{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6a1b6d82-182c-4b2b-b7cd-7104e6ac07bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "import control\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6d10472-57e1-4df9-ba32-b120d5233407",
   "metadata": {},
   "source": [
    "# 1 Root Locus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7175ab4e-4df3-4746-8152-14ce4d74f85d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sympy_to_control(tf):\n",
    "    s = sympy.symbols('s')\n",
    "    num, den = sympy.fraction(tf)\n",
    "    num = sympy.poly(num, s)\n",
    "    den = sympy.poly(den, s)\n",
    "    n = np.array(num.all_coeffs(), dtype=float)\n",
    "    d = np.array(den.all_coeffs(), dtype=float)\n",
    "    return control.tf(n, d)\n",
    "\n",
    "def rlocus(tf, *args, **kwargs):\n",
    "    return control.rlocus(sympy_to_control(tf), *args, **kwargs)\n",
    "\n",
    "def step_response(tf, *args, **kwargs):\n",
    "    return control.step_response(sympy_to_control(tf), *args, **kwargs)\n",
    "\n",
    "def forced_response(tf, *args, **kwargs):\n",
    "    return control.forced_response(sympy_to_control(tf), *args, **kwargs)\n",
    "\n",
    "def wrap_deg(angle):\n",
    "    while angle > 180:\n",
    "        angle -= 360\n",
    "    while angle < -180:\n",
    "        angle += 360\n",
    "    return angle\n",
    "\n",
    "def zpk(tf):\n",
    "    s = sympy.symbols('s')\n",
    "    num, den = sympy.fraction(tf)\n",
    "    num = sympy.poly(num, s)\n",
    "    den = sympy.poly(den, s)\n",
    "    zeros = sympy.roots(num, multiple=True)\n",
    "    poles = sympy.roots(den, multiple=True)\n",
    "    Gzp = 1\n",
    "    for z in zeros:\n",
    "        Gzp *= (s - z)\n",
    "    for p in poles:\n",
    "        Gzp /= (s - p)\n",
    "    k = sympy.simplify(tf/Gzp)\n",
    "    return  zeros, poles, k\n",
    "    \n",
    "def root_locus_problem(G):\n",
    "    s = sympy.symbols('s')\n",
    "    zeros, poles, gain = zpk(G)\n",
    "\n",
    "    print('\\n====================================')\n",
    "    print('Part 1')\n",
    "    print('zeros:', zeros)\n",
    "    print('poles:', poles)\n",
    "\n",
    "    print('\\n====================================')\n",
    "    print('Part 2')\n",
    "    n = len(poles)\n",
    "    m = len(zeros)\n",
    "    num_asymptotes = n - m\n",
    "    print('num asymptotes:', n-m)\n",
    "\n",
    "    if gain > 0:\n",
    "        angle_start = 180\n",
    "    else:\n",
    "        angle_start = 0\n",
    "        \n",
    "    asymptotes = np.array([ wrap_deg((angle_start + 360*j)/num_asymptotes) for j in range(num_asymptotes)])\n",
    "    print('asymptotes deg:', asymptotes)\n",
    "\n",
    "    centroid = (np.sum(poles) -np.sum(zeros))/(n - m)\n",
    "    print('centroid', centroid)\n",
    "\n",
    "    print('\\n====================================')\n",
    "    print('Part 3: Break away/in')\n",
    "    K = sympy.symbols('K', real=True)\n",
    "    f_K = sympy.solve(K*G + 1)[0][K]\n",
    "    break_away_in = sympy.solve(f_K.diff(s))\n",
    "    print('candidate break awak/in', break_away_in)\n",
    "\n",
    "    print('\\n====================================')\n",
    "    print('Part 4: Imaginary Crossing')\n",
    "    omega = sympy.symbols('omega', real=True)\n",
    "    G_jw = G.subs(s, sympy.I*omega).expand(complex=True).collect(sympy.I)\n",
    "    print('re(G(j omega)):', sympy.re(K*G_jw).simplify(), '= -1')\n",
    "    print('im(G(j omega)):', sympy.im(K*G_jw).simplify(), '= 0')\n",
    "    omega = sympy.symbols('omega', real=True)\n",
    "    print(sympy.solve(sympy.im((K*G).subs(s, sympy.I*omega)), omega))\n",
    "    sol_omega = np.array(sympy.solve(sympy.im((K*G).subs(s, sympy.I*omega)), omega), dtype=float)\n",
    "    try:\n",
    "        omega_val = sol_omega[np.argwhere(sol_omega > 0)[0][0]]\n",
    "        print('omega:', omega_val)\n",
    "        K_val = sympy.solve(sympy.re((K*G_jw)).subs(omega, omega_val).simplify() + 1, K)[0]\n",
    "        print('K:', K_val)\n",
    "    except IndexError as e:\n",
    "        print(e)\n",
    "        print('no imaginary crossing')\n",
    "\n",
    "    print('\\n====================================')\n",
    "    print('Part 5: Angle of Arrival/ Departure')\n",
    "    arrival = {}\n",
    "    departure = {}\n",
    "    for i_s, s in enumerate(zeros):\n",
    "        arrival[s] = angle_start\n",
    "        for i_p, p in enumerate(poles):\n",
    "            arrival[s] += wrap_deg(np.rad2deg(np.angle(complex(s - p))))\n",
    "        for i_z, z in enumerate(zeros):\n",
    "            if i_z == i_s:\n",
    "                continue\n",
    "            arrival[s] -= wrap_deg(np.rad2deg(np.angle(complex(s - z))))\n",
    "\n",
    "    for i_s, s in enumerate(poles):\n",
    "        departure[s] = angle_start\n",
    "        for i_p, p in enumerate(poles):\n",
    "            if i_p == i_s:\n",
    "                continue\n",
    "            departure[s] -= wrap_deg(np.rad2deg(np.angle(complex(s - p))))\n",
    "        for i_z, z in enumerate(zeros):\n",
    "            departure[s] += wrap_deg(np.rad2deg(np.angle(complex(s - z))))\n",
    "    \n",
    "    for k in arrival.keys():\n",
    "        if arrival[k] > 180:\n",
    "            arrival[k] -= 360\n",
    "            \n",
    "    for k in departure.keys():\n",
    "        if departure[k] > 180:\n",
    "            departure[k] -= 360\n",
    "    \n",
    "    # account for repeated poles/zeros\n",
    "    num, den = sympy.fraction(G)\n",
    "    zeros_mult = sympy.roots(num)\n",
    "    poles_mult = sympy.roots(den)\n",
    "    print(zeros_mult)\n",
    "    print(poles_mult)\n",
    "    for p in poles_mult.keys():\n",
    "        n = poles_mult[p]\n",
    "        departure[p] /= n\n",
    "\n",
    "    for z in zeros_mult.keys():\n",
    "        n = zeros_mult[z]\n",
    "        arrival[z] /= n\n",
    "    print('poles', poles)\n",
    "    print('zeros', zeros)\n",
    "\n",
    "    print('arrival: ', arrival)\n",
    "    print('departure: ', departure)\n",
    "    \n",
    "    print('\\n====================================')\n",
    "    print('Part 6: Draw Root Locus')\n",
    "    rlocus(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ca05290d-b901-493b-ba90-ffa0055112ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{\\left(s + 2\\right) \\left(s^{2} + 2 s + 1\\right)}$"
      ],
      "text/plain": [
       "1/((s + 2)*(s**2 + 2*s + 1))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = sympy.symbols('s')\n",
    "G = 1/((s**2 + 2*s + 1)*(s + 2))\n",
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "be332d99-dfe8-44d4-8653-ade66fa32a68",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "====================================\n",
      "Part 1\n",
      "zeros: []\n",
      "poles: [-2, -1, -1]\n",
      "\n",
      "====================================\n",
      "Part 2\n",
      "num asymptotes: 3\n",
      "asymptotes deg: [ 60. 180. -60.]\n",
      "centroid -4/3\n",
      "\n",
      "====================================\n",
      "Part 3: Break away/in\n",
      "candidate break awak/in [-5/3, -1]\n",
      "\n",
      "====================================\n",
      "Part 4: Imaginary Crossing\n",
      "re(G(j omega)): 2*K*(1 - 2*omega**2)/(omega**6 + 6*omega**4 + 9*omega**2 + 4) = -1\n",
      "im(G(j omega)): K*omega*(omega**2 - 5)/(omega**6 + 6*omega**4 + 9*omega**2 + 4) = 0\n",
      "[]\n",
      "index 0 is out of bounds for axis 0 with size 0\n",
      "no imaginary crossing\n",
      "\n",
      "====================================\n",
      "Part 5: Angle of Arrival/ Departure\n",
      "{}\n",
      "{-2: 1, -1: 2}\n",
      "poles [-2, -1, -1]\n",
      "zeros []\n",
      "arrival:  {}\n",
      "departure:  {-2: -180.0, -1: 90.0}\n",
      "\n",
      "====================================\n",
      "Part 6: Draw Root Locus\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": [
    "root_locus_problem(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "db9d4097-050b-477b-b77f-1eb2649b1326",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{s}{\\left(s + 1\\right) \\left(s + 2\\right)}$"
      ],
      "text/plain": [
       "-s/((s + 1)*(s + 2))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = -s/((s+1)*(s+2))\n",
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ef9213a7-d710-464a-b868-6421033a1ede",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "====================================\n",
      "Part 1\n",
      "zeros: [0]\n",
      "poles: [-2, -1]\n",
      "\n",
      "====================================\n",
      "Part 2\n",
      "num asymptotes: 1\n",
      "asymptotes deg: [0.]\n",
      "centroid -3\n",
      "\n",
      "====================================\n",
      "Part 3: Break away/in\n",
      "candidate break awak/in [-sqrt(2), sqrt(2)]\n",
      "\n",
      "====================================\n",
      "Part 4: Imaginary Crossing\n",
      "re(G(j omega)): -3*K*omega**2/(omega**4 + 5*omega**2 + 4) = -1\n",
      "im(G(j omega)): K*omega*(omega**2 - 2)/(omega**4 + 5*omega**2 + 4) = 0\n",
      "[0]\n",
      "index 0 is out of bounds for axis 0 with size 0\n",
      "no imaginary crossing\n",
      "\n",
      "====================================\n",
      "Part 5: Angle of Arrival/ Departure\n",
      "{0: 1}\n",
      "{-1: 1, -2: 1}\n",
      "poles [-2, -1]\n",
      "zeros [0]\n",
      "arrival:  {0: 0.0}\n",
      "departure:  {-2: 0.0, -1: 180.0}\n",
      "\n",
      "====================================\n",
      "Part 6: Draw Root Locus\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": [
    "root_locus_problem(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "32e94ad7-824f-44fb-8157-c1f6a8cc2f01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{s^{2} + 4}$"
      ],
      "text/plain": [
       "1/(s**2 + 4)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = 1/(s**2 + 4)\n",
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c0c58f20-b439-4d58-8e49-956263ed1a0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "s_d = -4 + 2*sympy.I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "917e4c32-4117-45c8-9fe6-96badf27805c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\pi}{4}$"
      ],
      "text/plain": [
       "pi/4"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.arg(G.subs(s, s_d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b2da96f5-197b-4efb-b24a-5e96d0a23635",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "360-315"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6923d81f-5e60-443f-b1f8-c9f17f8f5438",
   "metadata": {},
   "outputs": [],
   "source": [
    "K_PD = 8*(s+2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9f3ca952-73cb-4604-a787-582525cc51d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc3acf17b50>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "rlocus(G*K_PD);\n",
    "plt.plot(-4, 2, 'rs')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "cfebb995-6d31-4a83-9569-32d927886fd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -1$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.simplify((G*K_PD).subs(s, s_d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "50c6c32c-d9f9-4ee0-8e52-c33ab54815ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "K_PI = 1.002*(s + 0.01)/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9be50708-3ec1-4bbc-bafd-7f8c4cd48059",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 8.016 s + 16.11216 + \\frac{0.16032}{s}$"
      ],
      "text/plain": [
       "8.016*s + 16.11216 + 0.16032/s"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(K_PI*K_PD).expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "76724366-99b7-42f3-ad28-847592c94faf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1.002 s + 0.01002}{s}$"
      ],
      "text/plain": [
       "(1.002*s + 0.01002)/s"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_PI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "33b65dca-bf00-4046-80d2-34bd15b340dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1 - s}{s \\left(s + 1\\right)}$"
      ],
      "text/plain": [
       "(1 - s)/(s*(s + 1))"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = -(s-1)/(s*(s+1))\n",
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "4e8c49f1-1ada-4a02-b60a-80d93eb421fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "s_d = -1 + 1j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "76b061e2-0cf9-441f-99c7-94a345883ad7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 108.434948822922$"
      ],
      "text/plain": [
       "108.434948822922"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.N(sympy.arg(G.subs(s, s_d))*180/sympy.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "d33428e7-5b1b-4525-a0b4-9e8db6721175",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 71.565051177078$"
      ],
      "text/plain": [
       "71.5650511770780"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "180 - sympy.N(sympy.arg(G.subs(s, s_d))*180/sympy.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "9de79da3-e734-4219-884e-d7cd6ca83111",
   "metadata": {},
   "outputs": [],
   "source": [
    "K_lead = 2*(s+1)/(s+4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "c0b26962-bbdf-47e6-bfc5-3a208a73765c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 71.565051177078$"
      ],
      "text/plain": [
       "71.5650511770780"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.N(\n",
    "    sympy.arg(K_lead.subs(s, s_d))*180/sympy.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "e0600621-561e-4f33-9cbf-dea4ac84cdfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.0$"
      ],
      "text/plain": [
       "1.00000000000000"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.Abs((K_lead*G).subs(s, s_d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "42ce28be-6531-4820-a924-8d74f17d4284",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2.03$"
      ],
      "text/plain": [
       "2.03000000000000"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_lag = 1.015*(s + 0.04)/(s + 0.01)\n",
    "Kv = sympy.Abs((s*G*K_lead*K_lag).subs(s, 0))\n",
    "Kv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "3f655fd4-0bfe-488c-84ff-1386e3cd2a28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 s + 2}{s + 4}$"
      ],
      "text/plain": [
       "(2*s + 2)/(s + 4)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_lead"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "504327ca-7eda-4926-8f78-22e4669f1df9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2.03 \\left(1.0 s + 0.04\\right) \\left(s + 1\\right)}{\\left(1.0 s + 0.01\\right) \\left(s + 4\\right)}$"
      ],
      "text/plain": [
       "2.03*(1.0*s + 0.04)*(s + 1)/((1.0*s + 0.01)*(s + 4))"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(K_lead*K_lag).factor(s)"
   ]
  }
 ],
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