{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Root locus diagrams\n",
    "\n",
    "Root locus diagrams show where the roots of the characteristic equation lie for different values of controller gain. The control library has a built-in function for plotting these diagrams."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import control"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = control.tf([1, 0], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rlocus(order, tau_p, K):\n",
    "    Gp = 1/(tau_p*s + 1)**order\n",
    "    Gc = 1\n",
    "\n",
    "    L = Gp*Gc\n",
    "    CL = K*L/(1 + K*L)\n",
    "    control.root_locus(L);\n",
    "    control.pzmap(CL)\n",
    "    plt.title('')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7ef539c6f72d40299d04b6919c659bc1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=3, description='order', max=5, min=1), FloatSlider(value=1.05, descripti…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.rlocus(order, tau_p, K)>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interact(rlocus, order=(1, 5), tau_p=(0.1, 2.), tau_i=(1., 20), K=(0.01, 200))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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