rootlocus-python.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: stable-baselines3 in c:\\users\\harna\\anaconda3\\lib\\site-packages (1.6.2)\n",
      "Requirement already satisfied: gym==0.21 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from stable-baselines3) (0.21.0)\n",
      "Requirement already satisfied: numpy in c:\\users\\harna\\anaconda3\\lib\\site-packages (from stable-baselines3) (1.21.6)\n",
      "Requirement already satisfied: pandas in c:\\users\\harna\\anaconda3\\lib\\site-packages (from stable-baselines3) (1.3.5)\n",
      "Requirement already satisfied: torch>=1.11 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from stable-baselines3) (1.13.0)\n",
      "Requirement already satisfied: importlib-metadata~=4.13 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from stable-baselines3) (4.13.0)\n",
      "Requirement already satisfied: cloudpickle in c:\\users\\harna\\anaconda3\\lib\\site-packages (from stable-baselines3) (2.0.0)\n",
      "Requirement already satisfied: matplotlib in c:\\users\\harna\\anaconda3\\lib\\site-packages (from stable-baselines3) (3.5.3)\n",
      "Requirement already satisfied: typing-extensions>=3.6.4 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from importlib-metadata~=4.13->stable-baselines3) (4.4.0)\n",
      "Requirement already satisfied: zipp>=0.5 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from importlib-metadata~=4.13->stable-baselines3) (3.10.0)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from matplotlib->stable-baselines3) (2.8.2)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from matplotlib->stable-baselines3) (4.25.0)\n",
      "Requirement already satisfied: pillow>=6.2.0 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from matplotlib->stable-baselines3) (9.2.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from matplotlib->stable-baselines3) (1.4.2)\n",
      "Requirement already satisfied: packaging>=20.0 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from matplotlib->stable-baselines3) (21.3)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from matplotlib->stable-baselines3) (0.11.0)\n",
      "Requirement already satisfied: pyparsing>=2.2.1 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from matplotlib->stable-baselines3) (3.0.9)\n",
      "Requirement already satisfied: pytz>=2017.3 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from pandas->stable-baselines3) (2022.1)\n",
      "Requirement already satisfied: six>=1.5 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from python-dateutil>=2.7->matplotlib->stable-baselines3) (1.16.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "[notice] A new release of pip available: 22.3 -> 22.3.1\n",
      "[notice] To update, run: python.exe -m pip install --upgrade pip\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: PID in c:\\users\\harna\\anaconda3\\lib\\site-packages (3.0.4)\n",
      "Requirement already satisfied: psutil>=5.4.8 in c:\\users\\harna\\anaconda3\\lib\\site-packages (from PID) (5.9.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "[notice] A new release of pip available: 22.3 -> 22.3.1\n",
      "[notice] To update, run: python.exe -m pip install --upgrade pip\n"
     ]
    }
   ],
   "source": [
    "%pip install stable-baselines3\n",
    "%pip install PID"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def transfer_function(num, denum):\n",
    "  \"\"\"Pads list of poles and zeros.\n",
    "    Assumes `num` < `denum`.\n",
    "    Args:\n",
    "      num: coefficients of the zeros [coeff_n, coeff_(n-1), ..., coeff_0]\n",
    "      denum: coefficients of the poles: [coeff_n, coeff_(n-1), ..., coeff_0]\n",
    "    Returns:\n",
    "      tf: 2D numpy array [num, denum]\n",
    "  \"\"\"\n",
    "  num = np.array(num, dtype=np.float64)\n",
    "  denum = np.array(denum, dtype=np.float64)\n",
    "  size = len(denum) - len(num)\n",
    "  temp = np.zeros(size)\n",
    "  num = np.concatenate((temp, num))\n",
    "  tf = np.vstack((num, denum))\n",
    "  return tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_roots(tf, gains):\n",
    "  \"\"\"Computes the roots of the characteristic equation of the closed-loop system\n",
    "  of a given transfer function for a list of gain parameters.\n",
    "  Concretely, given TF = zeros/poles, and a gain value K, we solve for the\n",
    "  characteristic equation roots, that is the roots of poles + (K * zeros).\n",
    "  Args:\n",
    "    tf: transfer function.\n",
    "    gains: list of gains.\n",
    "  Returns:\n",
    "    roots: numpy array containing the roots for each gain in gains.\n",
    "  \"\"\"\n",
    "  num, denum = tf[0], tf[1]\n",
    "  num_roots = len(np.roots(denum))\n",
    "  roots = []\n",
    "\n",
    "  for gain in gains:\n",
    "    ch_eq = denum +  gain*num\n",
    "    ch_roots = np.roots(ch_eq)\n",
    "    ch_roots.sort()\n",
    "    roots.append(ch_roots)\n",
    "\n",
    "  # convert final roots list into array\n",
    "  roots = np.vstack(roots)\n",
    "\n",
    "  return roots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_root_locus(gains, roots):\n",
    "  \"\"\"Plots the root locus of the closed loop system given the provided gains.\n",
    "  \"\"\"\n",
    "  # get real and imaginary values\n",
    "  real_vals = np.real(roots)\n",
    "  imag_vals = np.imag(roots)\n",
    "\n",
    "  # possible colors\n",
    "  colors = ['b', 'm', 'c', 'r', 'g']\n",
    "\n",
    "  # create figure and axis labels\n",
    "  fig, ax = plt.subplots()\n",
    "  ax.set_xlabel('Re')\n",
    "  ax.set_ylabel('Im')\n",
    "  ax.axvline(x=0, color='k', lw=1)\n",
    "  ax.grid(True, which='both')\n",
    "\n",
    "  # plots a blue \"x\" for the first roots\n",
    "  ax.scatter(real_vals[0, :], imag_vals[0, :],\n",
    "          marker='x',\n",
    "          color='blue')\n",
    "\n",
    "  # plots a red \"o\" for the last roots\n",
    "  ax.scatter(real_vals[-1, :], imag_vals[-1, :],\n",
    "          marker='o',\n",
    "          color='red')\n",
    "\n",
    "  gain_text = ['k = {:1.2f}'.format(k) for k in gains]\n",
    "\n",
    "  temp_real_vals = real_vals[1:-1, :]\n",
    "  temp_imag_vals = imag_vals[1:-1, :]\n",
    "  color_range = range(temp_real_vals.shape[1])\n",
    "\n",
    "  # plot the rest of the roots in different colors with respect to the regions\n",
    "  for r, i, j in zip(temp_real_vals.T, temp_imag_vals.T, color_range):\n",
    "    ax.plot(r, i, color=colors[j])\n",
    "\n",
    "  return fig, ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if __name__ == \"__main__\":\n",
    "  # open loop transfer function\n",
    "  num = [1, 4.25,2]\n",
    "  denum = [1, 10.5, 32, 44.5, 21]\n",
    "  GH = transfer_function(num, denum)\n",
    "\n",
    "  # create a list of evenly spaced gains\n",
    "  gains = np.linspace(0.0, 10.0, num=500)\n",
    "\n",
    "  roots = compute_roots(GH, gains)\n",
    "  fig, ax = plot_root_locus(gains, roots)\n",
    "  plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.15 ('base')",
   "language": "python",
   "name": "python3"
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