \uc0c1\ud0dc\ud574\ub97c \uc5bb\ub294 \ud750\ub984\uc774\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>17. Controllability \uc758\ubbf8<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294 Controllability\ub97c\n      \ucd08\uae30\uc0c1\ud0dc\uc5d0\uc11c \uc6d0\ud558\ub294 \uc0c1\ud0dc\uae4c\uc9c0\n      \uc785\ub825\uc73c\ub85c \uc774\ub3d9\ud560 \uc218 \uc788\ub294\uac00\uc758 \ubb38\uc81c\ub85c \ubcf8\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      x(t_0)\n      \u2192\n      u(t)\n      \u2192\n      x(t_1)\n    <\/div>\n\n    <p>\n      \ud2b9\ud788 \ucd08\uae30\uc0c1\ud0dc\ub97c\n      \ucd5c\uc885\uc801\uc73c\ub85c 0\uc73c\ub85c \ubcf4\ub0b4\ub294 \uacbd\uc6b0\ub97c \uc774\uc6a9\ud574 \uc720\ub3c4\ud55c\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>18. Controllability Matrix \uc720\ub3c4<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc0c1\ud0dc\ud574\uc5d0\uc11c Matrix Exponential\uc744\n      A\uc758 \uac70\ub4ed\uc81c\uacf1\uc73c\ub85c \uc804\uac1c\ud558\uba74\n      \ub2e4\uc74c \ud56d\ub4e4\uc774 \ub098\ud0c0\ub09c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      B,\\ AB,\\ A^2B,\\ \\cdots\n    <\/div>\n\n    <div class=\"formula\">\n      \\mathcal{C}\n      =\n      \\begin{bmatrix}\n      B &#038; AB &#038; A^2B &#038; \\cdots\n      \\end{bmatrix}\n    <\/div>\n\n    <p>\n      \uc774 \ud589\ub82c\uc774 \uc0c1\ud0dc\uacf5\uac04 \uc804\uccb4\ub97c \uc0dd\uc131\ud560 \uc218 \uc788\ub294\uc9c0\uac00\n      Controllability \ud310\ub2e8\uc758 \ud575\uc2ec\uc73c\ub85c \uae30\ub85d\ub418\uc5b4 \uc788\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>19. Observability<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      \\dot{x}\n      =\n      Ax + Bu\n    <\/div>\n\n    <div class=\"formula\">\n      y = Cx\n    <\/div>\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294\n      \ucd9c\ub825 y(t)\ub97c \uad00\ucc30\ud558\uc5ec\n      \ub0b4\ubd80 \uc0c1\ud0dc x(t)\ub97c \uc54c \uc218 \uc788\ub294\uc9c0\ub97c\n      Observability\ub85c \uc124\uba85\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"memory\">\n      <strong>\n        Observable :\n        y(t)\ub97c \uad00\ucc30\ud558\uc5ec x(t)\ub97c \uc54c \uc218 \uc788\ub294\uac00?\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>20. Observability Matrix<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc0c1\ud0dc\ud574\ub97c \ucd9c\ub825\uc2dd\uc5d0 \ub300\uc785\ud558\uace0\n      e<sup>At<\/sup>\ub97c \uc804\uac1c\ud558\uba74\n      C, CA, CA\u00b2 \u2026 \ud56d\uc774 \ub9cc\ub4e4\uc5b4\uc9c4\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \\mathcal{O}\n      =\n      \\begin{bmatrix}\n      C \\\\\n      CA \\\\\n      CA^2 \\\\\n      \\vdots\n      \\end{bmatrix}\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>21. Canonical Form\uacfc Controllability \uad00\uacc4<\/h2>\n\n  <div class=\"card\">\n\n    <pre>\n      Transfer Function\n              \u2502\n              \u25bc\n      State Space Model\n              \u2502\n              \u25bc\n      Controllability \ud655\uc778\n              \u2502\n              \u25bc\n      C = [B AB A\u00b2B ...]\n              \u2502\n        Full Rank\n              \u2502\n              \u25bc\n      Transformation Matrix T\n              \u2502\n              \u25bc\n      x = Tz\n              \u2502\n              \u25bc\n      A\u0304 = T\u207b\u00b9AT\n      B\u0304 = T\u207b\u00b9B\n              \u2502\n              \u25bc\n      Controllable Canonical Form\n    <\/pre>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>22. \uc804\uccb4 \ud575\uc2ec \uc815\ub9ac<\/h2>\n\n  <div class=\"table-wrap\">\n\n    <table>\n\n      <thead>\n        <tr>\n          <th>\ud56d\ubaa9<\/th>\n          <th>NeoStudio \ub0b4\uc6a9<\/th>\n        <\/tr>\n      <\/thead>\n\n      <tbody>\n\n        <tr>\n          <td><strong>Transfer Function \u2192 State Space<\/strong><\/td>\n          <td>\ubd84\ubaa8\u00b7\ubd84\uc790 \uacc4\uc218\ub85c A, B, C, D \uad6c\uc131<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>\uc0c1\ud0dc\ubcc0\ud658<\/strong><\/td>\n          <td>x = Tz<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>\ubcc0\ud658 \ud6c4 A<\/strong><\/td>\n          <td>A\u0304 = T\u207b\u00b9AT<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>\ubcc0\ud658 \ud6c4 B<\/strong><\/td>\n          <td>B\u0304 = T\u207b\u00b9B<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Controllability Matrix<\/strong><\/td>\n          <td>[B AB A\u00b2B \u2026]<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Matrix Exponential<\/strong><\/td>\n          <td>e<sup>At<\/sup> = I + At + A\u00b2t\u00b2\/2! + \u2026<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>State Transition Matrix<\/strong><\/td>\n          <td>\u03a6(t) = e<sup>At<\/sup><\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Non-homogeneous Solution<\/strong><\/td>\n          <td>e<sup>At<\/sup>x(0) + \u222be<sup>A(t-\u03c4)<\/sup>Bu(\u03c4)d\u03c4<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Observability Matrix<\/strong><\/td>\n          <td>[C; CA; CA\u00b2; \u2026]<\/td>\n        <\/tr>\n\n      <\/tbody>\n\n    <\/table>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <div class=\"warning\">\n    <strong>\n      \uc774 HTML\uc740 \ud398\uc774\uc9c0 \ubcf8\ubb38\uc774\ub098 \uc678\ubd80 \uac15\uc758\u00b7\uc77c\ubc18 \ucc38\uace0\uc790\ub8cc\ub97c \uc0ac\uc6a9\ud558\uc9c0 \uc54a\uace0,\n      NeoStudio PDF 3\uac1c, \ucd1d 10\ud398\uc774\uc9c0\ub97c \ud398\uc774\uc9c0\ubcc4 OCR\/\uc2dc\uac01 \ud310\ub3c5\ud558\uc5ec \uc791\uc131\ud588\ub2e4.\n\n      \uccab \ubc88\uc9f8 PDF\ub294 Transfer Function\uc5d0\uc11c\n      Controllable Canonical Form\uc744 \uc9c1\uc811 \uad6c\uc131\ud558\ub294 \uc608\uc81c\uc774\ub2e4.\n\n      \ub450 \ubc88\uc9f8 PDF\ub294 Controllability Matrix\ub97c \uc774\uc6a9\ud558\uc5ec\n      \uc0c1\ud0dc\ubcc0\ud658\ud589\ub82c T\ub97c \uad6c\ud558\uace0 Canonical Form\uc73c\ub85c \ubcc0\ud658\ud558\ub294 \uc720\ub3c4\uc774\ub2e4.\n\n      \uc138 \ubc88\uc9f8 PDF\ub294 Matrix Exponential,\n      Non-homogeneous State Equation,\n      Controllability, Observability\uc758 \ubcf5\uc2b5 \ub0b4\uc6a9\uc774\ub2e4.\n\n      \uc77c\ubd80 \uc190\uae00\uc528\uc758 \ud589\ub82c\uc6d0\uc18c\uc640 \uc911\uac04 \uc720\ub3c4\uc2dd\uc740\n      \ucde8\uc18c\uc120 \ub610\ub294 \ud310\ub3c5 \ubd88\uba85\ud655 \ubd80\ubd84\uc774 \uc788\uc5b4\n      \uc784\uc758\ub85c \ubcf4\uc644\ud558\uc9c0 \uc54a\uace0,\n      \uba85\ud655\ud558\uac8c \ud655\uc778\ub418\ub294 \ucd5c\uc885 \uad00\uacc4\ub9cc \ubc18\uc601\ud588\ub2e4.\n    <\/strong>\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <div class=\"keywords\">\n    Canonical Form,\n    Controllable Canonical Form,\n    Transfer Function,\n    State Space,\n    State Variable,\n    State Transformation,\n    Transformation Matrix,\n    Controllability,\n    Controllability Matrix,\n    Observability,\n    Observability Matrix,\n    Matrix Exponential,\n    State Transition Matrix\n  <\/div>\n\n<\/div>\n&#8220;`\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/jeong-hyeonmin.github.io\/control%20theory\/state-stace-design &#8220;`html Canonical Form \u00b7 Transfer Function State Space \u00b7 Controllable Canonical Form \u00b7 Transfer Function \u00b7 Matrix Exponential \u00b7 Controllability \u00b7 Observability 1. Transfer Function \u2192 Canonical Form \uccab \ubc88\uc9f8 NeoStudio PDF\uc5d0\uc11c\ub294 Transfer Function\uc73c\ub85c\ubd80\ud130 Canonical Form\uc758 \uc0c1\ud0dc\uacf5\uac04 \ud589\ub82c\uc744 \ubc14\ub85c \uad6c\uc131\ud558\ub294 \uc608\uc81c\ub97c \uc0ac\uc6a9\ud55c\ub2e4. G(s) = \\frac{s+2}{s^2+7s+12} \ubd84\ubaa8 \uacc4\uc218\uc640 \ubd84\uc790 \uacc4\uc218\ub97c \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \uc0c1\ud0dc\uacf5\uac04 \ud589\ub82c\uc744 \uad6c\uc131\ud55c\ub2e4. [&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":[1574,1539,1540,1214],"class_list":["post-7238","post","type-post","status-publish","format-standard","hentry","category-1185","tag-canonical-form","tag-controllability","tag-observability","tag-state-space"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/7238","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=7238"}],"version-history":[{"count":4,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/7238\/revisions"}],"predecessor-version":[{"id":9626,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/7238\/revisions\/9626"}],"wp:attachment":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/media?parent=7238"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/categories?post=7238"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/tags?post=7238"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}