{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Control PID\n",
    "\n",
    "***Linealizar ecuaciones diferenciales no lineales para diseñar controles PID***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Importamos librerias que utilizaremos en el notebook\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import sympy\n",
    "import control\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linealización en control \n",
    "\n",
    "El diseño de controladores se facilita cuando tenemos sistemas que son lineales. En el proceso de diseño de controladores. Se siguen la siguientes etapas.\n",
    "\n",
    "1. Se obtiene un **modelo no lineal**.\n",
    "2. Se obtiene un **modelo lineal** a través de linealización. \n",
    "3. Se **propone un controlador** para el modelo lineal.\n",
    "4. Se **prueba el controlador** en el sistema real. \n",
    "\n",
    "La linealización se hace para las ecuaciones diferenciales no lineales del sistema. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Funciones no lineales\n",
    "\n",
    "Antes de linealizar ecuaciones diferenciales, empecemos analizando funciones no lineales. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "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": [
    "x = numpy.linspace(-1, 1, 100)\n",
    "xpos = numpy.linspace(0.001, 1, 100)\n",
    "\n",
    "plt.figure()\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(x, numpy.exp(x), label=\"$e^x$\");           # Función exponencial\n",
    "ax.plot(x,x*x, label=\"$x^2$\");                     # Función cuadratica\n",
    "ax.plot(xpos, numpy.log10(xpos), label=\"$log(x)$\") # Función logaritmica\n",
    "ax.legend()\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Linealización de funciones\n",
    "\n",
    "Para linealizar funciones utilizamos la serie de _Taylor_. La cual se define como:\n",
    "\n",
    "$$f(x) = \\sum_{n=o}^\\infty \\, \\frac{f^{(n)}(a)}{n!}(x-a)^n$$\n",
    "\n",
    "escrita de otra forma:\n",
    "\n",
    "$$f(x) \\approx f(a) + \\frac{f'(a)}{1!}(x-a) + \\frac{f''(a)}{2!}(x-a)^2 + \\frac{f^{(3)}(a)}{3!}(x-a)^3 + \\cdots$$\n",
    "\n",
    "se toma únicamente el termino lineal.\n",
    "\n",
    "$$f(x) \\approx f(a) + \\frac{f'(a)}{1!}(x-a) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cd2d152f77f74422b35fada00eb20e91",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatSlider(value=1.0, description='a', max=2.0, min=-2.0), Output()))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Parametros del modelo\n",
    "\n",
    "a = widgets.FloatSlider(value=1,min=-2,max=2,step=0.1,description='a')\n",
    "\n",
    "## Definicion de la simulacion\n",
    "\n",
    "def exponencial(a):\n",
    "    x = numpy.linspace(-2,2,100)\n",
    "    y = numpy.exp(x)\n",
    "    yl = numpy.exp(a) + numpy.exp(a)*(x-a)\n",
    "    plt.plot(x,y)\n",
    "    plt.plot(x,yl)\n",
    "    plt.scatter(a,numpy.exp(a),c='k')\n",
    "    plt.title('Linealización de la función exponencial')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "\n",
    "## Presentación de los resultados    \n",
    "    \n",
    "plot_exponencial = widgets.interactive_output(exponencial,{'a':a})      \n",
    "widgets.HBox([a,plot_exponencial])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ejemplo Tanque\n",
    "\n",
    "La ecuación del tanque es la siguiente, donde $A$ es el area del tanque, $a$ es el area del orificio del tanque, $Q(t)$ es el caudal de entrada:\n",
    "\n",
    "$$A\\,\\frac{d\\,h(t)}{dt}+a\\sqrt{2g\\,h(t)}=Q(t)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Pasos para la linealización\n",
    "\n",
    "Los pasos para la linealización de ecuaciones diferenciales son los siguientes: \n",
    "    \n",
    "- Partimos de la ecuación diferencial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A \\frac{d}{d t} h{\\left(t \\right)} + \\sqrt{2} a \\sqrt{g h{\\left(t \\right)}} = Q{\\left(t \\right)}$"
      ],
      "text/plain": [
       "Eq(A*Derivative(h(t), t) + sqrt(2)*a*sqrt(g*h(t)), Q(t))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A,a,g,t,h,Q = sympy.symbols('A a g t h Q')\n",
    "hs = sympy.Function('h')(t)\n",
    "qs = sympy.Function('Q')(t)\n",
    "\n",
    "Eq_tanque = sympy.Eq(A*sympy.diff(hs,t)+a*sympy.sqrt(2*g*hs),qs); display(Eq_tanque)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Despejamos la derivada de mayor orden y definimos esta ecuación como una función."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F{\\left(h,Q \\right)} = \\frac{- \\sqrt{2} a \\sqrt{g h{\\left(t \\right)}} + Q{\\left(t \\right)}}{A}$"
      ],
      "text/plain": [
       "Eq(F(h, Q), (-sqrt(2)*a*sqrt(g*h(t)) + Q(t))/A)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F = sympy.Function('F')(h,Q)\n",
    "Fhq = sympy.solve(Eq_tanque,sympy.diff(hs,t))[0]\n",
    "Eq_tanque2 = sympy.Eq(F,Fhq); display(Eq_tanque2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Buscamos o imponemos el punto de linealización, normalmente se escoje el estado estacionario como punto de linealización. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle h_{ss} = \\frac{Q_{ss}^{2}}{2 a^{2} g}$"
      ],
      "text/plain": [
       "Eq(h_{ss}, Q_{ss}**2/(2*a**2*g))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q_{ss} = \\sqrt{2} a \\sqrt{g h_{ss}}$"
      ],
      "text/plain": [
       "Eq(Q_{ss}, sqrt(2)*a*sqrt(g*h_{ss}))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hss, qss = sympy.symbols('h_{ss} Q_{ss}')\n",
    "Eq_estacionario = sympy.Eq(hss,sympy.solve(Eq_tanque2.subs(F,0),hs)[0].subs(qs,qss)); display(Eq_estacionario)\n",
    "Eq_estacionario2 = sympy.Eq(qss,sympy.solve(Eq_tanque2.subs(F,0),qs)[0].subs(hs,hss)); display(Eq_estacionario2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Este es entonces el punto de linealización $(h_{ss},Q_{ss})$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Aplicamos serie de _Taylor_ a la función $F$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F{\\left(h,Q \\right)} = \\left(- Q_{ss} + Q{\\left(t \\right)}\\right) \\frac{\\partial}{\\partial Q_{ss}} F{\\left(h_{ss},Q_{ss} \\right)} + \\left(- h_{ss} + h{\\left(t \\right)}\\right) \\frac{\\partial}{\\partial h_{ss}} F{\\left(h_{ss},Q_{ss} \\right)} + F{\\left(h_{ss},Q_{ss} \\right)}$"
      ],
      "text/plain": [
       "Eq(F(h, Q), (-Q_{ss} + Q(t))*Derivative(F(h_{ss}, Q_{ss}), Q_{ss}) + (-h_{ss} + h(t))*Derivative(F(h_{ss}, Q_{ss}), h_{ss}) + F(h_{ss}, Q_{ss}))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "taylor = sympy.Eq(F,F.subs(h,hss).subs(Q,qss)+sympy.diff(F,h).subs(h,hss).subs(Q,qss)*(hs-hss)+sympy.diff(F,Q).subs(h,hss).subs(Q,qss)*(qs-qss))\n",
    "display(taylor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "para el tanque tenemos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F{\\left(h,Q \\right)} = - \\frac{\\sqrt{2} a \\sqrt{g h_{ss}} \\left(- h_{ss} + h{\\left(t \\right)}\\right)}{2 A h_{ss}} + \\frac{- Q_{ss} + Q{\\left(t \\right)}}{A} + \\frac{Q_{ss} - \\sqrt{2} a \\sqrt{g h_{ss}}}{A}$"
      ],
      "text/plain": [
       "Eq(F(h, Q), -sqrt(2)*a*sqrt(g*h_{ss})*(-h_{ss} + h(t))/(2*A*h_{ss}) + (-Q_{ss} + Q(t))/A + (Q_{ss} - sqrt(2)*a*sqrt(g*h_{ss}))/A)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lineal = sympy.Eq(F,Fhq.subs(hs,hss).subs(qs,qss)+sympy.diff(Fhq,hs).subs(hs,hss).subs(qs,qss)*(hs-hss)+sympy.diff(Fhq,qs).subs(hs,hss).subs(qs,qss)*(qs-qss))\n",
    "display(lineal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- La ecuación linearizada del tanque quedaría : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} h{\\left(t \\right)} = - \\frac{\\sqrt{2} a \\sqrt{g h_{ss}} \\left(- h_{ss} + h{\\left(t \\right)}\\right)}{2 A h_{ss}} + \\frac{- Q_{ss} + Q{\\left(t \\right)}}{A} + \\frac{Q_{ss} - \\sqrt{2} a \\sqrt{g h_{ss}}}{A}$"
      ],
      "text/plain": [
       "Eq(Derivative(h(t), t), -sqrt(2)*a*sqrt(g*h_{ss})*(-h_{ss} + h(t))/(2*A*h_{ss}) + (-Q_{ss} + Q(t))/A + (Q_{ss} - sqrt(2)*a*sqrt(g*h_{ss}))/A)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lineal2 = sympy.Eq(sympy.diff(hs,t),lineal.rhs)\n",
    "display(lineal2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- En la ecuación anterior vamos a remplazar las variable $h$ y $Q$ por las variables desviadas $h'$ y $Q'$.\n",
    "\n",
    "$$h' = h - h_{ss} \\qquad Q' = Q - Q_{ss}$$\n",
    "\n",
    "- Remplazando tenemos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{h'}{\\left(t \\right)} = - \\frac{\\sqrt{2} a \\sqrt{g h_{ss}} \\operatorname{h'}{\\left(t \\right)}}{2 A h_{ss}} + \\frac{\\operatorname{Q'}{\\left(t \\right)}}{A}$"
      ],
      "text/plain": [
       "Eq(Derivative(h'(t), t), -sqrt(2)*a*sqrt(g*h_{ss})*h'(t)/(2*A*h_{ss}) + Q'(t)/A)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hp = sympy.Function(\"h'\")(t)\n",
    "qp = sympy.Function(\"Q'\")(t)\n",
    "Eq_diff = lineal2.subs(hs,hp+hss).subs(qs,qp+qss).subs(qss,Eq_estacionario2.rhs)\n",
    "Eq_diff2 = sympy.Eq(sympy.simplify(Eq_diff.lhs),Eq_diff.rhs);\n",
    "display(Eq_diff2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Ejercicios de Linealización\n",
    "\n",
    "Linealizar las siguientes funciones:\n",
    "\n",
    "$$m\\frac{d^2y(t)}{dt^2}+b\\frac{dy(t)}{dt}+k\\,y(t)^3 = - F(t)$$\n",
    "\n",
    "$$\\frac{d^2y(t)}{dt^2} + \\sin(\\omega t)\\frac{dy(t)}{dt} + e^{t/\\tau}y(t) = 0$$\n",
    "\n",
    "$$t\\frac{d^2y(t)}{dt^2}+\\sin(\\omega t)\\frac{dy(t)}{dt} = 0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Root Locus\n",
    "\n",
    "El _root locus_ presenta los caminos de los polos en el plano complejo para un sistema en lazo cerrado en donde la ganancia del controlador $K$ varia de $0$ hasta $\\infty$.\n",
    "\n",
    "- **root**: o raíz, se refiere a la solución de la ecuación carácteristica de la funcion de transferencia. \n",
    "- **locus**: simplemente significa camino, posición o ubicación. \n",
    "\n",
    "Veremos como construir los caminos del _root locus_ a partir de la información de los polos en lazo abierto de un sistema. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ejemplo 1\n",
    "\n",
    "Consideremos un sistema de primer orden con una constante de tiempo $\\tau=2\\text{ seg}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{2 s + 1}$"
      ],
      "text/plain": [
       "1/(2*s + 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ss = sympy.Symbol('s'); G1A = 1/(1+2*ss); display(G1A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Este sistema tiene un polo que es $s=-0.5$. Si le agregamos al sistema un controlador con ganancia $K$ en lazo abierto. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{K}{2 s + 1}$"
      ],
      "text/plain": [
       "K/(2*s + 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sK = sympy.Symbol('K'); G1B = G1A*sK; display(G1B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "La posición de polo no cambia, el polo sigue siendo $s=-0.5$, ¿qué pasa en lazo cerrado?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "En lazo cerrado, tendremos la siguiente función de transferencia. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{K}{K + 2 s + 1}$"
      ],
      "text/plain": [
       "K/(K + 2*s + 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G1C = sympy.simplify(G1B/(1+G1B)); display(G1C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Aquí vemos, que la posición del polo depende del valor que tome $K$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle s = - \\frac{K}{2} - \\frac{1}{2}$"
      ],
      "text/plain": [
       "Eq(s, -K/2 - 1/2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G1Cpole = sympy.Eq(ss,sympy.solve(sympy.denom(G1C),ss)[0]); display(G1Cpole)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Comienza en $s=-0.5$ cuando $K=0$, y este polo se vuelve más negativo cuando $K$ se incrementa. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "En la siguiente figura interactiva se puede ver el comportamiento del polo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2430c3cb67804306a90775cbb3ba51bf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatSlider(value=1.0, description='Ganacia $K$', max=20.0, orientation='vertical'), Output()))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Parametros del modelo\n",
    "\n",
    "param_K = widgets.FloatSlider(value=1,min=0,max=20,step=0.1,description='Ganacia $K$', orientation=\"vertical\")\n",
    "\n",
    "## Definicion de la simulacion\n",
    "\n",
    "def root_locus_ejemplo_1(K):\n",
    "    kvals = numpy.linspace(0,20,100)\n",
    "    real  = -(kvals+1)/2\n",
    "    imag  = kvals*0\n",
    "    plt.plot(real,imag,c='k')\n",
    "    plt.scatter(-(K+1)/2,0,marker=\"x\")\n",
    "    plt.title('Root locus para el ejemplo 1 con función de transferencia $1/(2\\,s+1)$')\n",
    "    plt.xlabel('Real')\n",
    "    plt.ylabel('Imaginario')\n",
    "\n",
    "## Presentación de los resultados    \n",
    "    \n",
    "plot_root_locus_ejemplo_1 = widgets.interactive_output(root_locus_ejemplo_1,{'K':param_K})      \n",
    "widgets.HBox([param_K,plot_root_locus_ejemplo_1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "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_ejemplo_1(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Del mismo modo se puede usar la funcion *root_locus* de la libreria **control**, para obtener la gráfica. La función toma como entrada la funcion de transferencia en lazo abierto sin controlador.\n",
    "\n",
    "$$\\frac{1}{2\\,s+1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "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": [
    "G1D = control.tf(1,[2,1]);\n",
    "control.root_locus(G1D);\n",
    "plt.axvspan(0, 0.5, facecolor='r', alpha=0.5)\n",
    "plt.xlim(-1.5,0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La zona en rojo corresponde a los valores reales positivos, esta zona se conoce como lo región inestrable, si hay al menos un polo del sistema en esta zona el sistema será inestable. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Grafica del root locus manual \n",
    "\n",
    "1. El número de _locis_ (caminos) es igual al orden de la ecuación característica.\n",
    "2. Cada _locis_ empieza en un polo del lazo abierto ($K=0$) y termina en un cero del lazo abierto o en infinito ($K=\\infty$).\n",
    "3. Los _locis_ recorren el eje real, o recorren caminos simétricos con respecto al eje real cuando empiezan en polos conjugados. \n",
    "4. Un punto en el eje real es parte de un _locis_ si el número de polos y ceros a la derecha de ese punto es impar. \n",
    "5. Lejos de los polos y ceros del lazo abierto, los _locis_ se vuelven asimptoticos a una lineas que tienen angulos $\\alpha_n$ con respecto al eje real.\n",
    "\n",
    "    $$\\alpha_n=\\pm \\frac{n\\pi}{P-Z} \\qquad\\text{donde,}\\quad n=1,3,5,..., P-Z$$\n",
    "\n",
    "6. Las asimptotas intersectan al eje real en un punto $S$, conocido como centroide del mapa de polos y ceros, dado por:\n",
    "\n",
    "    $$S=\\frac{\\Sigma \\text{polos} - \\Sigma \\text{ceros}}{P-Z}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ejemplo 2\n",
    "\n",
    "Analicemos la siguiente función de transferencia. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{0.5 s + 1}{s \\left(0.3 s + 1\\right) \\left(0.4 s^{2} + 0.6 s + 1\\right)}$"
      ],
      "text/plain": [
       "(0.5*s + 1)/(s*(0.3*s + 1)*(0.4*s**2 + 0.6*s + 1))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s   = control.tf([1,0],1)\n",
    "G2s = (1+0.5*ss)/(ss*(1+0.3*ss)*(1+0.6*ss+0.4*ss**2)); display(G2s)\n",
    "G2  = (1+0.5*s )/(s *(1+0.3*s )*(1+0.6*s +0.4*s **2)); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- ¿Cuántos polos tiene, y cuánto valen?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tiene P = 4 polos y valen: \n",
      "\n",
      "(-3.3333333333333357+0j)\n",
      "(-0.7499999999999991+1.3919410907075038j)\n",
      "(-0.7499999999999991-1.3919410907075038j)\n",
      "0j\n"
     ]
    }
   ],
   "source": [
    "polos_G2 = control.pole(G2)\n",
    "print(\"Tiene P = %d polos y valen: \\n\\n%s\" % (len(polos_G2),'\\n'.join(map(str, polos_G2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- ¿Cuántos ceros tiene, y cuánto valen?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tiene Z = 1 ceros y vale: \n",
      "\n",
      "(-2+0j)\n"
     ]
    }
   ],
   "source": [
    "ceros_G2 = control.zero(G2)\n",
    "print(\"Tiene Z = %d ceros y vale: \\n\\n%s\" % (len(ceros_G2),'\\n'.join(map(str, ceros_G2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- ¿Cuál es la ecuación característica? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle s \\left(0.3 s + 1\\right) \\left(0.4 s^{2} + 0.6 s + 1\\right) = 0$"
      ],
      "text/plain": [
       "Eq(s*(0.3*s + 1)*(0.4*s**2 + 0.6*s + 1), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Eq_caracteristica = sympy.Eq(sympy.denom(G2s),0); display(Eq_caracteristica)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- ¿Cómo graficamos el _root locus_ de esta función de transferencia? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Se puede partir del mapa de polos y ceros y de la reglas para graficarlo manualmente. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "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": [
    "control.pzmap(G2);\n",
    "plt.axvspan(0, 4, facecolor='r', alpha=0.5)\n",
    "plt.xlim(-5,3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "O directamente con la función *root_locus*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "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": [
    "control.root_locus(G2);\n",
    "plt.axvspan(0, 4, facecolor='r', alpha=0.5)\n",
    "plt.xlim(-10,4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Existe un valor limite para $K$ el cual hace que los caminos pasen de la zona real negativa a la zona real positiva.** Este valor se conoce como $K_u$ la ganacia última del sistema. Para encontrarlo se puede usar criterio de _Routh_ o usando la función _margin_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Calculo manual de la matriz de *Routh*\n",
    "\n",
    "Para la matriz de *Routh* debemos empezar por encontra la ecuación característica del sistema en lazo cerrado."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.5 K s + K + 0.12 s^{4} + 0.58 s^{3} + 0.9 s^{2} + s$"
      ],
      "text/plain": [
       "0.5*K*s + K + 0.12*s**4 + 0.58*s**3 + 0.9*s**2 + s"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "carac2 = sympy.expand(sympy.denom(sympy.simplify(G2s*sK/(1+G2s*sK)))); display(carac2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Buscamos los coeficientes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El valor que acompaña a s^0 es K\n",
      "El valor que acompaña a s^1 es 0.5*K + 1\n",
      "El valor que acompaña a s^2 es 0.900000000000000\n",
      "El valor que acompaña a s^3 es 0.580000000000000\n",
      "El valor que acompaña a s^4 es 0.120000000000000\n"
     ]
    }
   ],
   "source": [
    "coeff2 = [];\n",
    "for i in range(5):\n",
    "    coeff2.append(carac2.coeff(ss,i)); print(\"El valor que acompaña a s^%d es %s\" % (i,coeff2[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Completamos la matriz de *Routh*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s⁴ \t 0.12 \t\t\t\t\t\t 0.90 \t\t K\n",
      "s³ \t 0.58 \t\t\t\t\t\t 0.5*K + 1 \t 0\n",
      "s² \t 0.693103448275862 - 0.103448275862069*K \t K\n",
      "s¹ \t X\n",
      "s⁰ \t K\n",
      "\n",
      " donde X = (0.0517241379310345*K**2 + 0.336896551724138*K - 0.693103448275862)/(0.103448275862069*K - 0.693103448275862)\n"
     ]
    }
   ],
   "source": [
    "print(\"s⁴ \\t %3.2f \\t\\t\\t\\t\\t\\t %3.2f \\t\\t %s\" %(coeff2[4],coeff2[2],coeff2[0]))\n",
    "print(\"s³ \\t %3.2f \\t\\t\\t\\t\\t\\t %s \\t %s\"      %(coeff2[3],coeff2[1],0))\n",
    "\n",
    "s21 = sympy.simplify((coeff2[3]*coeff2[2]-coeff2[4]*coeff2[1])/coeff2[3])\n",
    "\n",
    "print(\"s² \\t %s \\t %s\"      %(s21,coeff2[0]))\n",
    "\n",
    "s11 = sympy.simplify((s21*coeff2[1]-coeff2[3]*sK)/s21)\n",
    "\n",
    "print(\"s¹ \\t X\")\n",
    "print(\"s⁰ \\t K\")\n",
    "\n",
    "print(\"\\n donde X = %s\"%(s11))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La primer columna de la matriz debe toda tener el mismo signo. Ya que los dos primeros elementos son positivos el resto también. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-8.15624601369002, 1.64291268035669]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(sympy.solve(s11,sK))\n",
    "\n",
    "s11.subs(sK,1.6); # Verificamos la desigualdad. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De aqui tenemos que... $K_u= 1.643$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Usando la función _margin_ tenemos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6429126803566858"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "margin_G2,_,_,_ = control.margin(G2)\n",
    "display(margin_G2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El primer valor reportado es la ganacia última $K_u \\approx 1.643$\n",
    "\n",
    "Podemos verificar que pasa al sistema en lazo cerrado con valores de $K$ alrededor de $K_u$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "98b997c3e33c4c99a7a87a233b8dd2f7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(Output(), FloatSlider(value=1.6, description='Ganacia $K$', max=2.0, min=1.0, step=0.01)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Parametros del modelo\n",
    "\n",
    "param_K = widgets.FloatSlider(value=1.6,min=1,max=2,step=0.01,description='Ganacia $K$')\n",
    "\n",
    "## Definicion de la simulacion\n",
    "\n",
    "def respuesta_ejemplo_2(K):\n",
    "    G2_close_loop = control.feedback(G2*K,1)\n",
    "    t, y = control.step_response(G2_close_loop)\n",
    "    plt.plot(t,y)\n",
    "    plt.title('Respuesta temporal para el sistema \\n%s' % (G2_close_loop))\n",
    "    plt.xlabel('tiempo')\n",
    "    plt.ylabel('amplitud')\n",
    "\n",
    "## Presentación de los resultados    \n",
    "    \n",
    "plot_respuesta_ejemplo_2 = widgets.interactive_output(respuesta_ejemplo_2,{'K':param_K})      \n",
    "widgets.VBox([plot_respuesta_ejemplo_2,param_K])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Para $K=1.5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "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": [
    "respuesta_ejemplo_2(1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Para $K=1.65$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "respuesta_ejemplo_2(1.65)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ejercicio\n",
    "\n",
    "Para la siguiente función: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{s \\left(s + 1\\right) \\left(s + 8\\right)}$"
      ],
      "text/plain": [
       "1/(s*(s + 1)*(s + 8))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G3 = 1/(ss*(ss+1)*(ss+8)); display(G3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Realizar:\n",
    "\n",
    "- Encontrar el *root locus*\n",
    "- Identificar la ganancia última\n",
    "- Estudiar la respuesta temporal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Aproximación del retardo\n",
    "\n",
    "Para considerar el retardo en los sistemas y diseñar el controlador PID, debemos aproximar el retardo:\n",
    "    \n",
    "- Por serie de _Taylor_\n",
    "\n",
    "$$f(x) = \\sum_{n=0}^{\\infty}\\frac{f^{(n)}(a)}{n!}(x-a)^n \\qquad\\text{de ahí,}\\quad e^{-\\theta s}\\approx (1-\\theta s) $$\n",
    "\n",
    "- Por aproximación de _Padé_. Para el retardo tenemos\n",
    "\n",
    "$$e^{-\\theta s}\\approx \\frac{1+\\frac{\\theta s}{2}}{1-\\frac{\\theta s}{2}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![USS New Mexico (BB-40) in 1921](uss-new-mexico.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Control PID\n",
    "\n",
    "**¿Qué es PID?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PID es un control **p**roporcional **i**ntegral **d**erivativo. Se representa por la siguiente ecuación: \n",
    "\n",
    "$$u(t) = K_p\\,e(t) + K_i \\int_0^t e(\\tau)d\\tau + Kd_\\, \\frac{e(t)}{dt}$$\n",
    "\n",
    "Los coefficientes $K_p$, $K_i$ y $K_d$ se definen positivos. La anterior expresión puede ser escrita en el dominio de _Laplace_ de la siguiente forma: \n",
    "\n",
    "$$K(s)= K_p + \\frac{K_i}{s}+K_d\\,s$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### PID en las peliculas\n",
    "\n",
    "Intensamente (*inside-out*)\n",
    "\n",
    "<table>\n",
    "    <tbody>\n",
    "        <tr>\n",
    "            <td style=\"vertical-align:top\">\n",
    "                <img src=\"logo.png\" width=\"110px\"/>\n",
    "            </td>\n",
    "            <td style=\"vertical-align:bottom\">\n",
    "                <img src=\"anger.png\" width=\"150px\"/>\n",
    "            </td>\n",
    "            <td style=\"vertical-align:bottom\">\n",
    "                <img src=\"disgust.png\" width=\"120px\"/>\n",
    "            </td>\n",
    "            <td style=\"vertical-align:bottom\">\n",
    "                <img src=\"fear.png\" width=\"110px\"/>\n",
    "            </td>\n",
    "        </tr>\n",
    "        <tr>\n",
    "            <td></td>\n",
    "            <td style=\"text-align:center; color:#ae2d26; font-size:2em\">Proporcional</td>\n",
    "            <td style=\"text-align:center; color:#1b3f23; font-size:2em\">Integral</td>\n",
    "            <td style=\"text-align:center; color:#6e5993; font-size:2em\">Derivativo</td>\n",
    "        </tr>\n",
    "         <tr>\n",
    "             <td></td>\n",
    "            <td style=\"text-align:center; color:#ae2d26; font-size:1.3em\">reactivo</td>\n",
    "            <td style=\"text-align:center; color:#1b3f23; font-size:1.3em\">vengativa</td>\n",
    "            <td style=\"text-align:center; color:#6e5993; font-size:1.3em\">miedoso</td>\n",
    "        </tr>\n",
    "         <tr>\n",
    "             <td></td>\n",
    "             <td style=\"text-align:center; color:#ae2d26; font-size:1.5em\">furia</td>\n",
    "             <td style=\"text-align:center; color:#1b3f23; font-size:1.5em\">asco</td>\n",
    "             <td style=\"text-align:center; color:#6e5993; font-size:1.5em\">miedo</td>\n",
    "        </tr>\n",
    "    </tbody>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing PID-one-block.gv\n"
     ]
    }
   ],
   "source": [
    "%%file PID-one-block.gv\n",
    "// PID in one block\n",
    "digraph {\n",
    "    rankdir=LR\n",
    "    B [shape=rectangle,label=\"Kp + Ki/s + Kd s\", style=filled, fillcolor=lightgray]\n",
    "    node[shape=\"none\"]   \n",
    "    E -> B -> U\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing PID-four-blocks.gv\n"
     ]
    }
   ],
   "source": [
    "%%file PID-four-blocks.gv\n",
    "// PID block diagram using several blocks\n",
    "digraph {\n",
    "    graph [splines=ortho]\n",
    "    rankdir=LR\n",
    "    \n",
    "    E[shape=none,width=0.4]\n",
    "    U[shape=none,width=0.4]\n",
    "    \n",
    "    node[style=filled, fillcolor=lightgray]\n",
    "    Sum [shape=circle, label=\"+\"]\n",
    "    Kpp [shape=point, fillcolor=black]\n",
    "    \n",
    "    node[shape=rectangle,width=0.7,height=0.7,fixedsize=true]\n",
    "    Kp  [label=\"Kp\"]\n",
    "    One [label=\"1\"]\n",
    "    Ti  [label=\"1 / Ti s\"]\n",
    "    Td  [label=\"Td s\"]\n",
    "\n",
    "    // Edges\n",
    "    E  -> Kp \n",
    "    Kp -> Kpp [dir=none] \n",
    "    Kpp-> One\n",
    "    Kpp-> Ti\n",
    "    Kpp-> Td\n",
    "    One-> Sum\n",
    "    Ti -> Sum\n",
    "    Td -> Sum\n",
    "    Sum-> U\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from graphviz import Source"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "sourcefile = 'PID-one-block.gv' \n",
    "gv = open(sourcefile)\n",
    "dot = Source(gv.read(),format=\"svg\",filename = sourcefile)\n",
    "dot.render(sourcefile,view=False);\n",
    "\n",
    "sourcefile = 'PID-four-blocks.gv' \n",
    "gv = open(sourcefile)\n",
    "dot = Source(gv.read(),format=\"svg\",filename = sourcefile)\n",
    "dot.render(sourcefile,view=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Diagrama de bloques de un PID\n",
    "\n",
    "Tomando la función de transferencia del **PID**\n",
    "\n",
    "![pid](PID-one-block.gv.svg)\n",
    "\n",
    "Separando el bloque en tres de manera práctica tenemos:\n",
    "\n",
    "![pid four block](PID-four-blocks.gv.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Expresión del PID de forma práctica\n",
    "\n",
    "La forma clásica de la función de transferencia del **PID** es:\n",
    "\n",
    "$$\\frac{U(s)}{E(s)} = K_p + \\frac{K_i}{s} + K_d\\,s$$\n",
    "\n",
    "En la práctica esta función se representa de la siguiente forma: \n",
    "\n",
    "$$\\frac{U(s)}{E(s)} = K_p \\left(1 + \\frac{K_i}{K_p}\\frac{1}{s} + \\frac{K_d}{K_p} s \\right) = K_p \\left(1 + \\frac{1}{T_i\\, s} + T_d\\, s \\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Variaciones del controlador PID\n",
    "\n",
    "Aquí presentamos las combinaciones para el **PID** que funcionan bien en la mayoria de los casos.\n",
    "\n",
    "| | | | Descripción                                |\n",
    "|-|-|-|:-------------------------------------------|\n",
    "|P| | | Control proporcional                       |\n",
    "| |I| | Control integral                           |\n",
    "|P|I| | Control proporcional integral              |\n",
    "|P| |D| Control proporcional derivativo            |\n",
    "|P|I|D| Control proporcional integral derivativo   |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing closed_loop.gv\n"
     ]
    }
   ],
   "source": [
    "%%file closed_loop.gv\n",
    "// Closed loop diagram\n",
    "digraph {\n",
    "    graph [splines=ortho]\n",
    "    rankdir=LR\n",
    "    \n",
    "    NS [shape=point, fillcolor=black,pos=\"4.75,0!\"]\n",
    "    \n",
    "    node[shape=none,width=0.4]\n",
    "    R[label=\"R(s)\",pos=\"0,0!\"]\n",
    "    C[label=\"C(s)\",pos=\"5.5,0!\"]\n",
    "    \n",
    "    node[style=filled, fillcolor=lightgray]\n",
    "    Sum [shape=circle, label=\"+\", pos=\"1,0!\"]\n",
    "    \n",
    "    node[shape=rectangle,width=0.7,height=0.7,fixedsize=true]\n",
    "    K   [label=\"K(s)\",pos=\"2.5,0!\"]\n",
    "    G   [label=\"G(s)\",pos=\"4,0!\"]\n",
    "    H   [label=\"H(s)\",pos=\"4,-1!\"]\n",
    "\n",
    "    // Edges\n",
    "    R  -> Sum\n",
    "    Sum-> K [label=\"E(s)\"]\n",
    "    K  -> G [taillabel = \"  U(s)\"]\n",
    "    G  -> NS [dir=none]\n",
    "    NS -> C\n",
    "    NS -> H\n",
    "    H  -> Sum [taillabel=\"B(s)  \", headlabel=\"-  \"]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "sourcefile = 'closed_loop.gv' \n",
    "gv = open(sourcefile)\n",
    "dot = Source(gv.read(),engine=\"neato\",format=\"svg\",filename = sourcefile)\n",
    "dot.render(sourcefile,view=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Control del **Error**\n",
    "\n",
    "Esta es la representación de bloques de un sistema en lazo cerrado incluyendo un controlador. \n",
    "\n",
    "![closed loop](closed_loop.gv.svg)\n",
    "\n",
    "- La función de transferencia para la salida es:\n",
    "\n",
    "$$\\frac{C(s)}{R(s)} = \\frac{K(s)G(s)}{1+K(s)G(s)H(s)}$$\n",
    "\n",
    "- Encontremos la función de transferencia del error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "La función de transferencia del error la calculamos sabiendo que:\n",
    "\n",
    "$$E(s) = R(s)-B(s) \\qquad\\text{y}\\qquad B(s)=H(s)C(s)$$\n",
    "\n",
    "Obtenemos lo siguiente: \n",
    "\n",
    "$$\\frac{E(s)}{R(s)} = \\frac{1}{1+K(s)G(s)H(s)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Controlar un proceso puede reducirse a :\n",
    "\n",
    "> \"Encontra el método que nos permita eliminar el error estacionario entre la medida y la referencia\".\n",
    "\n",
    "Suponiendo una función de transferencial polinomial:\n",
    "\n",
    "$$G(s)=\\frac{b_0+b_1\\, s+ \\cdots+ b_m\\, s^m}{a_0+a_1\\, s+ \\cdots+ b_n\\, s^n}$$\n",
    "\n",
    "aplicando el teorema del valor final al error $E(s)$, con un escalón como entrada $R(s) = A/s$ y asumiendo $K(s)=H(s)=1$, tenemos:\n",
    "\n",
    "$$\\lim_{t\\to\\infty} e(t) = \\lim_{s\\to 0} s\\, E(s) = \\frac{A}{1+g_{\\infty}} \\qquad\\text{con,}\\quad g_{\\infty} = \\lim_{s\\to 0} G(s) = \\frac{b_0}{a_0}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Sintonia Manual de **PID**\n",
    "\n",
    "La siguinte tabla muestra el efecto que tiene incrementar un parámetro de forma independiente:\n",
    "\n",
    "|Parámetro| $t_r$    | $M_p$    | $t_s$    | $E_{ss}$ |Estabilidad            |\n",
    "|:-------:|:--------:|:--------:|:--------:|:--------:|:----------------------|\n",
    "|$K_p$    |$\\searrow$|$\\nearrow$|          |$\\searrow$|degrada                |\n",
    "|$K_i$    |$\\searrow$|$\\nearrow$|$\\nearrow$|elimina   |degrada                |\n",
    "|$K_d$    |          |$\\searrow$|$\\searrow$|          |mejora si $K_D$ pequeño|\n",
    "\n",
    "recordemos que $t_r$ es el tiempo de subida, $M_p$ es el máximo pico, $t_s$ es el tiempo de establecimiento, $E_{ss}$ es el error estacionario. \n",
    "\n",
    "En general se sintoniza el PID empezando por **P**, luego **I** y finalmente **D**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Ejemplo sintonia manual\n",
    "\n",
    "![sintonia](http://cpm.davinsony.com/clases/gif/PID_compensation.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Método de sintonía de *Ziegler-Nichols*\n",
    "\n",
    "Encontrando $K_u$ de forma experimental.\n",
    "\n",
    "Es un método heuristico para sintonizar el **PID**, creado en 1942. Para este método se inicia con un controlador proporcional puro **P** y se empieza a aumentar la ganancia $K_p$ hasta que el sistema se vuelva oscilatorio (oscilaciones que se mantienen en el tiempo), esta ganancia que genera este comportamiento denota la ganancia ultima $K_u$. Este movimiento de la salida tiene asociado un periodo $T_u$ de oscilación. Con estos dos valores se calculan los valores del **PID**, siguiendo la próxima tabla. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Tabla de sintonía de *Ziegler-Nichols*\n",
    "\n",
    "|Tipo de controlador    | $K_p$   | $T_i$   | $T_d$  |\n",
    "|:----------------------|:-------:|:-------:|:------:|\n",
    "|P                      |$0.50K_u$|         |        |\n",
    "|PI                     |$0.45K_u$|$T_u/1.2$|        |\n",
    "|PD                     |$0.80K_u$|         |$T_u/8$ |\n",
    "|PID clásico            |$0.60K_u$|$T_u/2$  |$T_u/8$ |\n",
    "|PID con poco sobrepico |$0.33K_u$|$T_u/2$  |$T_u/3$ |\n",
    "|PID sin sobrepico      |$0.20K_u$|$T_u/2$  |$T_u/3$ |\n",
    "\n",
    "$K_u$ también puede ser encontrado utilizando el margen de ganancia (funcion *control.margin*). El periodo $T_u$ esta relacionado con la frecuencia a la cual ocurre el margen de ganancia. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ejemplo 1 \n",
    "\n",
    "Analicemos la función de transferencia del error del primer ejemplo trabajado, cuya funcion de transferencia se presenta a continuación:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{2 s + 1}$"
      ],
      "text/plain": [
       "1/(2*s + 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(G1A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "veamos que pasa con la función del error para este sistema en el tiempo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7c76f6392b9b4e3cb9938ec159a914fc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(Output(), FloatSlider(value=1.0, description='Ganacia $K$', min=1.0, step=1.0)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Parametros del modelo\n",
    "\n",
    "param_K = widgets.FloatSlider(value=1,min=1,max=100,step=1,description='Ganacia $K$')\n",
    "\n",
    "## Definicion de la simulacion\n",
    "\n",
    "def respuesta_error_1(K):\n",
    "    E1 = 1/(1+K*G1D)\n",
    "    t, y = control.step_response(E1)\n",
    "    plt.plot(t,y)\n",
    "    plt.title('Respuesta temporal para el sistema \\n%s' % (E1))\n",
    "    plt.xlabel('tiempo')\n",
    "    plt.ylabel('amplitud')\n",
    "\n",
    "## Presentación de los resultados    \n",
    "    \n",
    "plot_respuesta_error_1 = widgets.interactive_output(respuesta_error_1,{'K':param_K})      \n",
    "widgets.VBox([plot_respuesta_error_1,param_K])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "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": [
    "respuesta_error_1(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Para este sistema no existe un valor $K>0$ que haga el sistema inestable. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Ejemplo 2\n",
    "\n",
    "Analicemos el ejemplo número 2, cuya función de transferencia es presentada acontinuación."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{0.5 s + 1}{0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s}$$"
      ],
      "text/plain": [
       "TransferFunction(array([0.5, 1. ]), array([0.12, 0.58, 0.9 , 1.  , 0.  ]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(G2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- ¿Cuál es la respuesta temporal para la función de transferencia del error de este sistema?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d4322deef813470d87cf29885a3186b1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(Output(), FloatSlider(value=1.0, description='Ganacia $K$', max=2.0, min=1.0, step=0.01)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Parametros del modelo\n",
    "\n",
    "param_K = widgets.FloatSlider(value=1,min=1,max=2,step=0.01,description='Ganacia $K$')\n",
    "\n",
    "## Definicion de la simulacion\n",
    "\n",
    "def respuesta_error_2(K):\n",
    "    E2 = 1/(1+K*G2)\n",
    "    t, y = control.step_response(E2)\n",
    "    plt.plot(t,y)\n",
    "    plt.title('Respuesta temporal para el sistema \\n%s' % (E2))\n",
    "    plt.xlabel('tiempo')\n",
    "    plt.ylabel('amplitud')\n",
    "\n",
    "## Presentación de los resultados    \n",
    "    \n",
    "plot_respuesta_error_2 = widgets.interactive_output(respuesta_error_2,{'K':param_K})      \n",
    "widgets.VBox([plot_respuesta_error_2,param_K])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "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": [
    "respuesta_error_2(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- ¿Qué pasa con el sistema teniendo un control diferente al control proporcional **P**?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Control por posicionamiento de polos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s}{0.12 s^4 + 0.58 s^3 + 0.9 s^2 + 1.8 s + 1.6}$$"
      ],
      "text/plain": [
       "TransferFunction(array([0.12, 0.58, 0.9 , 1.  , 0.  ]), array([0.12, 0.58, 0.9 , 1.8 , 1.6 ]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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": [
    "K = 1.6\n",
    "E6 = 1/(1+K*G2); display(E6)\n",
    "\n",
    "t,y = control.step_response(E6);\n",
    "plt.plot(t,y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{0.213 s^5 + 1.029 s^4 + 1.597 s^3 + 1.775 s^2}{0.213 s^5 + 1.029 s^4 + 1.942 s^3 + 2.755 s^2 + 0.7462 s + 0.328}$$"
      ],
      "text/plain": [
       "TransferFunction(array([0.21298915, 1.02944757, 1.59741864, 1.7749096 , 0.        ,\n",
       "       0.        ]), array([0.21298915, 1.02944757, 1.94185189, 2.75486128, 0.74617035,\n",
       "       0.328     ]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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": [
    "Ku = 1.64\n",
    "Tu = 2*3.14159/1.77\n",
    "Ti = Tu/2\n",
    "Td = Tu/3\n",
    "K = 0.2 * Ku *(1+1/(Ti*s)+Td*s)\n",
    "E6 = 1/(1+K*G2); display(E6)\n",
    "\n",
    "t,y = control.step_response(E6);\n",
    "plt.plot(t,y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s}{0.12 s^4 + 1.58 s^3 + 4.4 s^2 + 6.5 s + 5}$$"
      ],
      "text/plain": [
       "TransferFunction(array([0.12, 0.58, 0.9 , 1.  , 0.  ]), array([0.12, 1.58, 4.4 , 6.5 , 5.  ]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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": [
    "K = (2.5 + 1.5*s + 1*s**2)*2;\n",
    "E6 = 1/(1+K*G2); display(E6)\n",
    "\n",
    "t,y = control.step_response(E6);\n",
    "plt.plot(t,y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle s^{2} + 1.5 s + 2.49999999803039$"
      ],
      "text/plain": [
       "s**2 + 1.5*s + 2.49999999803039"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.expand((ss - (-0.75+1.39194109j))*(ss-((-0.75-1.39194109j))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "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": [
    "control.root_locus(K*G2);"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}