{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1d2fd0d0-d274-4de7-8731-c75133fdc1c8",
   "metadata": {},
   "source": [
    "# 6章 制御系の設計仕様"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "57fee953-1de8-4ba9-a915-2e778308e38a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from control.matlab import *\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "#plt.rcParams['font.family'] ='sans-serif' #使用するフォント\n",
    "plt.rcParams['font.family'] = 'Times New Roman' # font familyの設定\n",
    "plt.rcParams['mathtext.fontset'] = 'cm' # math fontの設定\n",
    "plt.rcParams['xtick.direction'] = 'in' #x軸の目盛線が内向き('in')か外向き('out')か双方向か('inout')\n",
    "plt.rcParams['ytick.direction'] = 'in' #y軸の目盛線が内向き('in')か外向き('out')か双方向か('inout')\n",
    "plt.rcParams['xtick.major.width'] = 1.0 #x軸主目盛り線の線幅\n",
    "plt.rcParams['ytick.major.width'] = 1.0 #y軸主目盛り線の線幅\n",
    "plt.rcParams['font.size'] = 11 #フォントの大きさ\n",
    "plt.rcParams['axes.linewidth'] = 0.5 # 軸の線幅edge linewidth。囲みの太さ\n",
    "plt.rcParams['mathtext.default'] = 'it'#'regular'\n",
    "plt.rcParams['axes.xmargin'] = '0'\n",
    "plt.rcParams['axes.ymargin'] = '0.05'\n",
    "plt.rcParams['savefig.facecolor'] = 'None'\n",
    "plt.rcParams['savefig.edgecolor'] = 'None'\n",
    "\n",
    "plt.rcParams[\"legend.fancybox\"] = True     # 丸角\n",
    "# plt.rcParams[\"legend.framealpha\"] = 1    # 透明度の指定、0で塗りつぶしなし\n",
    "# plt.rcParams[\"legend.edgecolor\"] = 'gray' # edgeの色を変更\n",
    "plt.rcParams[\"legend.handlelength\"] = 1.8  # 凡例の線の長さを調節\n",
    "plt.rcParams[\"legend.labelspacing\"] = 0.4  # 垂直方向（縦）の距離の各凡例の距離\n",
    "plt.rcParams[\"legend.handletextpad\"] = 0.7 # 凡例の線と文字の距離の長さ\n",
    "plt.rcParams[\"legend.markerscale\"] = 1.0   # 点がある場合のmarker scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4cdaf8ac-26e0-4150-8afe-e6ee76f79b65",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linestyle_generator():\n",
    "    linestyle = ['-', '--', '-.', ':']\n",
    "    lineID = 0\n",
    "    while True:\n",
    "        yield linestyle[lineID]\n",
    "        lineID = (lineID + 1) % len(linestyle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "84719b81-ef1b-4d5e-898d-6d608e4a7965",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_set(fig_ax, *args):\n",
    "    fig_ax.set_xlabel(args[0])\n",
    "    fig_ax.set_ylabel(args[1])\n",
    "    fig_ax.grid(ls=':', lw=0.5)\n",
    "    if len(args)==3:\n",
    "        fig_ax.legend(loc=args[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "838a4bdf-fb29-4aa6-bb70-d54274c53354",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bodeplot_set(fig_ax, *args):\n",
    "    fig_ax[0].grid(which=\"both\", ls=':', lw=0.5)\n",
    "    fig_ax[0].set_ylabel('Gain [dB]')\n",
    "\n",
    "    fig_ax[1].grid(which=\"both\", ls=':', lw=0.5)\n",
    "    fig_ax[1].set_xlabel('$\\omega$ [rad/s]')\n",
    "    fig_ax[1].set_ylabel('Phase [deg]')\n",
    "    \n",
    "    if len(args) > 0:\n",
    "        fig_ax[1].legend(loc=args[0])\n",
    "    if len(args) > 1:\n",
    "        fig_ax[0].legend(loc=args[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2e508b5-d985-4461-8eb0-9b05d0bcdab4",
   "metadata": {},
   "source": [
    "## 章末問題"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d1e92ea3-3a04-4bc0-82d8-36730c248be2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----- zeta = 0.7071067811865475\n",
      "peak time:  1.1101183183057821\n",
      "overshoot:  0.04321379266071301\n",
      "-----\n",
      "tp =  1.1107207345395915\n",
      "Amax =  0.0432139182637723\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 章末問題１(1)\n",
    "# 最大行き過ぎ量\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "zeta = 1/np.sqrt(2)\n",
    "omega_n = 4\n",
    "\n",
    "P = tf([0, omega_n**2], [1, 2*zeta*omega_n, omega_n**2])\n",
    "y,t = step(P, np.arange(0, 5, 0.01))\n",
    "    \n",
    "pltargs = {'c':'k','ls': '-', 'lw':'1'}    \n",
    "ax.plot(t, y, **pltargs)\n",
    "    \n",
    "info = stepinfo(P)\n",
    "tp = np.pi/(omega_n*np.sqrt(1-zeta**2))\n",
    "ymax = 1 + np.e**(-np.pi*zeta/np.sqrt(1-zeta**2))\n",
    "\n",
    "print('----- zeta =', zeta)\n",
    "print('peak time: ', info['PeakTime'])\n",
    "print('overshoot: ', info['Overshoot']/100*dcgain(P))\n",
    "print('-----')\n",
    "print('tp = ', tp )\n",
    "print('Amax = ', ymax - 1)\n",
    "\n",
    "ax.axhline(1, color=\"k\", linewidth=0.5)\n",
    "ax.axvline(tp, color=\"g\", linewidth=0.5)\n",
    "ax.axhline(ymax, color=\"g\", linewidth=0.5)\n",
    "\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_ylim(0.8, 1.2)\n",
    "plot_set(ax, '$t$', '$y$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "3383cfb6-be14-415a-965a-b82396563182",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----- zeta = 0.3\n",
      "|y-ymax|<0.05:  2.558427881104495\n",
      "Appr1: 2.5357396777413435\n",
      "Appr2: 2.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 章末問題１(2)\n",
    "# 5%整定時間\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "zeta = 0.3\n",
    "omega_n = 4\n",
    "\n",
    "P = tf([0, omega_n**2], [1, 2*zeta*omega_n, omega_n**2])\n",
    "y,t = step(P, np.arange(0, 5, 0.01))\n",
    "    \n",
    "pltargs = {'c':'k','ls': '-', 'lw':'0.5'}    \n",
    "ax.plot(t, y, **pltargs)\n",
    "    \n",
    "info = stepinfo(P, SettlingTimeThreshold=0.05)\n",
    "    \n",
    "print('----- zeta =', zeta)\n",
    "print('|y-ymax|<0.05: ', info['SettlingTime'])\n",
    "print('Appr1:', (np.log(20/np.sqrt(1-zeta**2)))/(zeta*omega_n))\n",
    "print('Appr2:', 3/(zeta*omega_n))\n",
    "    \n",
    "# 包絡線 Appr1：赤線\n",
    "ybar1 = 1 + (1/np.sqrt(1-zeta**2))*np.e**(-zeta*omega_n*t)\n",
    "ybar2 = 1 - (1/np.sqrt(1-zeta**2))*np.e**(-zeta*omega_n*t)\n",
    "ax.plot(t, ybar1, c='r')\n",
    "ax.plot(t, ybar2, c='r')\n",
    "\n",
    "# 包絡線（近似）Appr2：青線\n",
    "ybar1 = 1 + np.e**(-zeta*omega_n*t)\n",
    "ybar2 = 1 - np.e**(-zeta*omega_n*t)\n",
    "ax.plot(t, ybar1, c='b')\n",
    "ax.plot(t, ybar2, c='b')\n",
    "\n",
    "ax.axhline(1, color=\"k\", linewidth=0.5)\n",
    "ax.axhline(1.05, color=\"g\", linewidth=0.5)\n",
    "ax.axhline(0.95, color=\"g\", linewidth=0.5)\n",
    "\n",
    "ax.axvline( (np.log(20/np.sqrt(1-zeta**2)))/(zeta*omega_n), color=\"r\", linewidth=0.5)\n",
    "ax.axvline(3/(zeta*omega_n), color=\"b\", linewidth=0.5)\n",
    "\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_ylim(0.8, 1.2)\n",
    "plot_set(ax, '$t$', '$y$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "374a2e8d-9514-4afe-b7f5-5e6f7fbbdd53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----- zeta = 0.3\n",
      "|y-ymax|<0.02:  2.849158322139097\n",
      "Appr1: 3.2993152876364724\n",
      "Appr2: 3.3333333333333335\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 章末問題１(2)\n",
    "# 2%整定時間\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "zeta = 0.3\n",
    "omega_n = 4\n",
    "\n",
    "P = tf([0, omega_n**2], [1, 2*zeta*omega_n, omega_n**2])\n",
    "y,t = step(P, np.arange(0, 5, 0.01))\n",
    "    \n",
    "pltargs = {'c':'k','ls': '-', 'lw':'0.5'}    \n",
    "ax.plot(t, y, **pltargs)\n",
    "    \n",
    "info = stepinfo(P)\n",
    "    \n",
    "print('----- zeta =', zeta)\n",
    "print('|y-ymax|<0.02: ', info['SettlingTime'])\n",
    "print('Appr1:', (np.log(50/np.sqrt(1-zeta**2)))/(zeta*omega_n))\n",
    "print('Appr2:', 4/(zeta*omega_n))\n",
    "    \n",
    "# 包絡線 Appr1：赤線\n",
    "ybar1 = 1 + (1/np.sqrt(1-zeta**2))*np.e**(-zeta*omega_n*t)\n",
    "ybar2 = 1 - (1/np.sqrt(1-zeta**2))*np.e**(-zeta*omega_n*t)\n",
    "ax.plot(t, ybar1, c='r')\n",
    "ax.plot(t, ybar2, c='r')\n",
    "\n",
    "# 包絡線（近似） Appr2：青線\n",
    "ybar1 = 1 + np.e**(-zeta*omega_n*t)\n",
    "ybar2 = 1 - np.e**(-zeta*omega_n*t)\n",
    "ax.plot(t, ybar1, c='b')\n",
    "ax.plot(t, ybar2, c='b')\n",
    "\n",
    "ax.axhline(1, color=\"k\", linewidth=0.5)\n",
    "ax.axhline(1.02, color=\"g\", linewidth=0.5)\n",
    "ax.axhline(0.98, color=\"g\", linewidth=0.5)\n",
    "\n",
    "ax.axvline((np.log(50/np.sqrt(1-zeta**2)))/(zeta*omega_n), color=\"r\", linewidth=0.5)\n",
    "ax.axvline(4/(zeta*omega_n), color=\"b\", linewidth=0.5)\n",
    "\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_ylim(0.8, 1.2)\n",
    "plot_set(ax, '$t$', '$y$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "06e769e8-df99-4c5d-b4ea-9eb838044c1b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----- zeta = 0.7071067811865475\n",
      "rise time:  0.5180552152093649\n",
      "-----\n",
      "tr =  0.8330405509046935\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 章末問題１(3)\n",
    "# 立ち上がり時間\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "zeta = 1/np.sqrt(2)\n",
    "omega_n = 4\n",
    "\n",
    "P = tf([0, omega_n**2], [1, 2*zeta*omega_n, omega_n**2])\n",
    "y,t = step(P, np.arange(0, 5, 0.01))\n",
    "    \n",
    "pltargs = {'c':'k','ls': '-', 'lw':'1'}    \n",
    "ax.plot(t, y, **pltargs)\n",
    "    \n",
    "info = stepinfo(P)\n",
    "tr = 1/(omega_n*np.sqrt(1-zeta**2))*np.arctan2(np.sqrt(1-zeta**2),-zeta)\n",
    "\n",
    "print('----- zeta =', zeta)\n",
    "print('rise time: ', info['RiseTime'])\n",
    "print('-----')\n",
    "print('tr = ', tr )\n",
    "\n",
    "ax.axhline(1, color=\"k\", linewidth=0.5)\n",
    "ax.axhline(0.9, color=\"g\", linewidth=0.5)\n",
    "ax.axhline(0.1, color=\"g\", linewidth=0.5)\n",
    "ax.axvline(tr, color=\"r\", linewidth=0.5)\n",
    "\n",
    "ax.set_xlim(0, 5)\n",
    "plot_set(ax, '$t$', '$y$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "723cb487-d733-42c3-b153-54de7323b1fe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "peak freq [rad/s]: 3.622154055254967\n",
      "peak gain: 1.7471413945365304\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 章末問題２\n",
    "# ピークゲイン\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "zeta = 0.3\n",
    "omega_n = 4\n",
    "\n",
    "P = tf([0, omega_n**2], [1, 2*zeta*omega_n, omega_n**2])\n",
    "y,t = step(P, np.arange(0, 5, 0.01))\n",
    "\n",
    "gain, phase, w = bode(P, logspace(-1,2, 1000), plot=False)\n",
    "    \n",
    "pltargs = {'c':'k', 'ls':'-', 'lw':'1'}\n",
    "ax.semilogx(w, 20*np.log10(gain), **pltargs)\n",
    "\n",
    "ax.grid(which=\"both\", ls=':', lw=0.5)\n",
    "ax.set_xlabel('$\\omega$ [rad/s]')\n",
    "ax.set_ylabel('Phase [deg]')\n",
    "\n",
    "omega_p = omega_n * np.sqrt(1 - 2*zeta**2)\n",
    "Mp = dcgain(P)/(2*zeta*np.sqrt(1-zeta**2))\n",
    "\n",
    "ax.axhline(20*np.log10(Mp), color=\"g\", linewidth=0.5)\n",
    "ax.axvline(omega_p, color=\"r\", linewidth=0.5)\n",
    "\n",
    "print('peak freq [rad/s]:', omega_p)\n",
    "print('peak gain:', Mp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "539bc376-3b3f-47b0-8ddf-d8a3d975e922",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2% settling time:  3.9771924333533515\n",
      "5% settling time:  3.0003381514770897\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 章末問題３\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "T = 1\n",
    "\n",
    "P = tf([0, 1], [T, 1])\n",
    "y,t = step(P, np.arange(0, 5, 0.01))\n",
    "    \n",
    "pltargs = {'c':'k','ls': '-', 'lw':'1'}    \n",
    "ax.plot(t, y, **pltargs)\n",
    "    \n",
    "info = stepinfo(P)\n",
    "print('2% settling time: ', info['SettlingTime'])\n",
    "info = stepinfo(P, SettlingTimeThreshold=0.05)\n",
    "print('5% settling time: ', info['SettlingTime'])\n",
    "\n",
    "ax.axvline(T, color=\"k\", linewidth=0.5)\n",
    "ax.axhline(1-1/np.e, color=\"k\", linewidth=0.5)\n",
    "\n",
    "ax.axvline(2*T, color=\"g\", linewidth=0.5)\n",
    "ax.axhline(1-1/np.e**2, color=\"g\", linewidth=0.5)\n",
    "\n",
    "ax.axvline(3*T, color=\"b\", linewidth=0.5)\n",
    "ax.axhline(1-1/np.e**3, color=\"b\", linewidth=0.5)\n",
    "\n",
    "ax.axvline(4*T, color=\"r\", linewidth=0.5)\n",
    "ax.axhline(1-1/np.e**4, color=\"r\", linewidth=0.5)\n",
    "\n",
    "ax.set_xlim(0, 5)\n",
    "plot_set(ax, '$t$', '$y$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d836a172-eb4f-468e-ad2b-8034a092ff11",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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